chloeli/qwen-2.5-1.5B-instruct-sft-lora-countdown-deepseek-correct-seq8k-1k
Text Generation
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Updated
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16
Dataset Viewer
nums
sequencelengths 4
4
| target
int64 10
100
| search_type
stringclasses 2
values | heuristic
stringclasses 1
value | messages_sos_react
listlengths 2
2
| token_length_sos_react
int64 428
40.6k
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|---|---|---|---|---|---|
[
90,
11,
37,
95
]
| 55 | dfs | sum_heuristic | [
{
"content": "Combine these initial numbers [90, 11, 37, 95] using only arithmetic operations (+, -, *, /) to reach the target value 55. All initial numbers must be used exactly once.\nConclude with the final result in EXACTLY this format:\n```\nSOLUTION: YES/NO\nOPERATIONS: list of string of operations performed, each string involving only 1 operation. For example, ['A+B=C','C+D=E'] is allowed, ['A+B+D=E'] is not allowed\nRESULT: final_value\n```\n",
"role": "user"
},
{
"content": "We have these numbers [90, 11, 37, 95]. Our goal is to produce 55. Let's show the search process step by step:\nOne possible strategy is to use a Depth-First Search (DFS) guided by a **sum-based** heuristic, which computes the average of the absolute differences between each number and the target number.\nLower scores indicate that, on average, the numbers are closer to the target, making the state more promising for reaching the target via additive operations.\n\n\nCurrent State #0: 55:[90, 11, 37, 95]. Operations so far : [].\n\nThought : Expand Node #0’s 1st child to build next frontier.\nAction : Exploring operation 90-11=79. \nResulting numbers: [37, 95, 79].\nHeuristic score : (|37-55| + |95-55| + |79-55|)/3 = (18 + 40 + 24)/3 = 27.33\nGenerated Node #0,0: 55:[37, 95, 79] Operation: 90-11=79\n\nThought : Expand Node #0,0’s 1st child to build next frontier.\nAction : Exploring operation 95-37=58. \nResulting numbers: [79, 58].\nHeuristic score : (|79-55| + |58-55|)/2 = (24 + 3)/2 = 13.50\nGenerated Node #0,0,0: 55:[79, 58] Operation: 95-37=58\n\nThought : Expand Node #0,0,0’s 1st child to build next frontier.\nAction : Exploring operation 79-58=21. \nResulting numbers: [21].\n21,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 27.333333333333332\nCurrent State #0,0: 55:[37, 95, 79]. Operations so far : ['90-11=79'].\n\nThought : Expand Node #0,0’s 2nd child to build next frontier.\nAction : Exploring operation 79-37=42. \nResulting numbers: [95, 42].\nHeuristic score : (|95-55| + |42-55|)/2 = (40 + 13)/2 = 26.50\nGenerated Node #0,0,1: 55:[95, 42] Operation: 79-37=42\n\nThought : Expand Node #0,0,1’s 1st child to build next frontier.\nAction : Exploring operation 95-42=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 27.333333333333332\nCurrent State #0,0: 55:[37, 95, 79]. Operations so far : ['90-11=79'].\n\nThought : Expand Node #0,0’s 3rd child to build next frontier.\nAction : Exploring operation 95-79=16. \nResulting numbers: [37, 16].\nHeuristic score : (|37-55| + |16-55|)/2 = (18 + 39)/2 = 28.50\nGenerated Node #0,0,2: 55:[37, 16] Operation: 95-79=16\n\nThought : Expand Node #0,0,2’s 1st child to build next frontier.\nAction : Exploring operation 37+16=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 27.333333333333332\nCurrent State #0,0: 55:[37, 95, 79]. Operations so far : ['90-11=79'].\n\nThought : Expand Node #0,0’s 4th child to build next frontier.\nAction : Exploring operation 37+95=132. \nResulting numbers: [79, 132].\nHeuristic score : (|79-55| + |132-55|)/2 = (24 + 77)/2 = 50.50\nGenerated Node #0,0,3: 55:[79, 132] Operation: 37+95=132\n\nThought : Expand Node #0,0,3’s 1st child to build next frontier.\nAction : Exploring operation 132-79=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 27.333333333333332\nCurrent State #0,0: 55:[37, 95, 79]. Operations so far : ['90-11=79'].\n\nThought : Expand Node #0,0’s 5th child to build next frontier.\nAction : Exploring operation 37+79=116. \nResulting numbers: [95, 116].\nHeuristic score : (|95-55| + |116-55|)/2 = (40 + 61)/2 = 50.50\nGenerated Node #0,0,4: 55:[95, 116] Operation: 37+79=116\n\nThought : Expand Node #0,0,4’s 1st child to build next frontier.\nAction : Exploring operation 116-95=21. \nResulting numbers: [21].\n21,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 27.333333333333332\nCurrent State #0,0: 55:[37, 95, 79]. Operations so far : ['90-11=79'].\n\nThought : Expand Node #0,0’s 6th child to build next frontier.\nAction : Exploring operation 95+79=174. \nResulting numbers: [37, 174].\nHeuristic score : (|37-55| + |174-55|)/2 = (18 + 119)/2 = 68.50\nGenerated Node #0,0,5: 55:[37, 174] Operation: 95+79=174\n\nThought : Expand Node #0,0,5’s 1st child to build next frontier.\nAction : Exploring operation 174-37=137. \nResulting numbers: [137].\n137,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 27.333333333333332\nCurrent State #0,0: 55:[37, 95, 79]. Operations so far : ['90-11=79'].\n\nThought : Expand Node #0,0’s 7th child to build next frontier.\nAction : Exploring operation 37*79=2923. \nResulting numbers: [95, 2923].\nHeuristic score : (|95-55| + |2923-55|)/2 = (40 + 2868)/2 = 1454.00\nGenerated Node #0,0,6: 55:[95, 2923] Operation: 37*79=2923\n\nThought : Expand Node #0,0,6’s 1st child to build next frontier.\nAction : Exploring operation 2923-95=2828. \nResulting numbers: [2828].\n2828,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 27.333333333333332\nCurrent State #0,0: 55:[37, 95, 79]. Operations so far : ['90-11=79'].\n\nThought : Expand Node #0,0’s 8th child to build next frontier.\nAction : Exploring operation 37*95=3515. \nResulting numbers: [79, 3515].\nHeuristic score : (|79-55| + |3515-55|)/2 = (24 + 3460)/2 = 1742.00\nGenerated Node #0,0,7: 55:[79, 3515] Operation: 37*95=3515\n\nThought : Expand Node #0,0,7’s 1st child to build next frontier.\nAction : Exploring operation 3515-79=3436. \nResulting numbers: [3436].\n3436,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 27.333333333333332\nCurrent State #0,0: 55:[37, 95, 79]. Operations so far : ['90-11=79'].\n\nThought : Expand Node #0,0’s 9th child to build next frontier.\nAction : Exploring operation 95*79=7505. \nResulting numbers: [37, 7505].\nHeuristic score : (|37-55| + |7505-55|)/2 = (18 + 7450)/2 = 3734.00\nGenerated Node #0,0,8: 55:[37, 7505] Operation: 95*79=7505\n\nThought : Expand Node #0,0,8’s 1st child to build next frontier.\nAction : Exploring operation 7505-37=7468. \nResulting numbers: [7468].\n7468,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0 with lowest heuristic value 34.25\nCurrent State #0: 55:[90, 11, 37, 95]. Operations so far : [].\n\nThought : Expand Node #0’s 2nd child to build next frontier.\nAction : Exploring operation 11+37=48. \nResulting numbers: [90, 95, 48].\nHeuristic score : (|90-55| + |95-55| + |48-55|)/3 = (35 + 40 + 7)/3 = 27.33\nGenerated Node #0,1: 55:[90, 95, 48] Operation: 11+37=48\n\nThought : Expand Node #0,1’s 1st child to build next frontier.\nAction : Exploring operation 95-48=47. \nResulting numbers: [90, 47].\nHeuristic score : (|90-55| + |47-55|)/2 = (35 + 8)/2 = 21.50\nGenerated Node #0,1,0: 55:[90, 47] Operation: 95-48=47\n\nThought : Expand Node #0,1,0’s 1st child to build next frontier.\nAction : Exploring operation 90-47=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1 with lowest heuristic value 27.333333333333332\nCurrent State #0,1: 55:[90, 95, 48]. Operations so far : ['11+37=48'].\n\nThought : Expand Node #0,1’s 2nd child to build next frontier.\nAction : Exploring operation 90-48=42. \nResulting numbers: [95, 42].\nHeuristic score : (|95-55| + |42-55|)/2 = (40 + 13)/2 = 26.50\nGenerated Node #0,1,1: 55:[95, 42] Operation: 90-48=42\n\nThought : Expand Node #0,1,1’s 1st child to build next frontier.\nAction : Exploring operation 95-42=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1 with lowest heuristic value 27.333333333333332\nCurrent State #0,1: 55:[90, 95, 48]. Operations so far : ['11+37=48'].\n\nThought : Expand Node #0,1’s 3rd child to build next frontier.\nAction : Exploring operation 95-90=5. \nResulting numbers: [48, 5].\nHeuristic score : (|48-55| + |5-55|)/2 = (7 + 50)/2 = 28.50\nGenerated Node #0,1,2: 55:[48, 5] Operation: 95-90=5\n\nThought : Expand Node #0,1,2’s 1st child to build next frontier.\nAction : Exploring operation 48+5=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1 with lowest heuristic value 27.333333333333332\nCurrent State #0,1: 55:[90, 95, 48]. Operations so far : ['11+37=48'].\n\nThought : Expand Node #0,1’s 4th child to build next frontier.\nAction : Exploring operation 90+48=138. \nResulting numbers: [95, 138].\nHeuristic score : (|95-55| + |138-55|)/2 = (40 + 83)/2 = 61.50\nGenerated Node #0,1,3: 55:[95, 138] Operation: 90+48=138\n\nThought : Expand Node #0,1,3’s 1st child to build next frontier.\nAction : Exploring operation 138-95=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1 with lowest heuristic value 27.333333333333332\nCurrent State #0,1: 55:[90, 95, 48]. Operations so far : ['11+37=48'].\n\nThought : Expand Node #0,1’s 5th child to build next frontier.\nAction : Exploring operation 95+48=143. \nResulting numbers: [90, 143].\nHeuristic score : (|90-55| + |143-55|)/2 = (35 + 88)/2 = 61.50\nGenerated Node #0,1,4: 55:[90, 143] Operation: 95+48=143\n\nThought : Expand Node #0,1,4’s 1st child to build next frontier.\nAction : Exploring operation 143-90=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1 with lowest heuristic value 27.333333333333332\nCurrent State #0,1: 55:[90, 95, 48]. Operations so far : ['11+37=48'].\n\nThought : Expand Node #0,1’s 6th child to build next frontier.\nAction : Exploring operation 90+95=185. \nResulting numbers: [48, 185].\nHeuristic score : (|48-55| + |185-55|)/2 = (7 + 130)/2 = 68.50\nGenerated Node #0,1,5: 55:[48, 185] Operation: 90+95=185\n\nThought : Expand Node #0,1,5’s 1st child to build next frontier.\nAction : Exploring operation 185-48=137. \nResulting numbers: [137].\n137,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1 with lowest heuristic value 27.333333333333332\nCurrent State #0,1: 55:[90, 95, 48]. Operations so far : ['11+37=48'].\n\nThought : Expand Node #0,1’s 7th child to build next frontier.\nAction : Exploring operation 90*48=4320. \nResulting numbers: [95, 4320].\nHeuristic score : (|95-55| + |4320-55|)/2 = (40 + 4265)/2 = 2152.50\nGenerated Node #0,1,6: 55:[95, 4320] Operation: 90*48=4320\n\nThought : Expand Node #0,1,6’s 1st child to build next frontier.\nAction : Exploring operation 4320-95=4225. \nResulting numbers: [4225].\n4225,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1 with lowest heuristic value 27.333333333333332\nCurrent State #0,1: 55:[90, 95, 48]. Operations so far : ['11+37=48'].\n\nThought : Expand Node #0,1’s 8th child to build next frontier.\nAction : Exploring operation 95*48=4560. \nResulting numbers: [90, 4560].\nHeuristic score : (|90-55| + |4560-55|)/2 = (35 + 4505)/2 = 2270.00\nGenerated Node #0,1,7: 55:[90, 4560] Operation: 95*48=4560\n\nThought : Expand Node #0,1,7’s 1st child to build next frontier.\nAction : Exploring operation 4560-90=4470. \nResulting numbers: [4470].\n4470,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1 with lowest heuristic value 27.333333333333332\nCurrent State #0,1: 55:[90, 95, 48]. Operations so far : ['11+37=48'].\n\nThought : Expand Node #0,1’s 9th child to build next frontier.\nAction : Exploring operation 90*95=8550. \nResulting numbers: [48, 8550].\nHeuristic score : (|48-55| + |8550-55|)/2 = (7 + 8495)/2 = 4251.00\nGenerated Node #0,1,8: 55:[48, 8550] Operation: 90*95=8550\n\nThought : Expand Node #0,1,8’s 1st child to build next frontier.\nAction : Exploring operation 8550-48=8502. \nResulting numbers: [8502].\n8502,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0 with lowest heuristic value 34.25\nCurrent State #0: 55:[90, 11, 37, 95]. Operations so far : [].\n\nThought : Expand Node #0’s 3rd child to build next frontier.\nAction : Exploring operation 95-11=84. \nResulting numbers: [90, 37, 84].\nHeuristic score : (|90-55| + |37-55| + |84-55|)/3 = (35 + 18 + 29)/3 = 27.33\nGenerated Node #0,2: 55:[90, 37, 84] Operation: 95-11=84\n\nThought : Expand Node #0,2’s 1st child to build next frontier.\nAction : Exploring operation 90-37=53. \nResulting numbers: [84, 53].\nHeuristic score : (|84-55| + |53-55|)/2 = (29 + 2)/2 = 15.50\nGenerated Node #0,2,0: 55:[84, 53] Operation: 90-37=53\n\nThought : Expand Node #0,2,0’s 1st child to build next frontier.\nAction : Exploring operation 84-53=31. \nResulting numbers: [31].\n31,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2 with lowest heuristic value 27.333333333333332\nCurrent State #0,2: 55:[90, 37, 84]. Operations so far : ['95-11=84'].\n\nThought : Expand Node #0,2’s 2nd child to build next frontier.\nAction : Exploring operation 84-37=47. \nResulting numbers: [90, 47].\nHeuristic score : (|90-55| + |47-55|)/2 = (35 + 8)/2 = 21.50\nGenerated Node #0,2,1: 55:[90, 47] Operation: 84-37=47\n\nThought : Expand Node #0,2,1’s 1st child to build next frontier.\nAction : Exploring operation 90-47=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2 with lowest heuristic value 27.333333333333332\nCurrent State #0,2: 55:[90, 37, 84]. Operations so far : ['95-11=84'].\n\nThought : Expand Node #0,2’s 3rd child to build next frontier.\nAction : Exploring operation 90-84=6. \nResulting numbers: [37, 6].\nHeuristic score : (|37-55| + |6-55|)/2 = (18 + 49)/2 = 33.50\nGenerated Node #0,2,2: 55:[37, 6] Operation: 90-84=6\n\nThought : Expand Node #0,2,2’s 1st child to build next frontier.\nAction : Exploring operation 37+6=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2 with lowest heuristic value 27.333333333333332\nCurrent State #0,2: 55:[90, 37, 84]. Operations so far : ['95-11=84'].\n\nThought : Expand Node #0,2’s 4th child to build next frontier.\nAction : Exploring operation 90+37=127. \nResulting numbers: [84, 127].\nHeuristic score : (|84-55| + |127-55|)/2 = (29 + 72)/2 = 50.50\nGenerated Node #0,2,3: 55:[84, 127] Operation: 90+37=127\n\nThought : Expand Node #0,2,3’s 1st child to build next frontier.\nAction : Exploring operation 127-84=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2 with lowest heuristic value 27.333333333333332\nCurrent State #0,2: 55:[90, 37, 84]. Operations so far : ['95-11=84'].\n\nThought : Expand Node #0,2’s 5th child to build next frontier.\nAction : Exploring operation 37+84=121. \nResulting numbers: [90, 121].\nHeuristic score : (|90-55| + |121-55|)/2 = (35 + 66)/2 = 50.50\nGenerated Node #0,2,4: 55:[90, 121] Operation: 37+84=121\n\nThought : Expand Node #0,2,4’s 1st child to build next frontier.\nAction : Exploring operation 121-90=31. \nResulting numbers: [31].\n31,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2 with lowest heuristic value 27.333333333333332\nCurrent State #0,2: 55:[90, 37, 84]. Operations so far : ['95-11=84'].\n\nThought : Expand Node #0,2’s 6th child to build next frontier.\nAction : Exploring operation 90+84=174. \nResulting numbers: [37, 174].\nHeuristic score : (|37-55| + |174-55|)/2 = (18 + 119)/2 = 68.50\nGenerated Node #0,2,5: 55:[37, 174] Operation: 90+84=174\n\nThought : Expand Node #0,2,5’s 1st child to build next frontier.\nAction : Exploring operation 174-37=137. \nResulting numbers: [137].\n137,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2 with lowest heuristic value 27.333333333333332\nCurrent State #0,2: 55:[90, 37, 84]. Operations so far : ['95-11=84'].\n\nThought : Expand Node #0,2’s 7th child to build next frontier.\nAction : Exploring operation 37*84=3108. \nResulting numbers: [90, 3108].\nHeuristic score : (|90-55| + |3108-55|)/2 = (35 + 3053)/2 = 1544.00\nGenerated Node #0,2,6: 55:[90, 3108] Operation: 37*84=3108\n\nThought : Expand Node #0,2,6’s 1st child to build next frontier.\nAction : Exploring operation 3108-90=3018. \nResulting numbers: [3018].\n3018,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2 with lowest heuristic value 27.333333333333332\nCurrent State #0,2: 55:[90, 37, 84]. Operations so far : ['95-11=84'].\n\nThought : Expand Node #0,2’s 8th child to build next frontier.\nAction : Exploring operation 90*37=3330. \nResulting numbers: [84, 3330].\nHeuristic score : (|84-55| + |3330-55|)/2 = (29 + 3275)/2 = 1652.00\nGenerated Node #0,2,7: 55:[84, 3330] Operation: 90*37=3330\n\nThought : Expand Node #0,2,7’s 1st child to build next frontier.\nAction : Exploring operation 3330-84=3246. \nResulting numbers: [3246].\n3246,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2 with lowest heuristic value 27.333333333333332\nCurrent State #0,2: 55:[90, 37, 84]. Operations so far : ['95-11=84'].\n\nThought : Expand Node #0,2’s 9th child to build next frontier.\nAction : Exploring operation 90*84=7560. \nResulting numbers: [37, 7560].\nHeuristic score : (|37-55| + |7560-55|)/2 = (18 + 7505)/2 = 3761.50\nGenerated Node #0,2,8: 55:[37, 7560] Operation: 90*84=7560\n\nThought : Expand Node #0,2,8’s 1st child to build next frontier.\nAction : Exploring operation 7560-37=7523. \nResulting numbers: [7523].\n7523,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0 with lowest heuristic value 34.25\nCurrent State #0: 55:[90, 11, 37, 95]. Operations so far : [].\n\nThought : Expand Node #0’s 4th child to build next frontier.\nAction : Exploring operation 95-37=58. \nResulting numbers: [90, 11, 58].\nHeuristic score : (|90-55| + |11-55| + |58-55|)/3 = (35 + 44 + 3)/3 = 27.33\nGenerated Node #0,3: 55:[90, 11, 58] Operation: 95-37=58\n\nThought : Expand Node #0,3’s 1st child to build next frontier.\nAction : Exploring operation 90-11=79. \nResulting numbers: [58, 79].\nHeuristic score : (|58-55| + |79-55|)/2 = (3 + 24)/2 = 13.50\nGenerated Node #0,3,0: 55:[58, 79] Operation: 90-11=79\n\nThought : Expand Node #0,3,0’s 1st child to build next frontier.\nAction : Exploring operation 79-58=21. \nResulting numbers: [21].\n21,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3 with lowest heuristic value 27.333333333333332\nCurrent State #0,3: 55:[90, 11, 58]. Operations so far : ['95-37=58'].\n\nThought : Expand Node #0,3’s 2nd child to build next frontier.\nAction : Exploring operation 58-11=47. \nResulting numbers: [90, 47].\nHeuristic score : (|90-55| + |47-55|)/2 = (35 + 8)/2 = 21.50\nGenerated Node #0,3,1: 55:[90, 47] Operation: 58-11=47\n\nThought : Expand Node #0,3,1’s 1st child to build next frontier.\nAction : Exploring operation 90-47=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3 with lowest heuristic value 27.333333333333332\nCurrent State #0,3: 55:[90, 11, 58]. Operations so far : ['95-37=58'].\n\nThought : Expand Node #0,3’s 3rd child to build next frontier.\nAction : Exploring operation 90+11=101. \nResulting numbers: [58, 101].\nHeuristic score : (|58-55| + |101-55|)/2 = (3 + 46)/2 = 24.50\nGenerated Node #0,3,2: 55:[58, 101] Operation: 90+11=101\n\nThought : Expand Node #0,3,2’s 1st child to build next frontier.\nAction : Exploring operation 101-58=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3 with lowest heuristic value 27.333333333333332\nCurrent State #0,3: 55:[90, 11, 58]. Operations so far : ['95-37=58'].\n\nThought : Expand Node #0,3’s 4th child to build next frontier.\nAction : Exploring operation 11+58=69. \nResulting numbers: [90, 69].\nHeuristic score : (|90-55| + |69-55|)/2 = (35 + 14)/2 = 24.50\nGenerated Node #0,3,3: 55:[90, 69] Operation: 11+58=69\n\nThought : Expand Node #0,3,3’s 1st child to build next frontier.\nAction : Exploring operation 90-69=21. \nResulting numbers: [21].\n21,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3 with lowest heuristic value 27.333333333333332\nCurrent State #0,3: 55:[90, 11, 58]. Operations so far : ['95-37=58'].\n\nThought : Expand Node #0,3’s 5th child to build next frontier.\nAction : Exploring operation 90-58=32. \nResulting numbers: [11, 32].\nHeuristic score : (|11-55| + |32-55|)/2 = (44 + 23)/2 = 33.50\nGenerated Node #0,3,4: 55:[11, 32] Operation: 90-58=32\n\nThought : Expand Node #0,3,4’s 1st child to build next frontier.\nAction : Exploring operation 11+32=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3 with lowest heuristic value 27.333333333333332\nCurrent State #0,3: 55:[90, 11, 58]. Operations so far : ['95-37=58'].\n\nThought : Expand Node #0,3’s 6th child to build next frontier.\nAction : Exploring operation 90+58=148. \nResulting numbers: [11, 148].\nHeuristic score : (|11-55| + |148-55|)/2 = (44 + 93)/2 = 68.50\nGenerated Node #0,3,5: 55:[11, 148] Operation: 90+58=148\n\nThought : Expand Node #0,3,5’s 1st child to build next frontier.\nAction : Exploring operation 148-11=137. \nResulting numbers: [137].\n137,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3 with lowest heuristic value 27.333333333333332\nCurrent State #0,3: 55:[90, 11, 58]. Operations so far : ['95-37=58'].\n\nThought : Expand Node #0,3’s 7th child to build next frontier.\nAction : Exploring operation 11*58=638. \nResulting numbers: [90, 638].\nHeuristic score : (|90-55| + |638-55|)/2 = (35 + 583)/2 = 309.00\nGenerated Node #0,3,6: 55:[90, 638] Operation: 11*58=638\n\nThought : Expand Node #0,3,6’s 1st child to build next frontier.\nAction : Exploring operation 638-90=548. \nResulting numbers: [548].\n548,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3 with lowest heuristic value 27.333333333333332\nCurrent State #0,3: 55:[90, 11, 58]. Operations so far : ['95-37=58'].\n\nThought : Expand Node #0,3’s 8th child to build next frontier.\nAction : Exploring operation 90*11=990. \nResulting numbers: [58, 990].\nHeuristic score : (|58-55| + |990-55|)/2 = (3 + 935)/2 = 469.00\nGenerated Node #0,3,7: 55:[58, 990] Operation: 90*11=990\n\nThought : Expand Node #0,3,7’s 1st child to build next frontier.\nAction : Exploring operation 990-58=932. \nResulting numbers: [932].\n932,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3 with lowest heuristic value 27.333333333333332\nCurrent State #0,3: 55:[90, 11, 58]. Operations so far : ['95-37=58'].\n\nThought : Expand Node #0,3’s 9th child to build next frontier.\nAction : Exploring operation 90*58=5220. \nResulting numbers: [11, 5220].\nHeuristic score : (|11-55| + |5220-55|)/2 = (44 + 5165)/2 = 2604.50\nGenerated Node #0,3,8: 55:[11, 5220] Operation: 90*58=5220\n\nThought : Expand Node #0,3,8’s 1st child to build next frontier.\nAction : Exploring operation 5220-11=5209. \nResulting numbers: [5209].\n5209,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0 with lowest heuristic value 34.25\nCurrent State #0: 55:[90, 11, 37, 95]. Operations so far : [].\n\nThought : Expand Node #0’s 5th child to build next frontier.\nAction : Exploring operation 90-37=53. \nResulting numbers: [11, 95, 53].\nHeuristic score : (|11-55| + |95-55| + |53-55|)/3 = (44 + 40 + 2)/3 = 28.67\nGenerated Node #0,4: 55:[11, 95, 53] Operation: 90-37=53\n\nThought : Expand Node #0,4’s 1st child to build next frontier.\nAction : Exploring operation 95-11=84. \nResulting numbers: [53, 84].\nHeuristic score : (|53-55| + |84-55|)/2 = (2 + 29)/2 = 15.50\nGenerated Node #0,4,0: 55:[53, 84] Operation: 95-11=84\n\nThought : Expand Node #0,4,0’s 1st child to build next frontier.\nAction : Exploring operation 84-53=31. \nResulting numbers: [31].\n31,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4 with lowest heuristic value 28.666666666666668\nCurrent State #0,4: 55:[11, 95, 53]. Operations so far : ['90-37=53'].\n\nThought : Expand Node #0,4’s 2nd child to build next frontier.\nAction : Exploring operation 11+53=64. \nResulting numbers: [95, 64].\nHeuristic score : (|95-55| + |64-55|)/2 = (40 + 9)/2 = 24.50\nGenerated Node #0,4,1: 55:[95, 64] Operation: 11+53=64\n\nThought : Expand Node #0,4,1’s 1st child to build next frontier.\nAction : Exploring operation 95-64=31. \nResulting numbers: [31].\n31,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4 with lowest heuristic value 28.666666666666668\nCurrent State #0,4: 55:[11, 95, 53]. Operations so far : ['90-37=53'].\n\nThought : Expand Node #0,4’s 3rd child to build next frontier.\nAction : Exploring operation 11+95=106. \nResulting numbers: [53, 106].\nHeuristic score : (|53-55| + |106-55|)/2 = (2 + 51)/2 = 26.50\nGenerated Node #0,4,2: 55:[53, 106] Operation: 11+95=106\n\nThought : Expand Node #0,4,2’s 1st child to build next frontier.\nAction : Exploring operation 106-53=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4 with lowest heuristic value 28.666666666666668\nCurrent State #0,4: 55:[11, 95, 53]. Operations so far : ['90-37=53'].\n\nThought : Expand Node #0,4’s 4th child to build next frontier.\nAction : Exploring operation 53-11=42. \nResulting numbers: [95, 42].\nHeuristic score : (|95-55| + |42-55|)/2 = (40 + 13)/2 = 26.50\nGenerated Node #0,4,3: 55:[95, 42] Operation: 53-11=42\n\nThought : Expand Node #0,4,3’s 1st child to build next frontier.\nAction : Exploring operation 95-42=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4 with lowest heuristic value 28.666666666666668\nCurrent State #0,4: 55:[11, 95, 53]. Operations so far : ['90-37=53'].\n\nThought : Expand Node #0,4’s 5th child to build next frontier.\nAction : Exploring operation 95-53=42. \nResulting numbers: [11, 42].\nHeuristic score : (|11-55| + |42-55|)/2 = (44 + 13)/2 = 28.50\nGenerated Node #0,4,4: 55:[11, 42] Operation: 95-53=42\n\nThought : Expand Node #0,4,4’s 1st child to build next frontier.\nAction : Exploring operation 11+42=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4 with lowest heuristic value 28.666666666666668\nCurrent State #0,4: 55:[11, 95, 53]. Operations so far : ['90-37=53'].\n\nThought : Expand Node #0,4’s 6th child to build next frontier.\nAction : Exploring operation 95+53=148. \nResulting numbers: [11, 148].\nHeuristic score : (|11-55| + |148-55|)/2 = (44 + 93)/2 = 68.50\nGenerated Node #0,4,5: 55:[11, 148] Operation: 95+53=148\n\nThought : Expand Node #0,4,5’s 1st child to build next frontier.\nAction : Exploring operation 148-11=137. \nResulting numbers: [137].\n137,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4 with lowest heuristic value 28.666666666666668\nCurrent State #0,4: 55:[11, 95, 53]. Operations so far : ['90-37=53'].\n\nThought : Expand Node #0,4’s 7th child to build next frontier.\nAction : Exploring operation 11*53=583. \nResulting numbers: [95, 583].\nHeuristic score : (|95-55| + |583-55|)/2 = (40 + 528)/2 = 284.00\nGenerated Node #0,4,6: 55:[95, 583] Operation: 11*53=583\n\nThought : Expand Node #0,4,6’s 1st child to build next frontier.\nAction : Exploring operation 583-95=488. \nResulting numbers: [488].\n488,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4 with lowest heuristic value 28.666666666666668\nCurrent State #0,4: 55:[11, 95, 53]. Operations so far : ['90-37=53'].\n\nThought : Expand Node #0,4’s 8th child to build next frontier.\nAction : Exploring operation 11*95=1045. \nResulting numbers: [53, 1045].\nHeuristic score : (|53-55| + |1045-55|)/2 = (2 + 990)/2 = 496.00\nGenerated Node #0,4,7: 55:[53, 1045] Operation: 11*95=1045\n\nThought : Expand Node #0,4,7’s 1st child to build next frontier.\nAction : Exploring operation 1045-53=992. \nResulting numbers: [992].\n992,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4 with lowest heuristic value 28.666666666666668\nCurrent State #0,4: 55:[11, 95, 53]. Operations so far : ['90-37=53'].\n\nThought : Expand Node #0,4’s 9th child to build next frontier.\nAction : Exploring operation 95*53=5035. \nResulting numbers: [11, 5035].\nHeuristic score : (|11-55| + |5035-55|)/2 = (44 + 4980)/2 = 2512.00\nGenerated Node #0,4,8: 55:[11, 5035] Operation: 95*53=5035\n\nThought : Expand Node #0,4,8’s 1st child to build next frontier.\nAction : Exploring operation 5035-11=5024. \nResulting numbers: [5024].\n5024,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0 with lowest heuristic value 34.25\nCurrent State #0: 55:[90, 11, 37, 95]. Operations so far : [].\n\nThought : Expand Node #0’s 6th child to build next frontier.\nAction : Exploring operation 90+11=101. \nResulting numbers: [37, 95, 101].\nHeuristic score : (|37-55| + |95-55| + |101-55|)/3 = (18 + 40 + 46)/3 = 34.67\nGenerated Node #0,5: 55:[37, 95, 101] Operation: 90+11=101\n\nThought : Expand Node #0,5’s 1st child to build next frontier.\nAction : Exploring operation 95-37=58. \nResulting numbers: [101, 58].\nHeuristic score : (|101-55| + |58-55|)/2 = (46 + 3)/2 = 24.50\nGenerated Node #0,5,0: 55:[101, 58] Operation: 95-37=58\n\nThought : Expand Node #0,5,0’s 1st child to build next frontier.\nAction : Exploring operation 101-58=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,5 with lowest heuristic value 34.666666666666664\nCurrent State #0,5: 55:[37, 95, 101]. Operations so far : ['90+11=101'].\n\nThought : Expand Node #0,5’s 2nd child to build next frontier.\nAction : Exploring operation 101-37=64. \nResulting numbers: [95, 64].\nHeuristic score : (|95-55| + |64-55|)/2 = (40 + 9)/2 = 24.50\nGenerated Node #0,5,1: 55:[95, 64] Operation: 101-37=64\n\nThought : Expand Node #0,5,1’s 1st child to build next frontier.\nAction : Exploring operation 95-64=31. \nResulting numbers: [31].\n31,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,5 with lowest heuristic value 34.666666666666664\nCurrent State #0,5: 55:[37, 95, 101]. Operations so far : ['90+11=101'].\n\nThought : Expand Node #0,5’s 3rd child to build next frontier.\nAction : Exploring operation 101-95=6. \nResulting numbers: [37, 6].\nHeuristic score : (|37-55| + |6-55|)/2 = (18 + 49)/2 = 33.50\nGenerated Node #0,5,2: 55:[37, 6] Operation: 101-95=6\n\nThought : Expand Node #0,5,2’s 1st child to build next frontier.\nAction : Exploring operation 37+6=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,5 with lowest heuristic value 34.666666666666664\nCurrent State #0,5: 55:[37, 95, 101]. Operations so far : ['90+11=101'].\n\nThought : Expand Node #0,5’s 4th child to build next frontier.\nAction : Exploring operation 37+95=132. \nResulting numbers: [101, 132].\nHeuristic score : (|101-55| + |132-55|)/2 = (46 + 77)/2 = 61.50\nGenerated Node #0,5,3: 55:[101, 132] Operation: 37+95=132\n\nThought : Expand Node #0,5,3’s 1st child to build next frontier.\nAction : Exploring operation 132-101=31. \nResulting numbers: [31].\n31,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,5 with lowest heuristic value 34.666666666666664\nCurrent State #0,5: 55:[37, 95, 101]. Operations so far : ['90+11=101'].\n\nThought : Expand Node #0,5’s 5th child to build next frontier.\nAction : Exploring operation 37+101=138. \nResulting numbers: [95, 138].\nHeuristic score : (|95-55| + |138-55|)/2 = (40 + 83)/2 = 61.50\nGenerated Node #0,5,4: 55:[95, 138] Operation: 37+101=138\n\nThought : Expand Node #0,5,4’s 1st child to build next frontier.\nAction : Exploring operation 138-95=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,5 with lowest heuristic value 34.666666666666664\nCurrent State #0,5: 55:[37, 95, 101]. Operations so far : ['90+11=101'].\n\nThought : Expand Node #0,5’s 6th child to build next frontier.\nAction : Exploring operation 95+101=196. \nResulting numbers: [37, 196].\nHeuristic score : (|37-55| + |196-55|)/2 = (18 + 141)/2 = 79.50\nGenerated Node #0,5,5: 55:[37, 196] Operation: 95+101=196\n\nThought : Expand Node #0,5,5’s 1st child to build next frontier.\nAction : Exploring operation 196-37=159. \nResulting numbers: [159].\n159,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,5 with lowest heuristic value 34.666666666666664\nCurrent State #0,5: 55:[37, 95, 101]. Operations so far : ['90+11=101'].\n\nThought : Expand Node #0,5’s 7th child to build next frontier.\nAction : Exploring operation 37*95=3515. \nResulting numbers: [101, 3515].\nHeuristic score : (|101-55| + |3515-55|)/2 = (46 + 3460)/2 = 1753.00\nGenerated Node #0,5,6: 55:[101, 3515] Operation: 37*95=3515\n\nThought : Expand Node #0,5,6’s 1st child to build next frontier.\nAction : Exploring operation 3515-101=3414. \nResulting numbers: [3414].\n3414,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,5 with lowest heuristic value 34.666666666666664\nCurrent State #0,5: 55:[37, 95, 101]. Operations so far : ['90+11=101'].\n\nThought : Expand Node #0,5’s 8th child to build next frontier.\nAction : Exploring operation 37*101=3737. \nResulting numbers: [95, 3737].\nHeuristic score : (|95-55| + |3737-55|)/2 = (40 + 3682)/2 = 1861.00\nGenerated Node #0,5,7: 55:[95, 3737] Operation: 37*101=3737\n\nThought : Expand Node #0,5,7’s 1st child to build next frontier.\nAction : Exploring operation 3737-95=3642. \nResulting numbers: [3642].\n3642,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,5 with lowest heuristic value 34.666666666666664\nCurrent State #0,5: 55:[37, 95, 101]. Operations so far : ['90+11=101'].\n\nThought : Expand Node #0,5’s 9th child to build next frontier.\nAction : Exploring operation 95*101=9595. \nResulting numbers: [37, 9595].\nHeuristic score : (|37-55| + |9595-55|)/2 = (18 + 9540)/2 = 4779.00\nGenerated Node #0,5,8: 55:[37, 9595] Operation: 95*101=9595\n\nThought : Expand Node #0,5,8’s 1st child to build next frontier.\nAction : Exploring operation 9595-37=9558. \nResulting numbers: [9558].\n9558,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0 with lowest heuristic value 34.25\nCurrent State #0: 55:[90, 11, 37, 95]. Operations so far : [].\n\nThought : Expand Node #0’s 7th child to build next frontier.\nAction : Exploring operation 37-11=26. \nResulting numbers: [90, 95, 26].\nHeuristic score : (|90-55| + |95-55| + |26-55|)/3 = (35 + 40 + 29)/3 = 34.67\nGenerated Node #0,6: 55:[90, 95, 26] Operation: 37-11=26\n\nThought : Expand Node #0,6’s 1st child to build next frontier.\nAction : Exploring operation 90-26=64. \nResulting numbers: [95, 64].\nHeuristic score : (|95-55| + |64-55|)/2 = (40 + 9)/2 = 24.50\nGenerated Node #0,6,0: 55:[95, 64] Operation: 90-26=64\n\nThought : Expand Node #0,6,0’s 1st child to build next frontier.\nAction : Exploring operation 95-64=31. \nResulting numbers: [31].\n31,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,6 with lowest heuristic value 34.666666666666664\nCurrent State #0,6: 55:[90, 95, 26]. Operations so far : ['37-11=26'].\n\nThought : Expand Node #0,6’s 2nd child to build next frontier.\nAction : Exploring operation 95-26=69. \nResulting numbers: [90, 69].\nHeuristic score : (|90-55| + |69-55|)/2 = (35 + 14)/2 = 24.50\nGenerated Node #0,6,1: 55:[90, 69] Operation: 95-26=69\n\nThought : Expand Node #0,6,1’s 1st child to build next frontier.\nAction : Exploring operation 90-69=21. \nResulting numbers: [21].\n21,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,6 with lowest heuristic value 34.666666666666664\nCurrent State #0,6: 55:[90, 95, 26]. Operations so far : ['37-11=26'].\n\nThought : Expand Node #0,6’s 3rd child to build next frontier.\nAction : Exploring operation 95-90=5. \nResulting numbers: [26, 5].\nHeuristic score : (|26-55| + |5-55|)/2 = (29 + 50)/2 = 39.50\nGenerated Node #0,6,2: 55:[26, 5] Operation: 95-90=5\n\nThought : Expand Node #0,6,2’s 1st child to build next frontier.\nAction : Exploring operation 26+5=31. \nResulting numbers: [31].\n31,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,6 with lowest heuristic value 34.666666666666664\nCurrent State #0,6: 55:[90, 95, 26]. Operations so far : ['37-11=26'].\n\nThought : Expand Node #0,6’s 4th child to build next frontier.\nAction : Exploring operation 90+26=116. \nResulting numbers: [95, 116].\nHeuristic score : (|95-55| + |116-55|)/2 = (40 + 61)/2 = 50.50\nGenerated Node #0,6,3: 55:[95, 116] Operation: 90+26=116\n\nThought : Expand Node #0,6,3’s 1st child to build next frontier.\nAction : Exploring operation 116-95=21. \nResulting numbers: [21].\n21,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,6 with lowest heuristic value 34.666666666666664\nCurrent State #0,6: 55:[90, 95, 26]. Operations so far : ['37-11=26'].\n\nThought : Expand Node #0,6’s 5th child to build next frontier.\nAction : Exploring operation 95+26=121. \nResulting numbers: [90, 121].\nHeuristic score : (|90-55| + |121-55|)/2 = (35 + 66)/2 = 50.50\nGenerated Node #0,6,4: 55:[90, 121] Operation: 95+26=121\n\nThought : Expand Node #0,6,4’s 1st child to build next frontier.\nAction : Exploring operation 121-90=31. \nResulting numbers: [31].\n31,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,6 with lowest heuristic value 34.666666666666664\nCurrent State #0,6: 55:[90, 95, 26]. Operations so far : ['37-11=26'].\n\nThought : Expand Node #0,6’s 6th child to build next frontier.\nAction : Exploring operation 90+95=185. \nResulting numbers: [26, 185].\nHeuristic score : (|26-55| + |185-55|)/2 = (29 + 130)/2 = 79.50\nGenerated Node #0,6,5: 55:[26, 185] Operation: 90+95=185\n\nThought : Expand Node #0,6,5’s 1st child to build next frontier.\nAction : Exploring operation 185-26=159. \nResulting numbers: [159].\n159,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,6 with lowest heuristic value 34.666666666666664\nCurrent State #0,6: 55:[90, 95, 26]. Operations so far : ['37-11=26'].\n\nThought : Expand Node #0,6’s 7th child to build next frontier.\nAction : Exploring operation 90*26=2340. \nResulting numbers: [95, 2340].\nHeuristic score : (|95-55| + |2340-55|)/2 = (40 + 2285)/2 = 1162.50\nGenerated Node #0,6,6: 55:[95, 2340] Operation: 90*26=2340\n\nThought : Expand Node #0,6,6’s 1st child to build next frontier.\nAction : Exploring operation 2340-95=2245. \nResulting numbers: [2245].\n2245,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,6 with lowest heuristic value 34.666666666666664\nCurrent State #0,6: 55:[90, 95, 26]. Operations so far : ['37-11=26'].\n\nThought : Expand Node #0,6’s 8th child to build next frontier.\nAction : Exploring operation 95*26=2470. \nResulting numbers: [90, 2470].\nHeuristic score : (|90-55| + |2470-55|)/2 = (35 + 2415)/2 = 1225.00\nGenerated Node #0,6,7: 55:[90, 2470] Operation: 95*26=2470\n\nThought : Expand Node #0,6,7’s 1st child to build next frontier.\nAction : Exploring operation 2470-90=2380. \nResulting numbers: [2380].\n2380,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,6 with lowest heuristic value 34.666666666666664\nCurrent State #0,6: 55:[90, 95, 26]. Operations so far : ['37-11=26'].\n\nThought : Expand Node #0,6’s 9th child to build next frontier.\nAction : Exploring operation 90*95=8550. \nResulting numbers: [26, 8550].\nHeuristic score : (|26-55| + |8550-55|)/2 = (29 + 8495)/2 = 4262.00\nGenerated Node #0,6,8: 55:[26, 8550] Operation: 90*95=8550\n\nThought : Expand Node #0,6,8’s 1st child to build next frontier.\nAction : Exploring operation 8550-26=8524. \nResulting numbers: [8524].\n8524,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0 with lowest heuristic value 34.25\nCurrent State #0: 55:[90, 11, 37, 95]. Operations so far : [].\n\nThought : Expand Node #0’s 8th child to build next frontier.\nAction : Exploring operation 11+95=106. \nResulting numbers: [90, 37, 106].\nHeuristic score : (|90-55| + |37-55| + |106-55|)/3 = (35 + 18 + 51)/3 = 34.67\nGenerated Node #0,7: 55:[90, 37, 106] Operation: 11+95=106\n\nThought : Expand Node #0,7’s 1st child to build next frontier.\nAction : Exploring operation 106-37=69. \nResulting numbers: [90, 69].\nHeuristic score : (|90-55| + |69-55|)/2 = (35 + 14)/2 = 24.50\nGenerated Node #0,7,0: 55:[90, 69] Operation: 106-37=69\n\nThought : Expand Node #0,7,0’s 1st child to build next frontier.\nAction : Exploring operation 90-69=21. \nResulting numbers: [21].\n21,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,7 with lowest heuristic value 34.666666666666664\nCurrent State #0,7: 55:[90, 37, 106]. Operations so far : ['11+95=106'].\n\nThought : Expand Node #0,7’s 2nd child to build next frontier.\nAction : Exploring operation 90-37=53. \nResulting numbers: [106, 53].\nHeuristic score : (|106-55| + |53-55|)/2 = (51 + 2)/2 = 26.50\nGenerated Node #0,7,1: 55:[106, 53] Operation: 90-37=53\n\nThought : Expand Node #0,7,1’s 1st child to build next frontier.\nAction : Exploring operation 106-53=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,7 with lowest heuristic value 34.666666666666664\nCurrent State #0,7: 55:[90, 37, 106]. Operations so far : ['11+95=106'].\n\nThought : Expand Node #0,7’s 3rd child to build next frontier.\nAction : Exploring operation 106-90=16. \nResulting numbers: [37, 16].\nHeuristic score : (|37-55| + |16-55|)/2 = (18 + 39)/2 = 28.50\nGenerated Node #0,7,2: 55:[37, 16] Operation: 106-90=16\n\nThought : Expand Node #0,7,2’s 1st child to build next frontier.\nAction : Exploring operation 37+16=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,7 with lowest heuristic value 34.666666666666664\nCurrent State #0,7: 55:[90, 37, 106]. Operations so far : ['11+95=106'].\n\nThought : Expand Node #0,7’s 4th child to build next frontier.\nAction : Exploring operation 90+37=127. \nResulting numbers: [106, 127].\nHeuristic score : (|106-55| + |127-55|)/2 = (51 + 72)/2 = 61.50\nGenerated Node #0,7,3: 55:[106, 127] Operation: 90+37=127\n\nThought : Expand Node #0,7,3’s 1st child to build next frontier.\nAction : Exploring operation 127-106=21. \nResulting numbers: [21].\n21,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,7 with lowest heuristic value 34.666666666666664\nCurrent State #0,7: 55:[90, 37, 106]. Operations so far : ['11+95=106'].\n\nThought : Expand Node #0,7’s 5th child to build next frontier.\nAction : Exploring operation 37+106=143. \nResulting numbers: [90, 143].\nHeuristic score : (|90-55| + |143-55|)/2 = (35 + 88)/2 = 61.50\nGenerated Node #0,7,4: 55:[90, 143] Operation: 37+106=143\n\nThought : Expand Node #0,7,4’s 1st child to build next frontier.\nAction : Exploring operation 143-90=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,7 with lowest heuristic value 34.666666666666664\nCurrent State #0,7: 55:[90, 37, 106]. Operations so far : ['11+95=106'].\n\nThought : Expand Node #0,7’s 6th child to build next frontier.\nAction : Exploring operation 90+106=196. \nResulting numbers: [37, 196].\nHeuristic score : (|37-55| + |196-55|)/2 = (18 + 141)/2 = 79.50\nGenerated Node #0,7,5: 55:[37, 196] Operation: 90+106=196\n\nThought : Expand Node #0,7,5’s 1st child to build next frontier.\nAction : Exploring operation 196-37=159. \nResulting numbers: [159].\n159,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,7 with lowest heuristic value 34.666666666666664\nCurrent State #0,7: 55:[90, 37, 106]. Operations so far : ['11+95=106'].\n\nThought : Expand Node #0,7’s 7th child to build next frontier.\nAction : Exploring operation 90*37=3330. \nResulting numbers: [106, 3330].\nHeuristic score : (|106-55| + |3330-55|)/2 = (51 + 3275)/2 = 1663.00\nGenerated Node #0,7,6: 55:[106, 3330] Operation: 90*37=3330\n\nThought : Expand Node #0,7,6’s 1st child to build next frontier.\nAction : Exploring operation 3330-106=3224. \nResulting numbers: [3224].\n3224,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,7 with lowest heuristic value 34.666666666666664\nCurrent State #0,7: 55:[90, 37, 106]. Operations so far : ['11+95=106'].\n\nThought : Expand Node #0,7’s 8th child to build next frontier.\nAction : Exploring operation 37*106=3922. \nResulting numbers: [90, 3922].\nHeuristic score : (|90-55| + |3922-55|)/2 = (35 + 3867)/2 = 1951.00\nGenerated Node #0,7,7: 55:[90, 3922] Operation: 37*106=3922\n\nThought : Expand Node #0,7,7’s 1st child to build next frontier.\nAction : Exploring operation 3922-90=3832. \nResulting numbers: [3832].\n3832,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,7 with lowest heuristic value 34.666666666666664\nCurrent State #0,7: 55:[90, 37, 106]. Operations so far : ['11+95=106'].\n\nThought : Expand Node #0,7’s 9th child to build next frontier.\nAction : Exploring operation 90*106=9540. \nResulting numbers: [37, 9540].\nHeuristic score : (|37-55| + |9540-55|)/2 = (18 + 9485)/2 = 4751.50\nGenerated Node #0,7,8: 55:[37, 9540] Operation: 90*106=9540\n\nThought : Expand Node #0,7,8’s 1st child to build next frontier.\nAction : Exploring operation 9540-37=9503. \nResulting numbers: [9503].\n9503,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0 with lowest heuristic value 34.25\nCurrent State #0: 55:[90, 11, 37, 95]. Operations so far : [].\n\nThought : Expand Node #0’s 9th child to build next frontier.\nAction : Exploring operation 95-90=5. \nResulting numbers: [11, 37, 5].\nHeuristic score : (|11-55| + |37-55| + |5-55|)/3 = (44 + 18 + 50)/3 = 37.33\nGenerated Node #0,8: 55:[11, 37, 5] Operation: 95-90=5\n\nThought : Expand Node #0,8’s 1st child to build next frontier.\nAction : Exploring operation 11*5=55. \nResulting numbers: [37, 55].\nHeuristic score : (|37-55| + |55-55|)/2 = (18 + 0)/2 = 9.00\nGenerated Node #0,8,0: 55:[37, 55] Operation: 11*5=55\n\nThought : Expand Node #0,8,0’s 1st child to build next frontier.\nAction : Exploring operation 37+55=92. \nResulting numbers: [92].\n92,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,8 with lowest heuristic value 37.333333333333336\nCurrent State #0,8: 55:[11, 37, 5]. Operations so far : ['95-90=5'].\n\nThought : Expand Node #0,8’s 2nd child to build next frontier.\nAction : Exploring operation 11+37=48. \nResulting numbers: [5, 48].\nHeuristic score : (|5-55| + |48-55|)/2 = (50 + 7)/2 = 28.50\nGenerated Node #0,8,1: 55:[5, 48] Operation: 11+37=48\n\nThought : Expand Node #0,8,1’s 1st child to build next frontier.\nAction : Exploring operation 5+48=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,8 with lowest heuristic value 37.333333333333336\nCurrent State #0,8: 55:[11, 37, 5]. Operations so far : ['95-90=5'].\n\nThought : Expand Node #0,8’s 3rd child to build next frontier.\nAction : Exploring operation 11+5=16. \nResulting numbers: [37, 16].\nHeuristic score : (|37-55| + |16-55|)/2 = (18 + 39)/2 = 28.50\nGenerated Node #0,8,2: 55:[37, 16] Operation: 11+5=16\n\nThought : Expand Node #0,8,2’s 1st child to build next frontier.\nAction : Exploring operation 37+16=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,8 with lowest heuristic value 37.333333333333336\nCurrent State #0,8: 55:[11, 37, 5]. Operations so far : ['95-90=5'].\n\nThought : Expand Node #0,8’s 4th child to build next frontier.\nAction : Exploring operation 37+5=42. \nResulting numbers: [11, 42].\nHeuristic score : (|11-55| + |42-55|)/2 = (44 + 13)/2 = 28.50\nGenerated Node #0,8,3: 55:[11, 42] Operation: 37+5=42\n\nThought : Expand Node #0,8,3’s 1st child to build next frontier.\nAction : Exploring operation 11+42=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,8 with lowest heuristic value 37.333333333333336\nCurrent State #0,8: 55:[11, 37, 5]. Operations so far : ['95-90=5'].\n\nThought : Expand Node #0,8’s 5th child to build next frontier.\nAction : Exploring operation 11-5=6. \nResulting numbers: [37, 6].\nHeuristic score : (|37-55| + |6-55|)/2 = (18 + 49)/2 = 33.50\nGenerated Node #0,8,4: 55:[37, 6] Operation: 11-5=6\n\nThought : Expand Node #0,8,4’s 1st child to build next frontier.\nAction : Exploring operation 37+6=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,8 with lowest heuristic value 37.333333333333336\nCurrent State #0,8: 55:[11, 37, 5]. Operations so far : ['95-90=5'].\n\nThought : Expand Node #0,8’s 6th child to build next frontier.\nAction : Exploring operation 37-5=32. \nResulting numbers: [11, 32].\nHeuristic score : (|11-55| + |32-55|)/2 = (44 + 23)/2 = 33.50\nGenerated Node #0,8,5: 55:[11, 32] Operation: 37-5=32\n\nThought : Expand Node #0,8,5’s 1st child to build next frontier.\nAction : Exploring operation 11+32=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,8 with lowest heuristic value 37.333333333333336\nCurrent State #0,8: 55:[11, 37, 5]. Operations so far : ['95-90=5'].\n\nThought : Expand Node #0,8’s 7th child to build next frontier.\nAction : Exploring operation 37-11=26. \nResulting numbers: [5, 26].\nHeuristic score : (|5-55| + |26-55|)/2 = (50 + 29)/2 = 39.50\nGenerated Node #0,8,6: 55:[5, 26] Operation: 37-11=26\n\nThought : Expand Node #0,8,6’s 1st child to build next frontier.\nAction : Exploring operation 5+26=31. \nResulting numbers: [31].\n31,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,8 with lowest heuristic value 37.333333333333336\nCurrent State #0,8: 55:[11, 37, 5]. Operations so far : ['95-90=5'].\n\nThought : Expand Node #0,8’s 8th child to build next frontier.\nAction : Exploring operation 37*5=185. \nResulting numbers: [11, 185].\nHeuristic score : (|11-55| + |185-55|)/2 = (44 + 130)/2 = 87.00\nGenerated Node #0,8,7: 55:[11, 185] Operation: 37*5=185\n\nThought : Expand Node #0,8,7’s 1st child to build next frontier.\nAction : Exploring operation 185-11=174. \nResulting numbers: [174].\n174,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,8 with lowest heuristic value 37.333333333333336\nCurrent State #0,8: 55:[11, 37, 5]. Operations so far : ['95-90=5'].\n\nThought : Expand Node #0,8’s 9th child to build next frontier.\nAction : Exploring operation 11*37=407. \nResulting numbers: [5, 407].\nHeuristic score : (|5-55| + |407-55|)/2 = (50 + 352)/2 = 201.00\nGenerated Node #0,8,8: 55:[5, 407] Operation: 11*37=407\n\nThought : Expand Node #0,8,8’s 1st child to build next frontier.\nAction : Exploring operation 407-5=402. \nResulting numbers: [402].\n402,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0 with lowest heuristic value 34.25\nCurrent State #0: 55:[90, 11, 37, 95]. Operations so far : [].\n\nThought : Expand Node #0’s 10th child to build next frontier.\nAction : Exploring operation 90+37=127. \nResulting numbers: [11, 95, 127].\nHeuristic score : (|11-55| + |95-55| + |127-55|)/3 = (44 + 40 + 72)/3 = 52.00\nGenerated Node #0,9: 55:[11, 95, 127] Operation: 90+37=127\n\nThought : Expand Node #0,9’s 1st child to build next frontier.\nAction : Exploring operation 127-95=32. \nResulting numbers: [11, 32].\nHeuristic score : (|11-55| + |32-55|)/2 = (44 + 23)/2 = 33.50\nGenerated Node #0,9,0: 55:[11, 32] Operation: 127-95=32\n\nThought : Expand Node #0,9,0’s 1st child to build next frontier.\nAction : Exploring operation 11+32=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,9 with lowest heuristic value 52.0\nCurrent State #0,9: 55:[11, 95, 127]. Operations so far : ['90+37=127'].\n\nThought : Expand Node #0,9’s 2nd child to build next frontier.\nAction : Exploring operation 95-11=84. \nResulting numbers: [127, 84].\nHeuristic score : (|127-55| + |84-55|)/2 = (72 + 29)/2 = 50.50\nGenerated Node #0,9,1: 55:[127, 84] Operation: 95-11=84\n\nThought : Expand Node #0,9,1’s 1st child to build next frontier.\nAction : Exploring operation 127-84=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,9 with lowest heuristic value 52.0\nCurrent State #0,9: 55:[11, 95, 127]. Operations so far : ['90+37=127'].\n\nThought : Expand Node #0,9’s 3rd child to build next frontier.\nAction : Exploring operation 127-11=116. \nResulting numbers: [95, 116].\nHeuristic score : (|95-55| + |116-55|)/2 = (40 + 61)/2 = 50.50\nGenerated Node #0,9,2: 55:[95, 116] Operation: 127-11=116\n\nThought : Expand Node #0,9,2’s 1st child to build next frontier.\nAction : Exploring operation 116-95=21. \nResulting numbers: [21].\n21,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,9 with lowest heuristic value 52.0\nCurrent State #0,9: 55:[11, 95, 127]. Operations so far : ['90+37=127'].\n\nThought : Expand Node #0,9’s 4th child to build next frontier.\nAction : Exploring operation 11+95=106. \nResulting numbers: [127, 106].\nHeuristic score : (|127-55| + |106-55|)/2 = (72 + 51)/2 = 61.50\nGenerated Node #0,9,3: 55:[127, 106] Operation: 11+95=106\n\nThought : Expand Node #0,9,3’s 1st child to build next frontier.\nAction : Exploring operation 127-106=21. \nResulting numbers: [21].\n21,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,9 with lowest heuristic value 52.0\nCurrent State #0,9: 55:[11, 95, 127]. Operations so far : ['90+37=127'].\n\nThought : Expand Node #0,9’s 5th child to build next frontier.\nAction : Exploring operation 11+127=138. \nResulting numbers: [95, 138].\nHeuristic score : (|95-55| + |138-55|)/2 = (40 + 83)/2 = 61.50\nGenerated Node #0,9,4: 55:[95, 138] Operation: 11+127=138\n\nThought : Expand Node #0,9,4’s 1st child to build next frontier.\nAction : Exploring operation 138-95=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,9 with lowest heuristic value 52.0\nCurrent State #0,9: 55:[11, 95, 127]. Operations so far : ['90+37=127'].\n\nThought : Expand Node #0,9’s 6th child to build next frontier.\nAction : Exploring operation 95+127=222. \nResulting numbers: [11, 222].\nHeuristic score : (|11-55| + |222-55|)/2 = (44 + 167)/2 = 105.50\nGenerated Node #0,9,5: 55:[11, 222] Operation: 95+127=222\n\nThought : Expand Node #0,9,5’s 1st child to build next frontier.\nAction : Exploring operation 222-11=211. \nResulting numbers: [211].\n211,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,9 with lowest heuristic value 52.0\nCurrent State #0,9: 55:[11, 95, 127]. Operations so far : ['90+37=127'].\n\nThought : Expand Node #0,9’s 7th child to build next frontier.\nAction : Exploring operation 11*95=1045. \nResulting numbers: [127, 1045].\nHeuristic score : (|127-55| + |1045-55|)/2 = (72 + 990)/2 = 531.00\nGenerated Node #0,9,6: 55:[127, 1045] Operation: 11*95=1045\n\nThought : Expand Node #0,9,6’s 1st child to build next frontier.\nAction : Exploring operation 1045-127=918. \nResulting numbers: [918].\n918,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,9 with lowest heuristic value 52.0\nCurrent State #0,9: 55:[11, 95, 127]. Operations so far : ['90+37=127'].\n\nThought : Expand Node #0,9’s 8th child to build next frontier.\nAction : Exploring operation 11*127=1397. \nResulting numbers: [95, 1397].\nHeuristic score : (|95-55| + |1397-55|)/2 = (40 + 1342)/2 = 691.00\nGenerated Node #0,9,7: 55:[95, 1397] Operation: 11*127=1397\n\nThought : Expand Node #0,9,7’s 1st child to build next frontier.\nAction : Exploring operation 1397-95=1302. \nResulting numbers: [1302].\n1302,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,9 with lowest heuristic value 52.0\nCurrent State #0,9: 55:[11, 95, 127]. Operations so far : ['90+37=127'].\n\nThought : Expand Node #0,9’s 9th child to build next frontier.\nAction : Exploring operation 95*127=12065. \nResulting numbers: [11, 12065].\nHeuristic score : (|11-55| + |12065-55|)/2 = (44 + 12010)/2 = 6027.00\nGenerated Node #0,9,8: 55:[11, 12065] Operation: 95*127=12065\n\nThought : Expand Node #0,9,8’s 1st child to build next frontier.\nAction : Exploring operation 12065-11=12054. \nResulting numbers: [12054].\n12054,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0 with lowest heuristic value 34.25\nCurrent State #0: 55:[90, 11, 37, 95]. Operations so far : [].\n\nThought : Expand Node #0’s 11th child to build next frontier.\nAction : Exploring operation 37+95=132. \nResulting numbers: [90, 11, 132].\nHeuristic score : (|90-55| + |11-55| + |132-55|)/3 = (35 + 44 + 77)/3 = 52.00\nGenerated Node #0,10: 55:[90, 11, 132] Operation: 37+95=132\n\nThought : Expand Node #0,10’s 1st child to build next frontier.\nAction : Exploring operation 132-90=42. \nResulting numbers: [11, 42].\nHeuristic score : (|11-55| + |42-55|)/2 = (44 + 13)/2 = 28.50\nGenerated Node #0,10,0: 55:[11, 42] Operation: 132-90=42\n\nThought : Expand Node #0,10,0’s 1st child to build next frontier.\nAction : Exploring operation 11+42=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,10 with lowest heuristic value 52.0\nCurrent State #0,10: 55:[90, 11, 132]. Operations so far : ['37+95=132'].\n\nThought : Expand Node #0,10’s 2nd child to build next frontier.\nAction : Exploring operation 132/11=12. \nResulting numbers: [90, 12].\nHeuristic score : (|90-55| + |12-55|)/2 = (35 + 43)/2 = 39.00\nGenerated Node #0,10,1: 55:[90, 12] Operation: 132/11=12\n\nThought : Expand Node #0,10,1’s 1st child to build next frontier.\nAction : Exploring operation 90-12=78. \nResulting numbers: [78].\n78,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,10 with lowest heuristic value 52.0\nCurrent State #0,10: 55:[90, 11, 132]. Operations so far : ['37+95=132'].\n\nThought : Expand Node #0,10’s 3rd child to build next frontier.\nAction : Exploring operation 90-11=79. \nResulting numbers: [132, 79].\nHeuristic score : (|132-55| + |79-55|)/2 = (77 + 24)/2 = 50.50\nGenerated Node #0,10,2: 55:[132, 79] Operation: 90-11=79\n\nThought : Expand Node #0,10,2’s 1st child to build next frontier.\nAction : Exploring operation 132-79=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,10 with lowest heuristic value 52.0\nCurrent State #0,10: 55:[90, 11, 132]. Operations so far : ['37+95=132'].\n\nThought : Expand Node #0,10’s 4th child to build next frontier.\nAction : Exploring operation 132-11=121. \nResulting numbers: [90, 121].\nHeuristic score : (|90-55| + |121-55|)/2 = (35 + 66)/2 = 50.50\nGenerated Node #0,10,3: 55:[90, 121] Operation: 132-11=121\n\nThought : Expand Node #0,10,3’s 1st child to build next frontier.\nAction : Exploring operation 121-90=31. \nResulting numbers: [31].\n31,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,10 with lowest heuristic value 52.0\nCurrent State #0,10: 55:[90, 11, 132]. Operations so far : ['37+95=132'].\n\nThought : Expand Node #0,10’s 5th child to build next frontier.\nAction : Exploring operation 90+11=101. \nResulting numbers: [132, 101].\nHeuristic score : (|132-55| + |101-55|)/2 = (77 + 46)/2 = 61.50\nGenerated Node #0,10,4: 55:[132, 101] Operation: 90+11=101\n\nThought : Expand Node #0,10,4’s 1st child to build next frontier.\nAction : Exploring operation 132-101=31. \nResulting numbers: [31].\n31,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,10 with lowest heuristic value 52.0\nCurrent State #0,10: 55:[90, 11, 132]. Operations so far : ['37+95=132'].\n\nThought : Expand Node #0,10’s 6th child to build next frontier.\nAction : Exploring operation 11+132=143. \nResulting numbers: [90, 143].\nHeuristic score : (|90-55| + |143-55|)/2 = (35 + 88)/2 = 61.50\nGenerated Node #0,10,5: 55:[90, 143] Operation: 11+132=143\n\nThought : Expand Node #0,10,5’s 1st child to build next frontier.\nAction : Exploring operation 143-90=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,10 with lowest heuristic value 52.0\nCurrent State #0,10: 55:[90, 11, 132]. Operations so far : ['37+95=132'].\n\nThought : Expand Node #0,10’s 7th child to build next frontier.\nAction : Exploring operation 90+132=222. \nResulting numbers: [11, 222].\nHeuristic score : (|11-55| + |222-55|)/2 = (44 + 167)/2 = 105.50\nGenerated Node #0,10,6: 55:[11, 222] Operation: 90+132=222\n\nThought : Expand Node #0,10,6’s 1st child to build next frontier.\nAction : Exploring operation 222-11=211. \nResulting numbers: [211].\n211,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,10 with lowest heuristic value 52.0\nCurrent State #0,10: 55:[90, 11, 132]. Operations so far : ['37+95=132'].\n\nThought : Expand Node #0,10’s 8th child to build next frontier.\nAction : Exploring operation 90*11=990. \nResulting numbers: [132, 990].\nHeuristic score : (|132-55| + |990-55|)/2 = (77 + 935)/2 = 506.00\nGenerated Node #0,10,7: 55:[132, 990] Operation: 90*11=990\n\nThought : Expand Node #0,10,7’s 1st child to build next frontier.\nAction : Exploring operation 990-132=858. \nResulting numbers: [858].\n858,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,10 with lowest heuristic value 52.0\nCurrent State #0,10: 55:[90, 11, 132]. Operations so far : ['37+95=132'].\n\nThought : Expand Node #0,10’s 9th child to build next frontier.\nAction : Exploring operation 11*132=1452. \nResulting numbers: [90, 1452].\nHeuristic score : (|90-55| + |1452-55|)/2 = (35 + 1397)/2 = 716.00\nGenerated Node #0,10,8: 55:[90, 1452] Operation: 11*132=1452\n\nThought : Expand Node #0,10,8’s 1st child to build next frontier.\nAction : Exploring operation 1452-90=1362. \nResulting numbers: [1362].\n1362,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,10 with lowest heuristic value 52.0\nCurrent State #0,10: 55:[90, 11, 132]. Operations so far : ['37+95=132'].\n\nThought : Expand Node #0,10’s 10th child to build next frontier.\nAction : Exploring operation 90*132=11880. \nResulting numbers: [11, 11880].\nHeuristic score : (|11-55| + |11880-55|)/2 = (44 + 11825)/2 = 5934.50\nGenerated Node #0,10,9: 55:[11, 11880] Operation: 90*132=11880\n\nThought : Expand Node #0,10,9’s 1st child to build next frontier.\nAction : Exploring operation 11880/11=1080. \nResulting numbers: [1080].\n1080,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0 with lowest heuristic value 34.25\nCurrent State #0: 55:[90, 11, 37, 95]. Operations so far : [].\n\nThought : Expand Node #0’s 12th child to build next frontier.\nAction : Exploring operation 90+95=185. \nResulting numbers: [11, 37, 185].\nHeuristic score : (|11-55| + |37-55| + |185-55|)/3 = (44 + 18 + 130)/3 = 64.00\nGenerated Node #0,11: 55:[11, 37, 185] Operation: 90+95=185\n\nThought : Expand Node #0,11’s 1st child to build next frontier.\nAction : Exploring operation 185/37=5. \nResulting numbers: [11, 5].\nHeuristic score : (|11-55| + |5-55|)/2 = (44 + 50)/2 = 47.00\nGenerated Node #0,11,0: 55:[11, 5] Operation: 185/37=5\n\nThought : Expand Node #0,11,0’s 1st child to build next frontier.\nAction : Exploring operation 11*5=55. \nResulting numbers: [55].\n55,55 equal: Goal Reached\n\n```\nSOLUTION: YES\nOPERATIONS: ['90+95=185', '185/37=5', '11*5=55']\nRESULT: 55\n```\n",
"role": "assistant"
}
]
| 23,845 |
[
5,
5,
33,
33
]
| 76 | dfs | sum_heuristic | [
{
"content": "Combine these initial numbers [5, 5, 33, 33] using only arithmetic operations (+, -, *, /) to reach the target value 76. All initial numbers must be used exactly once.\nConclude with the final result in EXACTLY this format:\n```\nSOLUTION: YES/NO\nOPERATIONS: list of string of operations performed, each string involving only 1 operation. For example, ['A+B=C','C+D=E'] is allowed, ['A+B+D=E'] is not allowed\nRESULT: final_value\n```\n",
"role": "user"
},
{
"content": "We have these numbers [5, 5, 33, 33]. Our goal is to produce 76. Let's show the search process step by step:\nOne possible strategy is to use a Depth-First Search (DFS) guided by a **sum-based** heuristic, which computes the average of the absolute differences between each number and the target number.\nLower scores indicate that, on average, the numbers are closer to the target, making the state more promising for reaching the target via additive operations.\n\n\nCurrent State #0: 76:[5, 5, 33, 33]. Operations so far : [].\n\nThought : Expand Node #0’s 1st child to build next frontier.\nAction : Exploring operation 5*5=25. \nResulting numbers: [33, 33, 25].\nHeuristic score : (|33-76| + |33-76| + |25-76|)/3 = (43 + 43 + 51)/3 = 45.67\nGenerated Node #0,0: 76:[33, 33, 25] Operation: 5*5=25\n\nThought : Expand Node #0,0’s 1st child to build next frontier.\nAction : Exploring operation 33+33=66. \nResulting numbers: [25, 66].\nHeuristic score : (|25-76| + |66-76|)/2 = (51 + 10)/2 = 30.50\nGenerated Node #0,0,0: 76:[25, 66] Operation: 33+33=66\n\nThought : Expand Node #0,0,0’s 1st child to build next frontier.\nAction : Exploring operation 25+66=91. \nResulting numbers: [91].\n91,76 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 45.666666666666664\nCurrent State #0,0: 76:[33, 33, 25]. Operations so far : ['5*5=25'].\n\nThought : Expand Node #0,0’s 2nd child to build next frontier.\nAction : Exploring operation 33+25=58. \nResulting numbers: [33, 58].\nHeuristic score : (|33-76| + |58-76|)/2 = (43 + 18)/2 = 30.50\nGenerated Node #0,0,1: 76:[33, 58] Operation: 33+25=58\n\nThought : Expand Node #0,0,1’s 1st child to build next frontier.\nAction : Exploring operation 33+58=91. \nResulting numbers: [91].\n91,76 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 45.666666666666664\nCurrent State #0,0: 76:[33, 33, 25]. Operations so far : ['5*5=25'].\n\nThought : Expand Node #0,0’s 3rd child to build next frontier.\nAction : Exploring operation 33+25=58. \nResulting numbers: [33, 58].\nHeuristic score : (|33-76| + |58-76|)/2 = (43 + 18)/2 = 30.50\nGenerated Node #0,0,2: 76:[33, 58] Operation: 33+25=58\n\nThought : Expand Node #0,0,2’s 1st child to build next frontier.\nAction : Exploring operation 33+58=91. \nResulting numbers: [91].\n91,76 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 45.666666666666664\nCurrent State #0,0: 76:[33, 33, 25]. Operations so far : ['5*5=25'].\n\nThought : Expand Node #0,0’s 4th child to build next frontier.\nAction : Exploring operation 33-25=8. \nResulting numbers: [33, 8].\nHeuristic score : (|33-76| + |8-76|)/2 = (43 + 68)/2 = 55.50\nGenerated Node #0,0,3: 76:[33, 8] Operation: 33-25=8\n\nThought : Expand Node #0,0,3’s 1st child to build next frontier.\nAction : Exploring operation 33+8=41. \nResulting numbers: [41].\n41,76 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 45.666666666666664\nCurrent State #0,0: 76:[33, 33, 25]. Operations so far : ['5*5=25'].\n\nThought : Expand Node #0,0’s 5th child to build next frontier.\nAction : Exploring operation 33-25=8. \nResulting numbers: [33, 8].\nHeuristic score : (|33-76| + |8-76|)/2 = (43 + 68)/2 = 55.50\nGenerated Node #0,0,4: 76:[33, 8] Operation: 33-25=8\n\nThought : Expand Node #0,0,4’s 1st child to build next frontier.\nAction : Exploring operation 33+8=41. \nResulting numbers: [41].\n41,76 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 45.666666666666664\nCurrent State #0,0: 76:[33, 33, 25]. Operations so far : ['5*5=25'].\n\nThought : Expand Node #0,0’s 6th child to build next frontier.\nAction : Exploring operation 33/33=1. \nResulting numbers: [25, 1].\nHeuristic score : (|25-76| + |1-76|)/2 = (51 + 75)/2 = 63.00\nGenerated Node #0,0,5: 76:[25, 1] Operation: 33/33=1\n\nThought : Expand Node #0,0,5’s 1st child to build next frontier.\nAction : Exploring operation 25+1=26. \nResulting numbers: [26].\n26,76 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 45.666666666666664\nCurrent State #0,0: 76:[33, 33, 25]. Operations so far : ['5*5=25'].\n\nThought : Expand Node #0,0’s 7th child to build next frontier.\nAction : Exploring operation 33-33=0. \nResulting numbers: [25, 0].\nHeuristic score : (|25-76| + |0-76|)/2 = (51 + 76)/2 = 63.50\nGenerated Node #0,0,6: 76:[25, 0] Operation: 33-33=0\n\nThought : Expand Node #0,0,6’s 1st child to build next frontier.\nAction : Exploring operation 25+0=25. \nResulting numbers: [25].\n25,76 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 45.666666666666664\nCurrent State #0,0: 76:[33, 33, 25]. Operations so far : ['5*5=25'].\n\nThought : Expand Node #0,0’s 8th child to build next frontier.\nAction : Exploring operation 33*25=825. \nResulting numbers: [33, 825].\nHeuristic score : (|33-76| + |825-76|)/2 = (43 + 749)/2 = 396.00\nGenerated Node #0,0,7: 76:[33, 825] Operation: 33*25=825\n\nThought : Expand Node #0,0,7’s 1st child to build next frontier.\nAction : Exploring operation 825/33=25. \nResulting numbers: [25].\n25,76 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 45.666666666666664\nCurrent State #0,0: 76:[33, 33, 25]. Operations so far : ['5*5=25'].\n\nThought : Expand Node #0,0’s 9th child to build next frontier.\nAction : Exploring operation 33*25=825. \nResulting numbers: [33, 825].\nHeuristic score : (|33-76| + |825-76|)/2 = (43 + 749)/2 = 396.00\nGenerated Node #0,0,8: 76:[33, 825] Operation: 33*25=825\n\nThought : Expand Node #0,0,8’s 1st child to build next frontier.\nAction : Exploring operation 825/33=25. \nResulting numbers: [25].\n25,76 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 45.666666666666664\nCurrent State #0,0: 76:[33, 33, 25]. Operations so far : ['5*5=25'].\n\nThought : Expand Node #0,0’s 10th child to build next frontier.\nAction : Exploring operation 33*33=1089. \nResulting numbers: [25, 1089].\nHeuristic score : (|25-76| + |1089-76|)/2 = (51 + 1013)/2 = 532.00\nGenerated Node #0,0,9: 76:[25, 1089] Operation: 33*33=1089\n\nThought : Expand Node #0,0,9’s 1st child to build next frontier.\nAction : Exploring operation 1089-25=1064. \nResulting numbers: [1064].\n1064,76 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0 with lowest heuristic value 57.0\nCurrent State #0: 76:[5, 5, 33, 33]. Operations so far : [].\n\nThought : Expand Node #0’s 2nd child to build next frontier.\nAction : Exploring operation 5+5=10. \nResulting numbers: [33, 33, 10].\nHeuristic score : (|33-76| + |33-76| + |10-76|)/3 = (43 + 43 + 66)/3 = 50.67\nGenerated Node #0,1: 76:[33, 33, 10] Operation: 5+5=10\n\nThought : Expand Node #0,1’s 1st child to build next frontier.\nAction : Exploring operation 33+33=66. \nResulting numbers: [10, 66].\nHeuristic score : (|10-76| + |66-76|)/2 = (66 + 10)/2 = 38.00\nGenerated Node #0,1,0: 76:[10, 66] Operation: 33+33=66\n\nThought : Expand Node #0,1,0’s 1st child to build next frontier.\nAction : Exploring operation 10+66=76. \nResulting numbers: [76].\n76,76 equal: Goal Reached\n\n```\nSOLUTION: YES\nOPERATIONS: ['5+5=10', '33+33=66', '10+66=76']\nRESULT: 76\n```\n",
"role": "assistant"
}
]
| 2,749 |
[
86,
8,
22,
89
]
| 58 | bfs_5 | sum_heuristic | [
{
"content": "Combine these initial numbers [86, 8, 22, 89] using only arithmetic operations (+, -, *, /) to reach the target value 58. All initial numbers must be used exactly once.\nConclude with the final result in EXACTLY this format:\n```\nSOLUTION: YES/NO\nOPERATIONS: list of string of operations performed, each string involving only 1 operation. For example, ['A+B=C','C+D=E'] is allowed, ['A+B+D=E'] is not allowed\nRESULT: final_value\n```\n",
"role": "user"
},
{
"content": "We have these numbers [86, 8, 22, 89]. Our goal is to produce 58. Let's show the search process step by step:\nOne possible strategy is to use a Breadth-First Search (BFS) with Beam Size 5 guided by a **sum-based** heuristic, which computes the average of the absolute differences between each number and the target number.\nLower scores indicate that, on average, the numbers are closer to the target, making the state more promising for reaching the target via additive operations.\n\n\nCurrent State #0: 58:[86, 8, 22, 89]. Operations so far : [].\n\nThought : Expand Node #0’s 1st child to build next frontier.\nAction : Exploring operation 89-22=67. \nResulting numbers: [86, 8, 67].\nHeuristic score : (|86-58| + |8-58| + |67-58|)/3 = (28 + 50 + 9)/3 = 29.00\nGenerated Node #0,0: 58:[86, 8, 67] Operation: 89-22=67\n\nThought : Expand Node #0’s 2nd child to build next frontier.\nAction : Exploring operation 8+22=30. \nResulting numbers: [86, 89, 30].\nHeuristic score : (|86-58| + |89-58| + |30-58|)/3 = (28 + 31 + 28)/3 = 29.00\nGenerated Node #0,1: 58:[86, 89, 30] Operation: 8+22=30\n\nThought : Expand Node #0’s 3rd child to build next frontier.\nAction : Exploring operation 86-8=78. \nResulting numbers: [22, 89, 78].\nHeuristic score : (|22-58| + |89-58| + |78-58|)/3 = (36 + 31 + 20)/3 = 29.00\nGenerated Node #0,2: 58:[22, 89, 78] Operation: 86-8=78\n\nThought : Expand Node #0’s 4th child to build next frontier.\nAction : Exploring operation 86-22=64. \nResulting numbers: [8, 89, 64].\nHeuristic score : (|8-58| + |89-58| + |64-58|)/3 = (50 + 31 + 6)/3 = 29.00\nGenerated Node #0,3: 58:[8, 89, 64] Operation: 86-22=64\n\nThought : Expand Node #0’s 5th child to build next frontier.\nAction : Exploring operation 89-8=81. \nResulting numbers: [86, 22, 81].\nHeuristic score : (|86-58| + |22-58| + |81-58|)/3 = (28 + 36 + 23)/3 = 29.00\nGenerated Node #0,4: 58:[86, 22, 81] Operation: 89-8=81\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 29.0\nCurrent State #0,0: 58:[86, 8, 67]. Operations so far : ['89-22=67'].\n\nThought : Expand Node #0,0’s 1st child to build next frontier.\nAction : Exploring operation 8+67=75. \nResulting numbers: [86, 75].\nHeuristic score : (|86-58| + |75-58|)/2 = (28 + 17)/2 = 22.50\nGenerated Node #0,0,0: 58:[86, 75] Operation: 8+67=75\n\nThought : Expand Node #0,0’s 2nd child to build next frontier.\nAction : Exploring operation 86-67=19. \nResulting numbers: [8, 19].\nHeuristic score : (|8-58| + |19-58|)/2 = (50 + 39)/2 = 44.50\nGenerated Node #0,0,1: 58:[8, 19] Operation: 86-67=19\n\nThought : Expand Node #0,0’s 3rd child to build next frontier.\nAction : Exploring operation 86+8=94. \nResulting numbers: [67, 94].\nHeuristic score : (|67-58| + |94-58|)/2 = (9 + 36)/2 = 22.50\nGenerated Node #0,0,2: 58:[67, 94] Operation: 86+8=94\n\nThought : Expand Node #0,0’s 4th child to build next frontier.\nAction : Exploring operation 86-8=78. \nResulting numbers: [67, 78].\nHeuristic score : (|67-58| + |78-58|)/2 = (9 + 20)/2 = 14.50\nGenerated Node #0,0,3: 58:[67, 78] Operation: 86-8=78\n\nThought : Expand Node #0,0’s 5th child to build next frontier.\nAction : Exploring operation 67-8=59. \nResulting numbers: [86, 59].\nHeuristic score : (|86-58| + |59-58|)/2 = (28 + 1)/2 = 14.50\nGenerated Node #0,0,4: 58:[86, 59] Operation: 67-8=59\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2 with lowest heuristic value 29.0\nCurrent State #0,2: 58:[22, 89, 78]. Operations so far : ['86-8=78'].\n\nThought : Expand Node #0,2’s 1st child to build next frontier.\nAction : Exploring operation 22+89=111. \nResulting numbers: [78, 111].\nHeuristic score : (|78-58| + |111-58|)/2 = (20 + 53)/2 = 36.50\nGenerated Node #0,2,0: 58:[78, 111] Operation: 22+89=111\n\nThought : Expand Node #0,2’s 2nd child to build next frontier.\nAction : Exploring operation 89-78=11. \nResulting numbers: [22, 11].\nHeuristic score : (|22-58| + |11-58|)/2 = (36 + 47)/2 = 41.50\nGenerated Node #0,2,1: 58:[22, 11] Operation: 89-78=11\n\nThought : Expand Node #0,2’s 3rd child to build next frontier.\nAction : Exploring operation 78-22=56. \nResulting numbers: [89, 56].\nHeuristic score : (|89-58| + |56-58|)/2 = (31 + 2)/2 = 16.50\nGenerated Node #0,2,2: 58:[89, 56] Operation: 78-22=56\n\nThought : Expand Node #0,2’s 4th child to build next frontier.\nAction : Exploring operation 22+78=100. \nResulting numbers: [89, 100].\nHeuristic score : (|89-58| + |100-58|)/2 = (31 + 42)/2 = 36.50\nGenerated Node #0,2,3: 58:[89, 100] Operation: 22+78=100\n\nThought : Expand Node #0,2’s 5th child to build next frontier.\nAction : Exploring operation 89-22=67. \nResulting numbers: [78, 67].\nHeuristic score : (|78-58| + |67-58|)/2 = (20 + 9)/2 = 14.50\nGenerated Node #0,2,4: 58:[78, 67] Operation: 89-22=67\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4 with lowest heuristic value 29.0\nCurrent State #0,4: 58:[86, 22, 81]. Operations so far : ['89-8=81'].\n\nThought : Expand Node #0,4’s 1st child to build next frontier.\nAction : Exploring operation 81-22=59. \nResulting numbers: [86, 59].\nHeuristic score : (|86-58| + |59-58|)/2 = (28 + 1)/2 = 14.50\nGenerated Node #0,4,0: 58:[86, 59] Operation: 81-22=59\n\nThought : Expand Node #0,4’s 2nd child to build next frontier.\nAction : Exploring operation 86+22=108. \nResulting numbers: [81, 108].\nHeuristic score : (|81-58| + |108-58|)/2 = (23 + 50)/2 = 36.50\nGenerated Node #0,4,1: 58:[81, 108] Operation: 86+22=108\n\nThought : Expand Node #0,4’s 3rd child to build next frontier.\nAction : Exploring operation 22+81=103. \nResulting numbers: [86, 103].\nHeuristic score : (|86-58| + |103-58|)/2 = (28 + 45)/2 = 36.50\nGenerated Node #0,4,2: 58:[86, 103] Operation: 22+81=103\n\nThought : Expand Node #0,4’s 4th child to build next frontier.\nAction : Exploring operation 86-22=64. \nResulting numbers: [81, 64].\nHeuristic score : (|81-58| + |64-58|)/2 = (23 + 6)/2 = 14.50\nGenerated Node #0,4,3: 58:[81, 64] Operation: 86-22=64\n\nThought : Expand Node #0,4’s 5th child to build next frontier.\nAction : Exploring operation 86-81=5. \nResulting numbers: [22, 5].\nHeuristic score : (|22-58| + |5-58|)/2 = (36 + 53)/2 = 44.50\nGenerated Node #0,4,4: 58:[22, 5] Operation: 86-81=5\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1 with lowest heuristic value 29.0\nCurrent State #0,1: 58:[86, 89, 30]. Operations so far : ['8+22=30'].\n\nThought : Expand Node #0,1’s 1st child to build next frontier.\nAction : Exploring operation 89-30=59. \nResulting numbers: [86, 59].\nHeuristic score : (|86-58| + |59-58|)/2 = (28 + 1)/2 = 14.50\nGenerated Node #0,1,0: 58:[86, 59] Operation: 89-30=59\n\nThought : Expand Node #0,1’s 2nd child to build next frontier.\nAction : Exploring operation 86-30=56. \nResulting numbers: [89, 56].\nHeuristic score : (|89-58| + |56-58|)/2 = (31 + 2)/2 = 16.50\nGenerated Node #0,1,1: 58:[89, 56] Operation: 86-30=56\n\nThought : Expand Node #0,1’s 3rd child to build next frontier.\nAction : Exploring operation 86+30=116. \nResulting numbers: [89, 116].\nHeuristic score : (|89-58| + |116-58|)/2 = (31 + 58)/2 = 44.50\nGenerated Node #0,1,2: 58:[89, 116] Operation: 86+30=116\n\nThought : Expand Node #0,1’s 4th child to build next frontier.\nAction : Exploring operation 89-86=3. \nResulting numbers: [30, 3].\nHeuristic score : (|30-58| + |3-58|)/2 = (28 + 55)/2 = 41.50\nGenerated Node #0,1,3: 58:[30, 3] Operation: 89-86=3\n\nThought : Expand Node #0,1’s 5th child to build next frontier.\nAction : Exploring operation 89+30=119. \nResulting numbers: [86, 119].\nHeuristic score : (|86-58| + |119-58|)/2 = (28 + 61)/2 = 44.50\nGenerated Node #0,1,4: 58:[86, 119] Operation: 89+30=119\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3 with lowest heuristic value 29.0\nCurrent State #0,3: 58:[8, 89, 64]. Operations so far : ['86-22=64'].\n\nThought : Expand Node #0,3’s 1st child to build next frontier.\nAction : Exploring operation 64-8=56. \nResulting numbers: [89, 56].\nHeuristic score : (|89-58| + |56-58|)/2 = (31 + 2)/2 = 16.50\nGenerated Node #0,3,0: 58:[89, 56] Operation: 64-8=56\n\nThought : Expand Node #0,3’s 2nd child to build next frontier.\nAction : Exploring operation 8+89=97. \nResulting numbers: [64, 97].\nHeuristic score : (|64-58| + |97-58|)/2 = (6 + 39)/2 = 22.50\nGenerated Node #0,3,1: 58:[64, 97] Operation: 8+89=97\n\nThought : Expand Node #0,3’s 3rd child to build next frontier.\nAction : Exploring operation 89-8=81. \nResulting numbers: [64, 81].\nHeuristic score : (|64-58| + |81-58|)/2 = (6 + 23)/2 = 14.50\nGenerated Node #0,3,2: 58:[64, 81] Operation: 89-8=81\n\nThought : Expand Node #0,3’s 4th child to build next frontier.\nAction : Exploring operation 8+64=72. \nResulting numbers: [89, 72].\nHeuristic score : (|89-58| + |72-58|)/2 = (31 + 14)/2 = 22.50\nGenerated Node #0,3,3: 58:[89, 72] Operation: 8+64=72\n\nThought : Expand Node #0,3’s 5th child to build next frontier.\nAction : Exploring operation 64/8=8. \nResulting numbers: [89, 8].\nHeuristic score : (|89-58| + |8-58|)/2 = (31 + 50)/2 = 40.50\nGenerated Node #0,3,4: 58:[89, 8] Operation: 64/8=8\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0,3 with lowest heuristic value 14.5\nCurrent State #0,0,3: 58:[67, 78]. Operations so far : ['89-22=67', '86-8=78'].\n\nThought : Expand Node #0,0,3’s 1st child to build next frontier.\nAction : Exploring operation 67+78=145. \nResulting numbers: [145].\n145,58 unequal: No Solution\n\nThought : Expand Node #0,0,3’s 2nd child to build next frontier.\nAction : Exploring operation 67*78=5226. \nResulting numbers: [5226].\n5226,58 unequal: No Solution\n\nThought : Expand Node #0,0,3’s 3rd child to build next frontier.\nAction : Exploring operation 78-67=11. \nResulting numbers: [11].\n11,58 unequal: No solution after expanding all children at current level ... backtracking \n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2,4 with lowest heuristic value 14.5\nCurrent State #0,2,4: 58:[78, 67]. Operations so far : ['86-8=78', '89-22=67'].\n\nThought : Expand Node #0,2,4’s 1st child to build next frontier.\nAction : Exploring operation 78-67=11. \nResulting numbers: [11].\n11,58 unequal: No Solution\n\nThought : Expand Node #0,2,4’s 2nd child to build next frontier.\nAction : Exploring operation 78*67=5226. \nResulting numbers: [5226].\n5226,58 unequal: No Solution\n\nThought : Expand Node #0,2,4’s 3rd child to build next frontier.\nAction : Exploring operation 78+67=145. \nResulting numbers: [145].\n145,58 unequal: No solution after expanding all children at current level ... backtracking \n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4,3 with lowest heuristic value 14.5\nCurrent State #0,4,3: 58:[81, 64]. Operations so far : ['89-8=81', '86-22=64'].\n\nThought : Expand Node #0,4,3’s 1st child to build next frontier.\nAction : Exploring operation 81+64=145. \nResulting numbers: [145].\n145,58 unequal: No Solution\n\nThought : Expand Node #0,4,3’s 2nd child to build next frontier.\nAction : Exploring operation 81-64=17. \nResulting numbers: [17].\n17,58 unequal: No Solution\n\nThought : Expand Node #0,4,3’s 3rd child to build next frontier.\nAction : Exploring operation 81*64=5184. \nResulting numbers: [5184].\n5184,58 unequal: No solution after expanding all children at current level ... backtracking \n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0,4 with lowest heuristic value 14.5\nCurrent State #0,0,4: 58:[86, 59]. Operations so far : ['89-22=67', '67-8=59'].\n\nThought : Expand Node #0,0,4’s 1st child to build next frontier.\nAction : Exploring operation 86*59=5074. \nResulting numbers: [5074].\n5074,58 unequal: No Solution\n\nThought : Expand Node #0,0,4’s 2nd child to build next frontier.\nAction : Exploring operation 86+59=145. \nResulting numbers: [145].\n145,58 unequal: No Solution\n\nThought : Expand Node #0,0,4’s 3rd child to build next frontier.\nAction : Exploring operation 86-59=27. \nResulting numbers: [27].\n27,58 unequal: No solution after expanding all children at current level ... backtracking \n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4,0 with lowest heuristic value 14.5\nCurrent State #0,4,0: 58:[86, 59]. Operations so far : ['89-8=81', '81-22=59'].\n\nThought : Expand Node #0,4,0’s 1st child to build next frontier.\nAction : Exploring operation 86+59=145. \nResulting numbers: [145].\n145,58 unequal: No Solution\n\nThought : Expand Node #0,4,0’s 2nd child to build next frontier.\nAction : Exploring operation 86*59=5074. \nResulting numbers: [5074].\n5074,58 unequal: No Solution\n\nThought : Expand Node #0,4,0’s 3rd child to build next frontier.\nAction : Exploring operation 86-59=27. \nResulting numbers: [27].\n27,58 unequal: No solution after expanding all children at current level ... backtracking \n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3,2 with lowest heuristic value 14.5\nCurrent State #0,3,2: 58:[64, 81]. Operations so far : ['86-22=64', '89-8=81'].\n\nThought : Expand Node #0,3,2’s 1st child to build next frontier.\nAction : Exploring operation 81-64=17. \nResulting numbers: [17].\n17,58 unequal: No Solution\n\nThought : Expand Node #0,3,2’s 2nd child to build next frontier.\nAction : Exploring operation 64*81=5184. \nResulting numbers: [5184].\n5184,58 unequal: No Solution\n\nThought : Expand Node #0,3,2’s 3rd child to build next frontier.\nAction : Exploring operation 64+81=145. \nResulting numbers: [145].\n145,58 unequal: No solution after expanding all children at current level ... backtracking \n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1,0 with lowest heuristic value 14.5\nCurrent State #0,1,0: 58:[86, 59]. Operations so far : ['8+22=30', '89-30=59'].\n\nThought : Expand Node #0,1,0’s 1st child to build next frontier.\nAction : Exploring operation 86+59=145. \nResulting numbers: [145].\n145,58 unequal: No Solution\n\nThought : Expand Node #0,1,0’s 2nd child to build next frontier.\nAction : Exploring operation 86*59=5074. \nResulting numbers: [5074].\n5074,58 unequal: No Solution\n\nThought : Expand Node #0,1,0’s 3rd child to build next frontier.\nAction : Exploring operation 86-59=27. \nResulting numbers: [27].\n27,58 unequal: No solution after expanding all children at current level ... backtracking \n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2,2 with lowest heuristic value 16.5\nCurrent State #0,2,2: 58:[89, 56]. Operations so far : ['86-8=78', '78-22=56'].\n\nThought : Expand Node #0,2,2’s 1st child to build next frontier.\nAction : Exploring operation 89-56=33. \nResulting numbers: [33].\n33,58 unequal: No Solution\n\nThought : Expand Node #0,2,2’s 2nd child to build next frontier.\nAction : Exploring operation 89+56=145. \nResulting numbers: [145].\n145,58 unequal: No Solution\n\nThought : Expand Node #0,2,2’s 3rd child to build next frontier.\nAction : Exploring operation 89*56=4984. \nResulting numbers: [4984].\n4984,58 unequal: No solution after expanding all children at current level ... backtracking \n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3,0 with lowest heuristic value 16.5\nCurrent State #0,3,0: 58:[89, 56]. Operations so far : ['86-22=64', '64-8=56'].\n\nThought : Expand Node #0,3,0’s 1st child to build next frontier.\nAction : Exploring operation 89*56=4984. \nResulting numbers: [4984].\n4984,58 unequal: No Solution\n\nThought : Expand Node #0,3,0’s 2nd child to build next frontier.\nAction : Exploring operation 89-56=33. \nResulting numbers: [33].\n33,58 unequal: No Solution\n\nThought : Expand Node #0,3,0’s 3rd child to build next frontier.\nAction : Exploring operation 89+56=145. \nResulting numbers: [145].\n145,58 unequal: No solution after expanding all children at current level ... backtracking \n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1,1 with lowest heuristic value 16.5\nCurrent State #0,1,1: 58:[89, 56]. Operations so far : ['8+22=30', '86-30=56'].\n\nThought : Expand Node #0,1,1’s 1st child to build next frontier.\nAction : Exploring operation 89-56=33. \nResulting numbers: [33].\n33,58 unequal: No Solution\n\nThought : Expand Node #0,1,1’s 2nd child to build next frontier.\nAction : Exploring operation 89*56=4984. \nResulting numbers: [4984].\n4984,58 unequal: No Solution\n\nThought : Expand Node #0,1,1’s 3rd child to build next frontier.\nAction : Exploring operation 89+56=145. \nResulting numbers: [145].\n145,58 unequal: No solution after expanding all children at current level ... backtracking \n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0,0 with lowest heuristic value 22.5\nCurrent State #0,0,0: 58:[86, 75]. Operations so far : ['89-22=67', '8+67=75'].\n\nThought : Expand Node #0,0,0’s 1st child to build next frontier.\nAction : Exploring operation 86*75=6450. \nResulting numbers: [6450].\n6450,58 unequal: No Solution\n\nThought : Expand Node #0,0,0’s 2nd child to build next frontier.\nAction : Exploring operation 86+75=161. \nResulting numbers: [161].\n161,58 unequal: No Solution\n\nThought : Expand Node #0,0,0’s 3rd child to build next frontier.\nAction : Exploring operation 86-75=11. \nResulting numbers: [11].\n11,58 unequal: No solution after expanding all children at current level ... backtracking \n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3,3 with lowest heuristic value 22.5\nCurrent State #0,3,3: 58:[89, 72]. Operations so far : ['86-22=64', '8+64=72'].\n\nThought : Expand Node #0,3,3’s 1st child to build next frontier.\nAction : Exploring operation 89*72=6408. \nResulting numbers: [6408].\n6408,58 unequal: No Solution\n\nThought : Expand Node #0,3,3’s 2nd child to build next frontier.\nAction : Exploring operation 89-72=17. \nResulting numbers: [17].\n17,58 unequal: No Solution\n\nThought : Expand Node #0,3,3’s 3rd child to build next frontier.\nAction : Exploring operation 89+72=161. \nResulting numbers: [161].\n161,58 unequal: No solution after expanding all children at current level ... backtracking \n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3,1 with lowest heuristic value 22.5\nCurrent State #0,3,1: 58:[64, 97]. Operations so far : ['86-22=64', '8+89=97'].\n\nThought : Expand Node #0,3,1’s 1st child to build next frontier.\nAction : Exploring operation 64+97=161. \nResulting numbers: [161].\n161,58 unequal: No Solution\n\nThought : Expand Node #0,3,1’s 2nd child to build next frontier.\nAction : Exploring operation 64*97=6208. \nResulting numbers: [6208].\n6208,58 unequal: No Solution\n\nThought : Expand Node #0,3,1’s 3rd child to build next frontier.\nAction : Exploring operation 97-64=33. \nResulting numbers: [33].\n33,58 unequal: No solution after expanding all children at current level ... backtracking \n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0,2 with lowest heuristic value 22.5\nCurrent State #0,0,2: 58:[67, 94]. Operations so far : ['89-22=67', '86+8=94'].\n\nThought : Expand Node #0,0,2’s 1st child to build next frontier.\nAction : Exploring operation 94-67=27. \nResulting numbers: [27].\n27,58 unequal: No Solution\n\nThought : Expand Node #0,0,2’s 2nd child to build next frontier.\nAction : Exploring operation 67+94=161. \nResulting numbers: [161].\n161,58 unequal: No Solution\n\nThought : Expand Node #0,0,2’s 3rd child to build next frontier.\nAction : Exploring operation 67*94=6298. \nResulting numbers: [6298].\n6298,58 unequal: No solution after expanding all children at current level ... backtracking \n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3,0,1 with lowest heuristic value 25\nCurrent State #0,3,0,1: 58:[33]. Operations so far : ['86-22=64', '64-8=56', '89-56=33'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1,1,0 with lowest heuristic value 25\nCurrent State #0,1,1,0: 58:[33]. Operations so far : ['8+22=30', '86-30=56', '89-56=33'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2,2,0 with lowest heuristic value 25\nCurrent State #0,2,2,0: 58:[33]. Operations so far : ['86-8=78', '78-22=56', '89-56=33'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3,1,2 with lowest heuristic value 25\nCurrent State #0,3,1,2: 58:[33]. Operations so far : ['86-22=64', '8+89=97', '97-64=33'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0,4,2 with lowest heuristic value 31\nCurrent State #0,0,4,2: 58:[27]. Operations so far : ['89-22=67', '67-8=59', '86-59=27'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0,2,0 with lowest heuristic value 31\nCurrent State #0,0,2,0: 58:[27]. Operations so far : ['89-22=67', '86+8=94', '94-67=27'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4,0,2 with lowest heuristic value 31\nCurrent State #0,4,0,2: 58:[27]. Operations so far : ['89-8=81', '81-22=59', '86-59=27'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1,0,2 with lowest heuristic value 31\nCurrent State #0,1,0,2: 58:[27]. Operations so far : ['8+22=30', '89-30=59', '86-59=27'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4,2 with lowest heuristic value 36.5\nCurrent State #0,4,2: 58:[86, 103]. Operations so far : ['89-8=81', '22+81=103'].\n\nThought : Expand Node #0,4,2’s 1st child to build next frontier.\nAction : Exploring operation 103-86=17. \nResulting numbers: [17].\n17,58 unequal: No Solution\n\nThought : Expand Node #0,4,2’s 2nd child to build next frontier.\nAction : Exploring operation 86+103=189. \nResulting numbers: [189].\n189,58 unequal: No Solution\n\nThought : Expand Node #0,4,2’s 3rd child to build next frontier.\nAction : Exploring operation 86*103=8858. \nResulting numbers: [8858].\n8858,58 unequal: No solution after expanding all children at current level ... backtracking \n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4,1 with lowest heuristic value 36.5\nCurrent State #0,4,1: 58:[81, 108]. Operations so far : ['89-8=81', '86+22=108'].\n\nThought : Expand Node #0,4,1’s 1st child to build next frontier.\nAction : Exploring operation 108-81=27. \nResulting numbers: [27].\n27,58 unequal: No Solution\n\nThought : Expand Node #0,4,1’s 2nd child to build next frontier.\nAction : Exploring operation 81*108=8748. \nResulting numbers: [8748].\n8748,58 unequal: No Solution\n\nThought : Expand Node #0,4,1’s 3rd child to build next frontier.\nAction : Exploring operation 81+108=189. \nResulting numbers: [189].\n189,58 unequal: No solution after expanding all children at current level ... backtracking \n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2,3 with lowest heuristic value 36.5\nCurrent State #0,2,3: 58:[89, 100]. Operations so far : ['86-8=78', '22+78=100'].\n\nThought : Expand Node #0,2,3’s 1st child to build next frontier.\nAction : Exploring operation 89+100=189. \nResulting numbers: [189].\n189,58 unequal: No Solution\n\nThought : Expand Node #0,2,3’s 2nd child to build next frontier.\nAction : Exploring operation 89*100=8900. \nResulting numbers: [8900].\n8900,58 unequal: No Solution\n\nThought : Expand Node #0,2,3’s 3rd child to build next frontier.\nAction : Exploring operation 100-89=11. \nResulting numbers: [11].\n11,58 unequal: No solution after expanding all children at current level ... backtracking \n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4,1,0 with lowest heuristic value 31\nCurrent State #0,4,1,0: 58:[27]. Operations so far : ['89-8=81', '86+22=108', '108-81=27'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2,0 with lowest heuristic value 36.5\nCurrent State #0,2,0: 58:[78, 111]. Operations so far : ['86-8=78', '22+89=111'].\n\nThought : Expand Node #0,2,0’s 1st child to build next frontier.\nAction : Exploring operation 111-78=33. \nResulting numbers: [33].\n33,58 unequal: No Solution\n\nThought : Expand Node #0,2,0’s 2nd child to build next frontier.\nAction : Exploring operation 78+111=189. \nResulting numbers: [189].\n189,58 unequal: No Solution\n\nThought : Expand Node #0,2,0’s 3rd child to build next frontier.\nAction : Exploring operation 78*111=8658. \nResulting numbers: [8658].\n8658,58 unequal: No solution after expanding all children at current level ... backtracking \n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3,4 with lowest heuristic value 40.5\nCurrent State #0,3,4: 58:[89, 8]. Operations so far : ['86-22=64', '64/8=8'].\n\nThought : Expand Node #0,3,4’s 1st child to build next frontier.\nAction : Exploring operation 89-8=81. \nResulting numbers: [81].\n81,58 unequal: No Solution\n\nThought : Expand Node #0,3,4’s 2nd child to build next frontier.\nAction : Exploring operation 89*8=712. \nResulting numbers: [712].\n712,58 unequal: No Solution\n\nThought : Expand Node #0,3,4’s 3rd child to build next frontier.\nAction : Exploring operation 89+8=97. \nResulting numbers: [97].\n97,58 unequal: No solution after expanding all children at current level ... backtracking \n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3,2,0 with lowest heuristic value 41\nCurrent State #0,3,2,0: 58:[17]. Operations so far : ['86-22=64', '89-8=81', '81-64=17'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4,3,1 with lowest heuristic value 41\nCurrent State #0,4,3,1: 58:[17]. Operations so far : ['89-8=81', '86-22=64', '81-64=17'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3,4,0 with lowest heuristic value 23\nCurrent State #0,3,4,0: 58:[81]. Operations so far : ['86-22=64', '64/8=8', '89-8=81'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2,0,0 with lowest heuristic value 25\nCurrent State #0,2,0,0: 58:[33]. Operations so far : ['86-8=78', '22+89=111', '111-78=33'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3,4,2 with lowest heuristic value 39\nCurrent State #0,3,4,2: 58:[97]. Operations so far : ['86-22=64', '64/8=8', '89+8=97'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3,3,1 with lowest heuristic value 41\nCurrent State #0,3,3,1: 58:[17]. Operations so far : ['86-22=64', '8+64=72', '89-72=17'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4,2,0 with lowest heuristic value 41\nCurrent State #0,4,2,0: 58:[17]. Operations so far : ['89-8=81', '22+81=103', '103-86=17'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2,1 with lowest heuristic value 41.5\nCurrent State #0,2,1: 58:[22, 11]. Operations so far : ['86-8=78', '89-78=11'].\n\nThought : Expand Node #0,2,1’s 1st child to build next frontier.\nAction : Exploring operation 22-11=11. \nResulting numbers: [11].\n11,58 unequal: No Solution\n\nThought : Expand Node #0,2,1’s 2nd child to build next frontier.\nAction : Exploring operation 22*11=242. \nResulting numbers: [242].\n242,58 unequal: No Solution\n\nThought : Expand Node #0,2,1’s 3rd child to build next frontier.\nAction : Exploring operation 22/11=2. \nResulting numbers: [2].\n2,58 unequal: No Solution\n\nThought : Expand Node #0,2,1’s 4th child to build next frontier.\nAction : Exploring operation 22+11=33. \nResulting numbers: [33].\n33,58 unequal: No solution after expanding all children at current level ... backtracking \n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1,3 with lowest heuristic value 41.5\nCurrent State #0,1,3: 58:[30, 3]. Operations so far : ['8+22=30', '89-86=3'].\n\nThought : Expand Node #0,1,3’s 1st child to build next frontier.\nAction : Exploring operation 30-3=27. \nResulting numbers: [27].\n27,58 unequal: No Solution\n\nThought : Expand Node #0,1,3’s 2nd child to build next frontier.\nAction : Exploring operation 30/3=10. \nResulting numbers: [10].\n10,58 unequal: No Solution\n\nThought : Expand Node #0,1,3’s 3rd child to build next frontier.\nAction : Exploring operation 30+3=33. \nResulting numbers: [33].\n33,58 unequal: No Solution\n\nThought : Expand Node #0,1,3’s 4th child to build next frontier.\nAction : Exploring operation 30*3=90. \nResulting numbers: [90].\n90,58 unequal: No solution after expanding all children at current level ... backtracking \n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4,4 with lowest heuristic value 44.5\nCurrent State #0,4,4: 58:[22, 5]. Operations so far : ['89-8=81', '86-81=5'].\n\nThought : Expand Node #0,4,4’s 1st child to build next frontier.\nAction : Exploring operation 22-5=17. \nResulting numbers: [17].\n17,58 unequal: No Solution\n\nThought : Expand Node #0,4,4’s 2nd child to build next frontier.\nAction : Exploring operation 22+5=27. \nResulting numbers: [27].\n27,58 unequal: No Solution\n\nThought : Expand Node #0,4,4’s 3rd child to build next frontier.\nAction : Exploring operation 22*5=110. \nResulting numbers: [110].\n110,58 unequal: No solution after expanding all children at current level ... backtracking \n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1,4 with lowest heuristic value 44.5\nCurrent State #0,1,4: 58:[86, 119]. Operations so far : ['8+22=30', '89+30=119'].\n\nThought : Expand Node #0,1,4’s 1st child to build next frontier.\nAction : Exploring operation 119-86=33. \nResulting numbers: [33].\n33,58 unequal: No Solution\n\nThought : Expand Node #0,1,4’s 2nd child to build next frontier.\nAction : Exploring operation 86*119=10234. \nResulting numbers: [10234].\n10234,58 unequal: No Solution\n\nThought : Expand Node #0,1,4’s 3rd child to build next frontier.\nAction : Exploring operation 86+119=205. \nResulting numbers: [205].\n205,58 unequal: No solution after expanding all children at current level ... backtracking \n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1,2 with lowest heuristic value 44.5\nCurrent State #0,1,2: 58:[89, 116]. Operations so far : ['8+22=30', '86+30=116'].\n\nThought : Expand Node #0,1,2’s 1st child to build next frontier.\nAction : Exploring operation 116-89=27. \nResulting numbers: [27].\n27,58 unequal: No Solution\n\nThought : Expand Node #0,1,2’s 2nd child to build next frontier.\nAction : Exploring operation 89*116=10324. \nResulting numbers: [10324].\n10324,58 unequal: No Solution\n\nThought : Expand Node #0,1,2’s 3rd child to build next frontier.\nAction : Exploring operation 89+116=205. \nResulting numbers: [205].\n205,58 unequal: No solution after expanding all children at current level ... backtracking \n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2,1,3 with lowest heuristic value 25\nCurrent State #0,2,1,3: 58:[33]. Operations so far : ['86-8=78', '89-78=11', '22+11=33'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1,4,0 with lowest heuristic value 25\nCurrent State #0,1,4,0: 58:[33]. Operations so far : ['8+22=30', '89+30=119', '119-86=33'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1,3,2 with lowest heuristic value 25\nCurrent State #0,1,3,2: 58:[33]. Operations so far : ['8+22=30', '89-86=3', '30+3=33'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1,2,0 with lowest heuristic value 31\nCurrent State #0,1,2,0: 58:[27]. Operations so far : ['8+22=30', '86+30=116', '116-89=27'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1,3,0 with lowest heuristic value 31\nCurrent State #0,1,3,0: 58:[27]. Operations so far : ['8+22=30', '89-86=3', '30-3=27'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4,4,1 with lowest heuristic value 31\nCurrent State #0,4,4,1: 58:[27]. Operations so far : ['89-8=81', '86-81=5', '22+5=27'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1,3,3 with lowest heuristic value 32\nCurrent State #0,1,3,3: 58:[90]. Operations so far : ['8+22=30', '89-86=3', '30*3=90'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4,4,0 with lowest heuristic value 41\nCurrent State #0,4,4,0: 58:[17]. Operations so far : ['89-8=81', '86-81=5', '22-5=17'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0,1 with lowest heuristic value 44.5\nCurrent State #0,0,1: 58:[8, 19]. Operations so far : ['89-22=67', '86-67=19'].\n\nThought : Expand Node #0,0,1’s 1st child to build next frontier.\nAction : Exploring operation 19-8=11. \nResulting numbers: [11].\n11,58 unequal: No Solution\n\nThought : Expand Node #0,0,1’s 2nd child to build next frontier.\nAction : Exploring operation 8+19=27. \nResulting numbers: [27].\n27,58 unequal: No Solution\n\nThought : Expand Node #0,0,1’s 3rd child to build next frontier.\nAction : Exploring operation 8*19=152. \nResulting numbers: [152].\n152,58 unequal: No solution after expanding all children at current level ... backtracking \n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2,4,0 with lowest heuristic value 47\nCurrent State #0,2,4,0: 58:[11]. Operations so far : ['86-8=78', '89-22=67', '78-67=11'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0,1,1 with lowest heuristic value 31\nCurrent State #0,0,1,1: 58:[27]. Operations so far : ['89-22=67', '86-67=19', '8+19=27'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2,3,2 with lowest heuristic value 47\nCurrent State #0,2,3,2: 58:[11]. Operations so far : ['86-8=78', '22+78=100', '100-89=11'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0,1,0 with lowest heuristic value 47\nCurrent State #0,0,1,0: 58:[11]. Operations so far : ['89-22=67', '86-67=19', '19-8=11'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0,3,2 with lowest heuristic value 47\nCurrent State #0,0,3,2: 58:[11]. Operations so far : ['89-22=67', '86-8=78', '78-67=11'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2,1,0 with lowest heuristic value 47\nCurrent State #0,2,1,0: 58:[11]. Operations so far : ['86-8=78', '89-78=11', '22-11=11'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0,0,2 with lowest heuristic value 47\nCurrent State #0,0,0,2: 58:[11]. Operations so far : ['89-22=67', '8+67=75', '86-75=11'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1,3,1 with lowest heuristic value 48\nCurrent State #0,1,3,1: 58:[10]. Operations so far : ['8+22=30', '89-86=3', '30/3=10'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4,4,2 with lowest heuristic value 52\nCurrent State #0,4,4,2: 58:[110]. Operations so far : ['89-8=81', '86-81=5', '22*5=110'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2,1,2 with lowest heuristic value 56\nCurrent State #0,2,1,2: 58:[2]. Operations so far : ['86-8=78', '89-78=11', '22/11=2'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4,3,0 with lowest heuristic value 87\nCurrent State #0,4,3,0: 58:[145]. Operations so far : ['89-8=81', '86-22=64', '81+64=145'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0,4,1 with lowest heuristic value 87\nCurrent State #0,0,4,1: 58:[145]. Operations so far : ['89-22=67', '67-8=59', '86+59=145'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2,4,2 with lowest heuristic value 87\nCurrent State #0,2,4,2: 58:[145]. Operations so far : ['86-8=78', '89-22=67', '78+67=145'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4,0,0 with lowest heuristic value 87\nCurrent State #0,4,0,0: 58:[145]. Operations so far : ['89-8=81', '81-22=59', '86+59=145'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0,3,0 with lowest heuristic value 87\nCurrent State #0,0,3,0: 58:[145]. Operations so far : ['89-22=67', '86-8=78', '67+78=145'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3,0,2 with lowest heuristic value 87\nCurrent State #0,3,0,2: 58:[145]. Operations so far : ['86-22=64', '64-8=56', '89+56=145'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2,2,1 with lowest heuristic value 87\nCurrent State #0,2,2,1: 58:[145]. Operations so far : ['86-8=78', '78-22=56', '89+56=145'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1,1,2 with lowest heuristic value 87\nCurrent State #0,1,1,2: 58:[145]. Operations so far : ['8+22=30', '86-30=56', '89+56=145'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1,0,0 with lowest heuristic value 87\nCurrent State #0,1,0,0: 58:[145]. Operations so far : ['8+22=30', '89-30=59', '86+59=145'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3,2,2 with lowest heuristic value 87\nCurrent State #0,3,2,2: 58:[145]. Operations so far : ['86-22=64', '89-8=81', '64+81=145'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0,1,2 with lowest heuristic value 94\nCurrent State #0,0,1,2: 58:[152]. Operations so far : ['89-22=67', '86-67=19', '8*19=152'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3,3,2 with lowest heuristic value 103\nCurrent State #0,3,3,2: 58:[161]. Operations so far : ['86-22=64', '8+64=72', '89+72=161'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0,0,1 with lowest heuristic value 103\nCurrent State #0,0,0,1: 58:[161]. Operations so far : ['89-22=67', '8+67=75', '86+75=161'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3,1,0 with lowest heuristic value 103\nCurrent State #0,3,1,0: 58:[161]. Operations so far : ['86-22=64', '8+89=97', '64+97=161'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0,2,1 with lowest heuristic value 103\nCurrent State #0,0,2,1: 58:[161]. Operations so far : ['89-22=67', '86+8=94', '67+94=161'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2,3,0 with lowest heuristic value 131\nCurrent State #0,2,3,0: 58:[189]. Operations so far : ['86-8=78', '22+78=100', '89+100=189'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4,1,2 with lowest heuristic value 131\nCurrent State #0,4,1,2: 58:[189]. Operations so far : ['89-8=81', '86+22=108', '81+108=189'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4,2,1 with lowest heuristic value 131\nCurrent State #0,4,2,1: 58:[189]. Operations so far : ['89-8=81', '22+81=103', '86+103=189'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2,0,1 with lowest heuristic value 131\nCurrent State #0,2,0,1: 58:[189]. Operations so far : ['86-8=78', '22+89=111', '78+111=189'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1,2,2 with lowest heuristic value 147\nCurrent State #0,1,2,2: 58:[205]. Operations so far : ['8+22=30', '86+30=116', '89+116=205'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1,4,2 with lowest heuristic value 147\nCurrent State #0,1,4,2: 58:[205]. Operations so far : ['8+22=30', '89+30=119', '86+119=205'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2,1,1 with lowest heuristic value 184\nCurrent State #0,2,1,1: 58:[242]. Operations so far : ['86-8=78', '89-78=11', '22*11=242'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3,4,1 with lowest heuristic value 654\nCurrent State #0,3,4,1: 58:[712]. Operations so far : ['86-22=64', '64/8=8', '89*8=712'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1,1,1 with lowest heuristic value 4926\nCurrent State #0,1,1,1: 58:[4984]. Operations so far : ['8+22=30', '86-30=56', '89*56=4984'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2,2,2 with lowest heuristic value 4926\nCurrent State #0,2,2,2: 58:[4984]. Operations so far : ['86-8=78', '78-22=56', '89*56=4984'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3,0,0 with lowest heuristic value 4926\nCurrent State #0,3,0,0: 58:[4984]. Operations so far : ['86-22=64', '64-8=56', '89*56=4984'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4,0,1 with lowest heuristic value 5016\nCurrent State #0,4,0,1: 58:[5074]. Operations so far : ['89-8=81', '81-22=59', '86*59=5074'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1,0,1 with lowest heuristic value 5016\nCurrent State #0,1,0,1: 58:[5074]. Operations so far : ['8+22=30', '89-30=59', '86*59=5074'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0,4,0 with lowest heuristic value 5016\nCurrent State #0,0,4,0: 58:[5074]. Operations so far : ['89-22=67', '67-8=59', '86*59=5074'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4,3,2 with lowest heuristic value 5126\nCurrent State #0,4,3,2: 58:[5184]. Operations so far : ['89-8=81', '86-22=64', '81*64=5184'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3,2,1 with lowest heuristic value 5126\nCurrent State #0,3,2,1: 58:[5184]. Operations so far : ['86-22=64', '89-8=81', '64*81=5184'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2,4,1 with lowest heuristic value 5168\nCurrent State #0,2,4,1: 58:[5226]. Operations so far : ['86-8=78', '89-22=67', '78*67=5226'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0,3,1 with lowest heuristic value 5168\nCurrent State #0,0,3,1: 58:[5226]. Operations so far : ['89-22=67', '86-8=78', '67*78=5226'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3,1,1 with lowest heuristic value 6150\nCurrent State #0,3,1,1: 58:[6208]. Operations so far : ['86-22=64', '8+89=97', '64*97=6208'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0,2,2 with lowest heuristic value 6240\nCurrent State #0,0,2,2: 58:[6298]. Operations so far : ['89-22=67', '86+8=94', '67*94=6298'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3,3,0 with lowest heuristic value 6350\nCurrent State #0,3,3,0: 58:[6408]. Operations so far : ['86-22=64', '8+64=72', '89*72=6408'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0,0,0 with lowest heuristic value 6392\nCurrent State #0,0,0,0: 58:[6450]. Operations so far : ['89-22=67', '8+67=75', '86*75=6450'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2,0,2 with lowest heuristic value 8600\nCurrent State #0,2,0,2: 58:[8658]. Operations so far : ['86-8=78', '22+89=111', '78*111=8658'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4,1,1 with lowest heuristic value 8690\nCurrent State #0,4,1,1: 58:[8748]. Operations so far : ['89-8=81', '86+22=108', '81*108=8748'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4,2,2 with lowest heuristic value 8800\nCurrent State #0,4,2,2: 58:[8858]. Operations so far : ['89-8=81', '22+81=103', '86*103=8858'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2,3,1 with lowest heuristic value 8842\nCurrent State #0,2,3,1: 58:[8900]. Operations so far : ['86-8=78', '22+78=100', '89*100=8900'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1,4,1 with lowest heuristic value 10176\nCurrent State #0,1,4,1: 58:[10234]. Operations so far : ['8+22=30', '89+30=119', '86*119=10234'].\n\nThought : Completed expansion of previous level. Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1,2,1 with lowest heuristic value 10266\nCurrent State #0,1,2,1: 58:[10324]. Operations so far : ['8+22=30', '86+30=116', '89*116=10324'].\n\n```\nSOLUTION: NO\nOPERATIONS: []\nRESULT: None\n```\n",
"role": "assistant"
}
]
| 16,117 |
[
37,
48,
26,
74
]
| 50 | dfs | sum_heuristic | [
{
"content": "Combine these initial numbers [37, 48, 26, 74] using only arithmetic operations (+, -, *, /) to reach the target value 50. All initial numbers must be used exactly once.\nConclude with the final result in EXACTLY this format:\n```\nSOLUTION: YES/NO\nOPERATIONS: list of string of operations performed, each string involving only 1 operation. For example, ['A+B=C','C+D=E'] is allowed, ['A+B+D=E'] is not allowed\nRESULT: final_value\n```\n",
"role": "user"
},
{
"content": "We have these numbers [37, 48, 26, 74]. Our goal is to produce 50. Let's show the search process step by step:\nOne possible strategy is to use a Depth-First Search (DFS) guided by a **sum-based** heuristic, which computes the average of the absolute differences between each number and the target number.\nLower scores indicate that, on average, the numbers are closer to the target, making the state more promising for reaching the target via additive operations.\n\n\nCurrent State #0: 50:[37, 48, 26, 74]. Operations so far : [].\n\nThought : Expand Node #0’s 1st child to build next frontier.\nAction : Exploring operation 74-26=48. \nResulting numbers: [37, 48, 48].\nHeuristic score : (|37-50| + |48-50| + |48-50|)/3 = (13 + 2 + 2)/3 = 5.67\nGenerated Node #0,0: 50:[37, 48, 48] Operation: 74-26=48\n\nThought : Expand Node #0,0’s 1st child to build next frontier.\nAction : Exploring operation 37+48=85. \nResulting numbers: [48, 85].\nHeuristic score : (|48-50| + |85-50|)/2 = (2 + 35)/2 = 18.50\nGenerated Node #0,0,0: 50:[48, 85] Operation: 37+48=85\n\nThought : Expand Node #0,0,0’s 1st child to build next frontier.\nAction : Exploring operation 85-48=37. \nResulting numbers: [37].\n37,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 5.666666666666667\nCurrent State #0,0: 50:[37, 48, 48]. Operations so far : ['74-26=48'].\n\nThought : Expand Node #0,0’s 2nd child to build next frontier.\nAction : Exploring operation 37+48=85. \nResulting numbers: [48, 85].\nHeuristic score : (|48-50| + |85-50|)/2 = (2 + 35)/2 = 18.50\nGenerated Node #0,0,1: 50:[48, 85] Operation: 37+48=85\n\nThought : Expand Node #0,0,1’s 1st child to build next frontier.\nAction : Exploring operation 85-48=37. \nResulting numbers: [37].\n37,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 5.666666666666667\nCurrent State #0,0: 50:[37, 48, 48]. Operations so far : ['74-26=48'].\n\nThought : Expand Node #0,0’s 3rd child to build next frontier.\nAction : Exploring operation 48-37=11. \nResulting numbers: [48, 11].\nHeuristic score : (|48-50| + |11-50|)/2 = (2 + 39)/2 = 20.50\nGenerated Node #0,0,2: 50:[48, 11] Operation: 48-37=11\n\nThought : Expand Node #0,0,2’s 1st child to build next frontier.\nAction : Exploring operation 48+11=59. \nResulting numbers: [59].\n59,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 5.666666666666667\nCurrent State #0,0: 50:[37, 48, 48]. Operations so far : ['74-26=48'].\n\nThought : Expand Node #0,0’s 4th child to build next frontier.\nAction : Exploring operation 48-37=11. \nResulting numbers: [48, 11].\nHeuristic score : (|48-50| + |11-50|)/2 = (2 + 39)/2 = 20.50\nGenerated Node #0,0,3: 50:[48, 11] Operation: 48-37=11\n\nThought : Expand Node #0,0,3’s 1st child to build next frontier.\nAction : Exploring operation 48+11=59. \nResulting numbers: [59].\n59,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 5.666666666666667\nCurrent State #0,0: 50:[37, 48, 48]. Operations so far : ['74-26=48'].\n\nThought : Expand Node #0,0’s 5th child to build next frontier.\nAction : Exploring operation 48+48=96. \nResulting numbers: [37, 96].\nHeuristic score : (|37-50| + |96-50|)/2 = (13 + 46)/2 = 29.50\nGenerated Node #0,0,4: 50:[37, 96] Operation: 48+48=96\n\nThought : Expand Node #0,0,4’s 1st child to build next frontier.\nAction : Exploring operation 96-37=59. \nResulting numbers: [59].\n59,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 5.666666666666667\nCurrent State #0,0: 50:[37, 48, 48]. Operations so far : ['74-26=48'].\n\nThought : Expand Node #0,0’s 6th child to build next frontier.\nAction : Exploring operation 48/48=1. \nResulting numbers: [37, 1].\nHeuristic score : (|37-50| + |1-50|)/2 = (13 + 49)/2 = 31.00\nGenerated Node #0,0,5: 50:[37, 1] Operation: 48/48=1\n\nThought : Expand Node #0,0,5’s 1st child to build next frontier.\nAction : Exploring operation 37+1=38. \nResulting numbers: [38].\n38,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 5.666666666666667\nCurrent State #0,0: 50:[37, 48, 48]. Operations so far : ['74-26=48'].\n\nThought : Expand Node #0,0’s 7th child to build next frontier.\nAction : Exploring operation 48-48=0. \nResulting numbers: [37, 0].\nHeuristic score : (|37-50| + |0-50|)/2 = (13 + 50)/2 = 31.50\nGenerated Node #0,0,6: 50:[37, 0] Operation: 48-48=0\n\nThought : Expand Node #0,0,6’s 1st child to build next frontier.\nAction : Exploring operation 37+0=37. \nResulting numbers: [37].\n37,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 5.666666666666667\nCurrent State #0,0: 50:[37, 48, 48]. Operations so far : ['74-26=48'].\n\nThought : Expand Node #0,0’s 8th child to build next frontier.\nAction : Exploring operation 37*48=1776. \nResulting numbers: [48, 1776].\nHeuristic score : (|48-50| + |1776-50|)/2 = (2 + 1726)/2 = 864.00\nGenerated Node #0,0,7: 50:[48, 1776] Operation: 37*48=1776\n\nThought : Expand Node #0,0,7’s 1st child to build next frontier.\nAction : Exploring operation 1776/48=37. \nResulting numbers: [37].\n37,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 5.666666666666667\nCurrent State #0,0: 50:[37, 48, 48]. Operations so far : ['74-26=48'].\n\nThought : Expand Node #0,0’s 9th child to build next frontier.\nAction : Exploring operation 37*48=1776. \nResulting numbers: [48, 1776].\nHeuristic score : (|48-50| + |1776-50|)/2 = (2 + 1726)/2 = 864.00\nGenerated Node #0,0,8: 50:[48, 1776] Operation: 37*48=1776\n\nThought : Expand Node #0,0,8’s 1st child to build next frontier.\nAction : Exploring operation 1776/48=37. \nResulting numbers: [37].\n37,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 5.666666666666667\nCurrent State #0,0: 50:[37, 48, 48]. Operations so far : ['74-26=48'].\n\nThought : Expand Node #0,0’s 10th child to build next frontier.\nAction : Exploring operation 48*48=2304. \nResulting numbers: [37, 2304].\nHeuristic score : (|37-50| + |2304-50|)/2 = (13 + 2254)/2 = 1133.50\nGenerated Node #0,0,9: 50:[37, 2304] Operation: 48*48=2304\n\nThought : Expand Node #0,0,9’s 1st child to build next frontier.\nAction : Exploring operation 2304-37=2267. \nResulting numbers: [2267].\n2267,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0 with lowest heuristic value 15.75\nCurrent State #0: 50:[37, 48, 26, 74]. Operations so far : [].\n\nThought : Expand Node #0’s 2nd child to build next frontier.\nAction : Exploring operation 37+26=63. \nResulting numbers: [48, 74, 63].\nHeuristic score : (|48-50| + |74-50| + |63-50|)/3 = (2 + 24 + 13)/3 = 13.00\nGenerated Node #0,1: 50:[48, 74, 63] Operation: 37+26=63\n\nThought : Expand Node #0,1’s 1st child to build next frontier.\nAction : Exploring operation 74-48=26. \nResulting numbers: [63, 26].\nHeuristic score : (|63-50| + |26-50|)/2 = (13 + 24)/2 = 18.50\nGenerated Node #0,1,0: 50:[63, 26] Operation: 74-48=26\n\nThought : Expand Node #0,1,0’s 1st child to build next frontier.\nAction : Exploring operation 63-26=37. \nResulting numbers: [37].\n37,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1 with lowest heuristic value 13.0\nCurrent State #0,1: 50:[48, 74, 63]. Operations so far : ['37+26=63'].\n\nThought : Expand Node #0,1’s 2nd child to build next frontier.\nAction : Exploring operation 74-63=11. \nResulting numbers: [48, 11].\nHeuristic score : (|48-50| + |11-50|)/2 = (2 + 39)/2 = 20.50\nGenerated Node #0,1,1: 50:[48, 11] Operation: 74-63=11\n\nThought : Expand Node #0,1,1’s 1st child to build next frontier.\nAction : Exploring operation 48+11=59. \nResulting numbers: [59].\n59,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1 with lowest heuristic value 13.0\nCurrent State #0,1: 50:[48, 74, 63]. Operations so far : ['37+26=63'].\n\nThought : Expand Node #0,1’s 3rd child to build next frontier.\nAction : Exploring operation 63-48=15. \nResulting numbers: [74, 15].\nHeuristic score : (|74-50| + |15-50|)/2 = (24 + 35)/2 = 29.50\nGenerated Node #0,1,2: 50:[74, 15] Operation: 63-48=15\n\nThought : Expand Node #0,1,2’s 1st child to build next frontier.\nAction : Exploring operation 74-15=59. \nResulting numbers: [59].\n59,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1 with lowest heuristic value 13.0\nCurrent State #0,1: 50:[48, 74, 63]. Operations so far : ['37+26=63'].\n\nThought : Expand Node #0,1’s 4th child to build next frontier.\nAction : Exploring operation 48+74=122. \nResulting numbers: [63, 122].\nHeuristic score : (|63-50| + |122-50|)/2 = (13 + 72)/2 = 42.50\nGenerated Node #0,1,3: 50:[63, 122] Operation: 48+74=122\n\nThought : Expand Node #0,1,3’s 1st child to build next frontier.\nAction : Exploring operation 122-63=59. \nResulting numbers: [59].\n59,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1 with lowest heuristic value 13.0\nCurrent State #0,1: 50:[48, 74, 63]. Operations so far : ['37+26=63'].\n\nThought : Expand Node #0,1’s 5th child to build next frontier.\nAction : Exploring operation 48+63=111. \nResulting numbers: [74, 111].\nHeuristic score : (|74-50| + |111-50|)/2 = (24 + 61)/2 = 42.50\nGenerated Node #0,1,4: 50:[74, 111] Operation: 48+63=111\n\nThought : Expand Node #0,1,4’s 1st child to build next frontier.\nAction : Exploring operation 111-74=37. \nResulting numbers: [37].\n37,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1 with lowest heuristic value 13.0\nCurrent State #0,1: 50:[48, 74, 63]. Operations so far : ['37+26=63'].\n\nThought : Expand Node #0,1’s 6th child to build next frontier.\nAction : Exploring operation 74+63=137. \nResulting numbers: [48, 137].\nHeuristic score : (|48-50| + |137-50|)/2 = (2 + 87)/2 = 44.50\nGenerated Node #0,1,5: 50:[48, 137] Operation: 74+63=137\n\nThought : Expand Node #0,1,5’s 1st child to build next frontier.\nAction : Exploring operation 137-48=89. \nResulting numbers: [89].\n89,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1 with lowest heuristic value 13.0\nCurrent State #0,1: 50:[48, 74, 63]. Operations so far : ['37+26=63'].\n\nThought : Expand Node #0,1’s 7th child to build next frontier.\nAction : Exploring operation 48*63=3024. \nResulting numbers: [74, 3024].\nHeuristic score : (|74-50| + |3024-50|)/2 = (24 + 2974)/2 = 1499.00\nGenerated Node #0,1,6: 50:[74, 3024] Operation: 48*63=3024\n\nThought : Expand Node #0,1,6’s 1st child to build next frontier.\nAction : Exploring operation 3024-74=2950. \nResulting numbers: [2950].\n2950,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1 with lowest heuristic value 13.0\nCurrent State #0,1: 50:[48, 74, 63]. Operations so far : ['37+26=63'].\n\nThought : Expand Node #0,1’s 8th child to build next frontier.\nAction : Exploring operation 48*74=3552. \nResulting numbers: [63, 3552].\nHeuristic score : (|63-50| + |3552-50|)/2 = (13 + 3502)/2 = 1757.50\nGenerated Node #0,1,7: 50:[63, 3552] Operation: 48*74=3552\n\nThought : Expand Node #0,1,7’s 1st child to build next frontier.\nAction : Exploring operation 3552-63=3489. \nResulting numbers: [3489].\n3489,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1 with lowest heuristic value 13.0\nCurrent State #0,1: 50:[48, 74, 63]. Operations so far : ['37+26=63'].\n\nThought : Expand Node #0,1’s 9th child to build next frontier.\nAction : Exploring operation 74*63=4662. \nResulting numbers: [48, 4662].\nHeuristic score : (|48-50| + |4662-50|)/2 = (2 + 4612)/2 = 2307.00\nGenerated Node #0,1,8: 50:[48, 4662] Operation: 74*63=4662\n\nThought : Expand Node #0,1,8’s 1st child to build next frontier.\nAction : Exploring operation 4662-48=4614. \nResulting numbers: [4614].\n4614,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0 with lowest heuristic value 15.75\nCurrent State #0: 50:[37, 48, 26, 74]. Operations so far : [].\n\nThought : Expand Node #0’s 3rd child to build next frontier.\nAction : Exploring operation 74-37=37. \nResulting numbers: [48, 26, 37].\nHeuristic score : (|48-50| + |26-50| + |37-50|)/3 = (2 + 24 + 13)/3 = 13.00\nGenerated Node #0,2: 50:[48, 26, 37] Operation: 74-37=37\n\nThought : Expand Node #0,2’s 1st child to build next frontier.\nAction : Exploring operation 26+37=63. \nResulting numbers: [48, 63].\nHeuristic score : (|48-50| + |63-50|)/2 = (2 + 13)/2 = 7.50\nGenerated Node #0,2,0: 50:[48, 63] Operation: 26+37=63\n\nThought : Expand Node #0,2,0’s 1st child to build next frontier.\nAction : Exploring operation 63-48=15. \nResulting numbers: [15].\n15,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2 with lowest heuristic value 13.0\nCurrent State #0,2: 50:[48, 26, 37]. Operations so far : ['74-37=37'].\n\nThought : Expand Node #0,2’s 2nd child to build next frontier.\nAction : Exploring operation 48+26=74. \nResulting numbers: [37, 74].\nHeuristic score : (|37-50| + |74-50|)/2 = (13 + 24)/2 = 18.50\nGenerated Node #0,2,1: 50:[37, 74] Operation: 48+26=74\n\nThought : Expand Node #0,2,1’s 1st child to build next frontier.\nAction : Exploring operation 74-37=37. \nResulting numbers: [37].\n37,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2 with lowest heuristic value 13.0\nCurrent State #0,2: 50:[48, 26, 37]. Operations so far : ['74-37=37'].\n\nThought : Expand Node #0,2’s 3rd child to build next frontier.\nAction : Exploring operation 48-26=22. \nResulting numbers: [37, 22].\nHeuristic score : (|37-50| + |22-50|)/2 = (13 + 28)/2 = 20.50\nGenerated Node #0,2,2: 50:[37, 22] Operation: 48-26=22\n\nThought : Expand Node #0,2,2’s 1st child to build next frontier.\nAction : Exploring operation 37+22=59. \nResulting numbers: [59].\n59,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2 with lowest heuristic value 13.0\nCurrent State #0,2: 50:[48, 26, 37]. Operations so far : ['74-37=37'].\n\nThought : Expand Node #0,2’s 4th child to build next frontier.\nAction : Exploring operation 37-26=11. \nResulting numbers: [48, 11].\nHeuristic score : (|48-50| + |11-50|)/2 = (2 + 39)/2 = 20.50\nGenerated Node #0,2,3: 50:[48, 11] Operation: 37-26=11\n\nThought : Expand Node #0,2,3’s 1st child to build next frontier.\nAction : Exploring operation 48+11=59. \nResulting numbers: [59].\n59,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2 with lowest heuristic value 13.0\nCurrent State #0,2: 50:[48, 26, 37]. Operations so far : ['74-37=37'].\n\nThought : Expand Node #0,2’s 5th child to build next frontier.\nAction : Exploring operation 48+37=85. \nResulting numbers: [26, 85].\nHeuristic score : (|26-50| + |85-50|)/2 = (24 + 35)/2 = 29.50\nGenerated Node #0,2,4: 50:[26, 85] Operation: 48+37=85\n\nThought : Expand Node #0,2,4’s 1st child to build next frontier.\nAction : Exploring operation 85-26=59. \nResulting numbers: [59].\n59,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2 with lowest heuristic value 13.0\nCurrent State #0,2: 50:[48, 26, 37]. Operations so far : ['74-37=37'].\n\nThought : Expand Node #0,2’s 6th child to build next frontier.\nAction : Exploring operation 48-37=11. \nResulting numbers: [26, 11].\nHeuristic score : (|26-50| + |11-50|)/2 = (24 + 39)/2 = 31.50\nGenerated Node #0,2,5: 50:[26, 11] Operation: 48-37=11\n\nThought : Expand Node #0,2,5’s 1st child to build next frontier.\nAction : Exploring operation 26+11=37. \nResulting numbers: [37].\n37,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2 with lowest heuristic value 13.0\nCurrent State #0,2: 50:[48, 26, 37]. Operations so far : ['74-37=37'].\n\nThought : Expand Node #0,2’s 7th child to build next frontier.\nAction : Exploring operation 26*37=962. \nResulting numbers: [48, 962].\nHeuristic score : (|48-50| + |962-50|)/2 = (2 + 912)/2 = 457.00\nGenerated Node #0,2,6: 50:[48, 962] Operation: 26*37=962\n\nThought : Expand Node #0,2,6’s 1st child to build next frontier.\nAction : Exploring operation 962-48=914. \nResulting numbers: [914].\n914,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2 with lowest heuristic value 13.0\nCurrent State #0,2: 50:[48, 26, 37]. Operations so far : ['74-37=37'].\n\nThought : Expand Node #0,2’s 8th child to build next frontier.\nAction : Exploring operation 48*26=1248. \nResulting numbers: [37, 1248].\nHeuristic score : (|37-50| + |1248-50|)/2 = (13 + 1198)/2 = 605.50\nGenerated Node #0,2,7: 50:[37, 1248] Operation: 48*26=1248\n\nThought : Expand Node #0,2,7’s 1st child to build next frontier.\nAction : Exploring operation 1248-37=1211. \nResulting numbers: [1211].\n1211,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2 with lowest heuristic value 13.0\nCurrent State #0,2: 50:[48, 26, 37]. Operations so far : ['74-37=37'].\n\nThought : Expand Node #0,2’s 9th child to build next frontier.\nAction : Exploring operation 48*37=1776. \nResulting numbers: [26, 1776].\nHeuristic score : (|26-50| + |1776-50|)/2 = (24 + 1726)/2 = 875.00\nGenerated Node #0,2,8: 50:[26, 1776] Operation: 48*37=1776\n\nThought : Expand Node #0,2,8’s 1st child to build next frontier.\nAction : Exploring operation 1776-26=1750. \nResulting numbers: [1750].\n1750,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0 with lowest heuristic value 15.75\nCurrent State #0: 50:[37, 48, 26, 74]. Operations so far : [].\n\nThought : Expand Node #0’s 4th child to build next frontier.\nAction : Exploring operation 48+26=74. \nResulting numbers: [37, 74, 74].\nHeuristic score : (|37-50| + |74-50| + |74-50|)/3 = (13 + 24 + 24)/3 = 20.33\nGenerated Node #0,3: 50:[37, 74, 74] Operation: 48+26=74\n\nThought : Expand Node #0,3’s 1st child to build next frontier.\nAction : Exploring operation 74-37=37. \nResulting numbers: [74, 37].\nHeuristic score : (|74-50| + |37-50|)/2 = (24 + 13)/2 = 18.50\nGenerated Node #0,3,0: 50:[74, 37] Operation: 74-37=37\n\nThought : Expand Node #0,3,0’s 1st child to build next frontier.\nAction : Exploring operation 74-37=37. \nResulting numbers: [37].\n37,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3 with lowest heuristic value 20.333333333333332\nCurrent State #0,3: 50:[37, 74, 74]. Operations so far : ['48+26=74'].\n\nThought : Expand Node #0,3’s 2nd child to build next frontier.\nAction : Exploring operation 74-37=37. \nResulting numbers: [74, 37].\nHeuristic score : (|74-50| + |37-50|)/2 = (24 + 13)/2 = 18.50\nGenerated Node #0,3,1: 50:[74, 37] Operation: 74-37=37\n\nThought : Expand Node #0,3,1’s 1st child to build next frontier.\nAction : Exploring operation 74-37=37. \nResulting numbers: [37].\n37,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3 with lowest heuristic value 20.333333333333332\nCurrent State #0,3: 50:[37, 74, 74]. Operations so far : ['48+26=74'].\n\nThought : Expand Node #0,3’s 3rd child to build next frontier.\nAction : Exploring operation 74/74=1. \nResulting numbers: [37, 1].\nHeuristic score : (|37-50| + |1-50|)/2 = (13 + 49)/2 = 31.00\nGenerated Node #0,3,2: 50:[37, 1] Operation: 74/74=1\n\nThought : Expand Node #0,3,2’s 1st child to build next frontier.\nAction : Exploring operation 37+1=38. \nResulting numbers: [38].\n38,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3 with lowest heuristic value 20.333333333333332\nCurrent State #0,3: 50:[37, 74, 74]. Operations so far : ['48+26=74'].\n\nThought : Expand Node #0,3’s 4th child to build next frontier.\nAction : Exploring operation 74-74=0. \nResulting numbers: [37, 0].\nHeuristic score : (|37-50| + |0-50|)/2 = (13 + 50)/2 = 31.50\nGenerated Node #0,3,3: 50:[37, 0] Operation: 74-74=0\n\nThought : Expand Node #0,3,3’s 1st child to build next frontier.\nAction : Exploring operation 37+0=37. \nResulting numbers: [37].\n37,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3 with lowest heuristic value 20.333333333333332\nCurrent State #0,3: 50:[37, 74, 74]. Operations so far : ['48+26=74'].\n\nThought : Expand Node #0,3’s 5th child to build next frontier.\nAction : Exploring operation 74/37=2. \nResulting numbers: [74, 2].\nHeuristic score : (|74-50| + |2-50|)/2 = (24 + 48)/2 = 36.00\nGenerated Node #0,3,4: 50:[74, 2] Operation: 74/37=2\n\nThought : Expand Node #0,3,4’s 1st child to build next frontier.\nAction : Exploring operation 74/2=37. \nResulting numbers: [37].\n37,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3 with lowest heuristic value 20.333333333333332\nCurrent State #0,3: 50:[37, 74, 74]. Operations so far : ['48+26=74'].\n\nThought : Expand Node #0,3’s 6th child to build next frontier.\nAction : Exploring operation 74/37=2. \nResulting numbers: [74, 2].\nHeuristic score : (|74-50| + |2-50|)/2 = (24 + 48)/2 = 36.00\nGenerated Node #0,3,5: 50:[74, 2] Operation: 74/37=2\n\nThought : Expand Node #0,3,5’s 1st child to build next frontier.\nAction : Exploring operation 74/2=37. \nResulting numbers: [37].\n37,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3 with lowest heuristic value 20.333333333333332\nCurrent State #0,3: 50:[37, 74, 74]. Operations so far : ['48+26=74'].\n\nThought : Expand Node #0,3’s 7th child to build next frontier.\nAction : Exploring operation 37+74=111. \nResulting numbers: [74, 111].\nHeuristic score : (|74-50| + |111-50|)/2 = (24 + 61)/2 = 42.50\nGenerated Node #0,3,6: 50:[74, 111] Operation: 37+74=111\n\nThought : Expand Node #0,3,6’s 1st child to build next frontier.\nAction : Exploring operation 111-74=37. \nResulting numbers: [37].\n37,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3 with lowest heuristic value 20.333333333333332\nCurrent State #0,3: 50:[37, 74, 74]. Operations so far : ['48+26=74'].\n\nThought : Expand Node #0,3’s 8th child to build next frontier.\nAction : Exploring operation 37+74=111. \nResulting numbers: [74, 111].\nHeuristic score : (|74-50| + |111-50|)/2 = (24 + 61)/2 = 42.50\nGenerated Node #0,3,7: 50:[74, 111] Operation: 37+74=111\n\nThought : Expand Node #0,3,7’s 1st child to build next frontier.\nAction : Exploring operation 111-74=37. \nResulting numbers: [37].\n37,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3 with lowest heuristic value 20.333333333333332\nCurrent State #0,3: 50:[37, 74, 74]. Operations so far : ['48+26=74'].\n\nThought : Expand Node #0,3’s 9th child to build next frontier.\nAction : Exploring operation 74+74=148. \nResulting numbers: [37, 148].\nHeuristic score : (|37-50| + |148-50|)/2 = (13 + 98)/2 = 55.50\nGenerated Node #0,3,8: 50:[37, 148] Operation: 74+74=148\n\nThought : Expand Node #0,3,8’s 1st child to build next frontier.\nAction : Exploring operation 148/37=4. \nResulting numbers: [4].\n4,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3 with lowest heuristic value 20.333333333333332\nCurrent State #0,3: 50:[37, 74, 74]. Operations so far : ['48+26=74'].\n\nThought : Expand Node #0,3’s 10th child to build next frontier.\nAction : Exploring operation 37*74=2738. \nResulting numbers: [74, 2738].\nHeuristic score : (|74-50| + |2738-50|)/2 = (24 + 2688)/2 = 1356.00\nGenerated Node #0,3,9: 50:[74, 2738] Operation: 37*74=2738\n\nThought : Expand Node #0,3,9’s 1st child to build next frontier.\nAction : Exploring operation 2738/74=37. \nResulting numbers: [37].\n37,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3 with lowest heuristic value 20.333333333333332\nCurrent State #0,3: 50:[37, 74, 74]. Operations so far : ['48+26=74'].\n\nThought : Expand Node #0,3’s 11th child to build next frontier.\nAction : Exploring operation 37*74=2738. \nResulting numbers: [74, 2738].\nHeuristic score : (|74-50| + |2738-50|)/2 = (24 + 2688)/2 = 1356.00\nGenerated Node #0,3,10: 50:[74, 2738] Operation: 37*74=2738\n\nThought : Expand Node #0,3,10’s 1st child to build next frontier.\nAction : Exploring operation 2738/74=37. \nResulting numbers: [37].\n37,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3 with lowest heuristic value 20.333333333333332\nCurrent State #0,3: 50:[37, 74, 74]. Operations so far : ['48+26=74'].\n\nThought : Expand Node #0,3’s 12th child to build next frontier.\nAction : Exploring operation 74*74=5476. \nResulting numbers: [37, 5476].\nHeuristic score : (|37-50| + |5476-50|)/2 = (13 + 5426)/2 = 2719.50\nGenerated Node #0,3,11: 50:[37, 5476] Operation: 74*74=5476\n\nThought : Expand Node #0,3,11’s 1st child to build next frontier.\nAction : Exploring operation 5476/37=148. \nResulting numbers: [148].\n148,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0 with lowest heuristic value 15.75\nCurrent State #0: 50:[37, 48, 26, 74]. Operations so far : [].\n\nThought : Expand Node #0’s 5th child to build next frontier.\nAction : Exploring operation 74-48=26. \nResulting numbers: [37, 26, 26].\nHeuristic score : (|37-50| + |26-50| + |26-50|)/3 = (13 + 24 + 24)/3 = 20.33\nGenerated Node #0,4: 50:[37, 26, 26] Operation: 74-48=26\n\nThought : Expand Node #0,4’s 1st child to build next frontier.\nAction : Exploring operation 26+26=52. \nResulting numbers: [37, 52].\nHeuristic score : (|37-50| + |52-50|)/2 = (13 + 2)/2 = 7.50\nGenerated Node #0,4,0: 50:[37, 52] Operation: 26+26=52\n\nThought : Expand Node #0,4,0’s 1st child to build next frontier.\nAction : Exploring operation 52-37=15. \nResulting numbers: [15].\n15,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4 with lowest heuristic value 20.333333333333332\nCurrent State #0,4: 50:[37, 26, 26]. Operations so far : ['74-48=26'].\n\nThought : Expand Node #0,4’s 2nd child to build next frontier.\nAction : Exploring operation 37+26=63. \nResulting numbers: [26, 63].\nHeuristic score : (|26-50| + |63-50|)/2 = (24 + 13)/2 = 18.50\nGenerated Node #0,4,1: 50:[26, 63] Operation: 37+26=63\n\nThought : Expand Node #0,4,1’s 1st child to build next frontier.\nAction : Exploring operation 63-26=37. \nResulting numbers: [37].\n37,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4 with lowest heuristic value 20.333333333333332\nCurrent State #0,4: 50:[37, 26, 26]. Operations so far : ['74-48=26'].\n\nThought : Expand Node #0,4’s 3rd child to build next frontier.\nAction : Exploring operation 37+26=63. \nResulting numbers: [26, 63].\nHeuristic score : (|26-50| + |63-50|)/2 = (24 + 13)/2 = 18.50\nGenerated Node #0,4,2: 50:[26, 63] Operation: 37+26=63\n\nThought : Expand Node #0,4,2’s 1st child to build next frontier.\nAction : Exploring operation 63-26=37. \nResulting numbers: [37].\n37,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4 with lowest heuristic value 20.333333333333332\nCurrent State #0,4: 50:[37, 26, 26]. Operations so far : ['74-48=26'].\n\nThought : Expand Node #0,4’s 4th child to build next frontier.\nAction : Exploring operation 26/26=1. \nResulting numbers: [37, 1].\nHeuristic score : (|37-50| + |1-50|)/2 = (13 + 49)/2 = 31.00\nGenerated Node #0,4,3: 50:[37, 1] Operation: 26/26=1\n\nThought : Expand Node #0,4,3’s 1st child to build next frontier.\nAction : Exploring operation 37+1=38. \nResulting numbers: [38].\n38,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4 with lowest heuristic value 20.333333333333332\nCurrent State #0,4: 50:[37, 26, 26]. Operations so far : ['74-48=26'].\n\nThought : Expand Node #0,4’s 5th child to build next frontier.\nAction : Exploring operation 37-26=11. \nResulting numbers: [26, 11].\nHeuristic score : (|26-50| + |11-50|)/2 = (24 + 39)/2 = 31.50\nGenerated Node #0,4,4: 50:[26, 11] Operation: 37-26=11\n\nThought : Expand Node #0,4,4’s 1st child to build next frontier.\nAction : Exploring operation 26+11=37. \nResulting numbers: [37].\n37,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4 with lowest heuristic value 20.333333333333332\nCurrent State #0,4: 50:[37, 26, 26]. Operations so far : ['74-48=26'].\n\nThought : Expand Node #0,4’s 6th child to build next frontier.\nAction : Exploring operation 37-26=11. \nResulting numbers: [26, 11].\nHeuristic score : (|26-50| + |11-50|)/2 = (24 + 39)/2 = 31.50\nGenerated Node #0,4,5: 50:[26, 11] Operation: 37-26=11\n\nThought : Expand Node #0,4,5’s 1st child to build next frontier.\nAction : Exploring operation 26+11=37. \nResulting numbers: [37].\n37,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4 with lowest heuristic value 20.333333333333332\nCurrent State #0,4: 50:[37, 26, 26]. Operations so far : ['74-48=26'].\n\nThought : Expand Node #0,4’s 7th child to build next frontier.\nAction : Exploring operation 26-26=0. \nResulting numbers: [37, 0].\nHeuristic score : (|37-50| + |0-50|)/2 = (13 + 50)/2 = 31.50\nGenerated Node #0,4,6: 50:[37, 0] Operation: 26-26=0\n\nThought : Expand Node #0,4,6’s 1st child to build next frontier.\nAction : Exploring operation 37+0=37. \nResulting numbers: [37].\n37,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4 with lowest heuristic value 20.333333333333332\nCurrent State #0,4: 50:[37, 26, 26]. Operations so far : ['74-48=26'].\n\nThought : Expand Node #0,4’s 8th child to build next frontier.\nAction : Exploring operation 26*26=676. \nResulting numbers: [37, 676].\nHeuristic score : (|37-50| + |676-50|)/2 = (13 + 626)/2 = 319.50\nGenerated Node #0,4,7: 50:[37, 676] Operation: 26*26=676\n\nThought : Expand Node #0,4,7’s 1st child to build next frontier.\nAction : Exploring operation 676-37=639. \nResulting numbers: [639].\n639,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4 with lowest heuristic value 20.333333333333332\nCurrent State #0,4: 50:[37, 26, 26]. Operations so far : ['74-48=26'].\n\nThought : Expand Node #0,4’s 9th child to build next frontier.\nAction : Exploring operation 37*26=962. \nResulting numbers: [26, 962].\nHeuristic score : (|26-50| + |962-50|)/2 = (24 + 912)/2 = 468.00\nGenerated Node #0,4,8: 50:[26, 962] Operation: 37*26=962\n\nThought : Expand Node #0,4,8’s 1st child to build next frontier.\nAction : Exploring operation 962/26=37. \nResulting numbers: [37].\n37,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4 with lowest heuristic value 20.333333333333332\nCurrent State #0,4: 50:[37, 26, 26]. Operations so far : ['74-48=26'].\n\nThought : Expand Node #0,4’s 10th child to build next frontier.\nAction : Exploring operation 37*26=962. \nResulting numbers: [26, 962].\nHeuristic score : (|26-50| + |962-50|)/2 = (24 + 912)/2 = 468.00\nGenerated Node #0,4,9: 50:[26, 962] Operation: 37*26=962\n\nThought : Expand Node #0,4,9’s 1st child to build next frontier.\nAction : Exploring operation 962/26=37. \nResulting numbers: [37].\n37,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0 with lowest heuristic value 15.75\nCurrent State #0: 50:[37, 48, 26, 74]. Operations so far : [].\n\nThought : Expand Node #0’s 6th child to build next frontier.\nAction : Exploring operation 37-26=11. \nResulting numbers: [48, 74, 11].\nHeuristic score : (|48-50| + |74-50| + |11-50|)/3 = (2 + 24 + 39)/3 = 21.67\nGenerated Node #0,5: 50:[48, 74, 11] Operation: 37-26=11\n\nThought : Expand Node #0,5’s 1st child to build next frontier.\nAction : Exploring operation 74-11=63. \nResulting numbers: [48, 63].\nHeuristic score : (|48-50| + |63-50|)/2 = (2 + 13)/2 = 7.50\nGenerated Node #0,5,0: 50:[48, 63] Operation: 74-11=63\n\nThought : Expand Node #0,5,0’s 1st child to build next frontier.\nAction : Exploring operation 63-48=15. \nResulting numbers: [15].\n15,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,5 with lowest heuristic value 21.666666666666668\nCurrent State #0,5: 50:[48, 74, 11]. Operations so far : ['37-26=11'].\n\nThought : Expand Node #0,5’s 2nd child to build next frontier.\nAction : Exploring operation 48+11=59. \nResulting numbers: [74, 59].\nHeuristic score : (|74-50| + |59-50|)/2 = (24 + 9)/2 = 16.50\nGenerated Node #0,5,1: 50:[74, 59] Operation: 48+11=59\n\nThought : Expand Node #0,5,1’s 1st child to build next frontier.\nAction : Exploring operation 74-59=15. \nResulting numbers: [15].\n15,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,5 with lowest heuristic value 21.666666666666668\nCurrent State #0,5: 50:[48, 74, 11]. Operations so far : ['37-26=11'].\n\nThought : Expand Node #0,5’s 3rd child to build next frontier.\nAction : Exploring operation 48-11=37. \nResulting numbers: [74, 37].\nHeuristic score : (|74-50| + |37-50|)/2 = (24 + 13)/2 = 18.50\nGenerated Node #0,5,2: 50:[74, 37] Operation: 48-11=37\n\nThought : Expand Node #0,5,2’s 1st child to build next frontier.\nAction : Exploring operation 74-37=37. \nResulting numbers: [37].\n37,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,5 with lowest heuristic value 21.666666666666668\nCurrent State #0,5: 50:[48, 74, 11]. Operations so far : ['37-26=11'].\n\nThought : Expand Node #0,5’s 4th child to build next frontier.\nAction : Exploring operation 74+11=85. \nResulting numbers: [48, 85].\nHeuristic score : (|48-50| + |85-50|)/2 = (2 + 35)/2 = 18.50\nGenerated Node #0,5,3: 50:[48, 85] Operation: 74+11=85\n\nThought : Expand Node #0,5,3’s 1st child to build next frontier.\nAction : Exploring operation 85-48=37. \nResulting numbers: [37].\n37,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,5 with lowest heuristic value 21.666666666666668\nCurrent State #0,5: 50:[48, 74, 11]. Operations so far : ['37-26=11'].\n\nThought : Expand Node #0,5’s 5th child to build next frontier.\nAction : Exploring operation 74-48=26. \nResulting numbers: [11, 26].\nHeuristic score : (|11-50| + |26-50|)/2 = (39 + 24)/2 = 31.50\nGenerated Node #0,5,4: 50:[11, 26] Operation: 74-48=26\n\nThought : Expand Node #0,5,4’s 1st child to build next frontier.\nAction : Exploring operation 11+26=37. \nResulting numbers: [37].\n37,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,5 with lowest heuristic value 21.666666666666668\nCurrent State #0,5: 50:[48, 74, 11]. Operations so far : ['37-26=11'].\n\nThought : Expand Node #0,5’s 6th child to build next frontier.\nAction : Exploring operation 48+74=122. \nResulting numbers: [11, 122].\nHeuristic score : (|11-50| + |122-50|)/2 = (39 + 72)/2 = 55.50\nGenerated Node #0,5,5: 50:[11, 122] Operation: 48+74=122\n\nThought : Expand Node #0,5,5’s 1st child to build next frontier.\nAction : Exploring operation 122-11=111. \nResulting numbers: [111].\n111,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,5 with lowest heuristic value 21.666666666666668\nCurrent State #0,5: 50:[48, 74, 11]. Operations so far : ['37-26=11'].\n\nThought : Expand Node #0,5’s 7th child to build next frontier.\nAction : Exploring operation 48*11=528. \nResulting numbers: [74, 528].\nHeuristic score : (|74-50| + |528-50|)/2 = (24 + 478)/2 = 251.00\nGenerated Node #0,5,6: 50:[74, 528] Operation: 48*11=528\n\nThought : Expand Node #0,5,6’s 1st child to build next frontier.\nAction : Exploring operation 528-74=454. \nResulting numbers: [454].\n454,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,5 with lowest heuristic value 21.666666666666668\nCurrent State #0,5: 50:[48, 74, 11]. Operations so far : ['37-26=11'].\n\nThought : Expand Node #0,5’s 8th child to build next frontier.\nAction : Exploring operation 74*11=814. \nResulting numbers: [48, 814].\nHeuristic score : (|48-50| + |814-50|)/2 = (2 + 764)/2 = 383.00\nGenerated Node #0,5,7: 50:[48, 814] Operation: 74*11=814\n\nThought : Expand Node #0,5,7’s 1st child to build next frontier.\nAction : Exploring operation 814-48=766. \nResulting numbers: [766].\n766,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,5 with lowest heuristic value 21.666666666666668\nCurrent State #0,5: 50:[48, 74, 11]. Operations so far : ['37-26=11'].\n\nThought : Expand Node #0,5’s 9th child to build next frontier.\nAction : Exploring operation 48*74=3552. \nResulting numbers: [11, 3552].\nHeuristic score : (|11-50| + |3552-50|)/2 = (39 + 3502)/2 = 1770.50\nGenerated Node #0,5,8: 50:[11, 3552] Operation: 48*74=3552\n\nThought : Expand Node #0,5,8’s 1st child to build next frontier.\nAction : Exploring operation 3552-11=3541. \nResulting numbers: [3541].\n3541,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0 with lowest heuristic value 15.75\nCurrent State #0: 50:[37, 48, 26, 74]. Operations so far : [].\n\nThought : Expand Node #0’s 7th child to build next frontier.\nAction : Exploring operation 48-26=22. \nResulting numbers: [37, 74, 22].\nHeuristic score : (|37-50| + |74-50| + |22-50|)/3 = (13 + 24 + 28)/3 = 21.67\nGenerated Node #0,6: 50:[37, 74, 22] Operation: 48-26=22\n\nThought : Expand Node #0,6’s 1st child to build next frontier.\nAction : Exploring operation 74-22=52. \nResulting numbers: [37, 52].\nHeuristic score : (|37-50| + |52-50|)/2 = (13 + 2)/2 = 7.50\nGenerated Node #0,6,0: 50:[37, 52] Operation: 74-22=52\n\nThought : Expand Node #0,6,0’s 1st child to build next frontier.\nAction : Exploring operation 52-37=15. \nResulting numbers: [15].\n15,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,6 with lowest heuristic value 21.666666666666668\nCurrent State #0,6: 50:[37, 74, 22]. Operations so far : ['48-26=22'].\n\nThought : Expand Node #0,6’s 2nd child to build next frontier.\nAction : Exploring operation 37+22=59. \nResulting numbers: [74, 59].\nHeuristic score : (|74-50| + |59-50|)/2 = (24 + 9)/2 = 16.50\nGenerated Node #0,6,1: 50:[74, 59] Operation: 37+22=59\n\nThought : Expand Node #0,6,1’s 1st child to build next frontier.\nAction : Exploring operation 74-59=15. \nResulting numbers: [15].\n15,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,6 with lowest heuristic value 21.666666666666668\nCurrent State #0,6: 50:[37, 74, 22]. Operations so far : ['48-26=22'].\n\nThought : Expand Node #0,6’s 3rd child to build next frontier.\nAction : Exploring operation 74-37=37. \nResulting numbers: [22, 37].\nHeuristic score : (|22-50| + |37-50|)/2 = (28 + 13)/2 = 20.50\nGenerated Node #0,6,2: 50:[22, 37] Operation: 74-37=37\n\nThought : Expand Node #0,6,2’s 1st child to build next frontier.\nAction : Exploring operation 22+37=59. \nResulting numbers: [59].\n59,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,6 with lowest heuristic value 21.666666666666668\nCurrent State #0,6: 50:[37, 74, 22]. Operations so far : ['48-26=22'].\n\nThought : Expand Node #0,6’s 4th child to build next frontier.\nAction : Exploring operation 37-22=15. \nResulting numbers: [74, 15].\nHeuristic score : (|74-50| + |15-50|)/2 = (24 + 35)/2 = 29.50\nGenerated Node #0,6,3: 50:[74, 15] Operation: 37-22=15\n\nThought : Expand Node #0,6,3’s 1st child to build next frontier.\nAction : Exploring operation 74-15=59. \nResulting numbers: [59].\n59,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,6 with lowest heuristic value 21.666666666666668\nCurrent State #0,6: 50:[37, 74, 22]. Operations so far : ['48-26=22'].\n\nThought : Expand Node #0,6’s 5th child to build next frontier.\nAction : Exploring operation 74+22=96. \nResulting numbers: [37, 96].\nHeuristic score : (|37-50| + |96-50|)/2 = (13 + 46)/2 = 29.50\nGenerated Node #0,6,4: 50:[37, 96] Operation: 74+22=96\n\nThought : Expand Node #0,6,4’s 1st child to build next frontier.\nAction : Exploring operation 96-37=59. \nResulting numbers: [59].\n59,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,6 with lowest heuristic value 21.666666666666668\nCurrent State #0,6: 50:[37, 74, 22]. Operations so far : ['48-26=22'].\n\nThought : Expand Node #0,6’s 6th child to build next frontier.\nAction : Exploring operation 74/37=2. \nResulting numbers: [22, 2].\nHeuristic score : (|22-50| + |2-50|)/2 = (28 + 48)/2 = 38.00\nGenerated Node #0,6,5: 50:[22, 2] Operation: 74/37=2\n\nThought : Expand Node #0,6,5’s 1st child to build next frontier.\nAction : Exploring operation 22*2=44. \nResulting numbers: [44].\n44,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,6 with lowest heuristic value 21.666666666666668\nCurrent State #0,6: 50:[37, 74, 22]. Operations so far : ['48-26=22'].\n\nThought : Expand Node #0,6’s 7th child to build next frontier.\nAction : Exploring operation 37+74=111. \nResulting numbers: [22, 111].\nHeuristic score : (|22-50| + |111-50|)/2 = (28 + 61)/2 = 44.50\nGenerated Node #0,6,6: 50:[22, 111] Operation: 37+74=111\n\nThought : Expand Node #0,6,6’s 1st child to build next frontier.\nAction : Exploring operation 111-22=89. \nResulting numbers: [89].\n89,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,6 with lowest heuristic value 21.666666666666668\nCurrent State #0,6: 50:[37, 74, 22]. Operations so far : ['48-26=22'].\n\nThought : Expand Node #0,6’s 8th child to build next frontier.\nAction : Exploring operation 37*22=814. \nResulting numbers: [74, 814].\nHeuristic score : (|74-50| + |814-50|)/2 = (24 + 764)/2 = 394.00\nGenerated Node #0,6,7: 50:[74, 814] Operation: 37*22=814\n\nThought : Expand Node #0,6,7’s 1st child to build next frontier.\nAction : Exploring operation 814/74=11. \nResulting numbers: [11].\n11,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,6 with lowest heuristic value 21.666666666666668\nCurrent State #0,6: 50:[37, 74, 22]. Operations so far : ['48-26=22'].\n\nThought : Expand Node #0,6’s 9th child to build next frontier.\nAction : Exploring operation 74*22=1628. \nResulting numbers: [37, 1628].\nHeuristic score : (|37-50| + |1628-50|)/2 = (13 + 1578)/2 = 795.50\nGenerated Node #0,6,8: 50:[37, 1628] Operation: 74*22=1628\n\nThought : Expand Node #0,6,8’s 1st child to build next frontier.\nAction : Exploring operation 1628/37=44. \nResulting numbers: [44].\n44,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,6 with lowest heuristic value 21.666666666666668\nCurrent State #0,6: 50:[37, 74, 22]. Operations so far : ['48-26=22'].\n\nThought : Expand Node #0,6’s 10th child to build next frontier.\nAction : Exploring operation 37*74=2738. \nResulting numbers: [22, 2738].\nHeuristic score : (|22-50| + |2738-50|)/2 = (28 + 2688)/2 = 1358.00\nGenerated Node #0,6,9: 50:[22, 2738] Operation: 37*74=2738\n\nThought : Expand Node #0,6,9’s 1st child to build next frontier.\nAction : Exploring operation 2738-22=2716. \nResulting numbers: [2716].\n2716,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0 with lowest heuristic value 15.75\nCurrent State #0: 50:[37, 48, 26, 74]. Operations so far : [].\n\nThought : Expand Node #0’s 8th child to build next frontier.\nAction : Exploring operation 26+74=100. \nResulting numbers: [37, 48, 100].\nHeuristic score : (|37-50| + |48-50| + |100-50|)/3 = (13 + 2 + 50)/3 = 21.67\nGenerated Node #0,7: 50:[37, 48, 100] Operation: 26+74=100\n\nThought : Expand Node #0,7’s 1st child to build next frontier.\nAction : Exploring operation 100-37=63. \nResulting numbers: [48, 63].\nHeuristic score : (|48-50| + |63-50|)/2 = (2 + 13)/2 = 7.50\nGenerated Node #0,7,0: 50:[48, 63] Operation: 100-37=63\n\nThought : Expand Node #0,7,0’s 1st child to build next frontier.\nAction : Exploring operation 63-48=15. \nResulting numbers: [15].\n15,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,7 with lowest heuristic value 21.666666666666668\nCurrent State #0,7: 50:[37, 48, 100]. Operations so far : ['26+74=100'].\n\nThought : Expand Node #0,7’s 2nd child to build next frontier.\nAction : Exploring operation 100-48=52. \nResulting numbers: [37, 52].\nHeuristic score : (|37-50| + |52-50|)/2 = (13 + 2)/2 = 7.50\nGenerated Node #0,7,1: 50:[37, 52] Operation: 100-48=52\n\nThought : Expand Node #0,7,1’s 1st child to build next frontier.\nAction : Exploring operation 52-37=15. \nResulting numbers: [15].\n15,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,7 with lowest heuristic value 21.666666666666668\nCurrent State #0,7: 50:[37, 48, 100]. Operations so far : ['26+74=100'].\n\nThought : Expand Node #0,7’s 3rd child to build next frontier.\nAction : Exploring operation 37+48=85. \nResulting numbers: [100, 85].\nHeuristic score : (|100-50| + |85-50|)/2 = (50 + 35)/2 = 42.50\nGenerated Node #0,7,2: 50:[100, 85] Operation: 37+48=85\n\nThought : Expand Node #0,7,2’s 1st child to build next frontier.\nAction : Exploring operation 100-85=15. \nResulting numbers: [15].\n15,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,7 with lowest heuristic value 21.666666666666668\nCurrent State #0,7: 50:[37, 48, 100]. Operations so far : ['26+74=100'].\n\nThought : Expand Node #0,7’s 4th child to build next frontier.\nAction : Exploring operation 48-37=11. \nResulting numbers: [100, 11].\nHeuristic score : (|100-50| + |11-50|)/2 = (50 + 39)/2 = 44.50\nGenerated Node #0,7,3: 50:[100, 11] Operation: 48-37=11\n\nThought : Expand Node #0,7,3’s 1st child to build next frontier.\nAction : Exploring operation 100-11=89. \nResulting numbers: [89].\n89,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,7 with lowest heuristic value 21.666666666666668\nCurrent State #0,7: 50:[37, 48, 100]. Operations so far : ['26+74=100'].\n\nThought : Expand Node #0,7’s 5th child to build next frontier.\nAction : Exploring operation 37+100=137. \nResulting numbers: [48, 137].\nHeuristic score : (|48-50| + |137-50|)/2 = (2 + 87)/2 = 44.50\nGenerated Node #0,7,4: 50:[48, 137] Operation: 37+100=137\n\nThought : Expand Node #0,7,4’s 1st child to build next frontier.\nAction : Exploring operation 137-48=89. \nResulting numbers: [89].\n89,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,7 with lowest heuristic value 21.666666666666668\nCurrent State #0,7: 50:[37, 48, 100]. Operations so far : ['26+74=100'].\n\nThought : Expand Node #0,7’s 6th child to build next frontier.\nAction : Exploring operation 48+100=148. \nResulting numbers: [37, 148].\nHeuristic score : (|37-50| + |148-50|)/2 = (13 + 98)/2 = 55.50\nGenerated Node #0,7,5: 50:[37, 148] Operation: 48+100=148\n\nThought : Expand Node #0,7,5’s 1st child to build next frontier.\nAction : Exploring operation 148/37=4. \nResulting numbers: [4].\n4,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,7 with lowest heuristic value 21.666666666666668\nCurrent State #0,7: 50:[37, 48, 100]. Operations so far : ['26+74=100'].\n\nThought : Expand Node #0,7’s 7th child to build next frontier.\nAction : Exploring operation 37*48=1776. \nResulting numbers: [100, 1776].\nHeuristic score : (|100-50| + |1776-50|)/2 = (50 + 1726)/2 = 888.00\nGenerated Node #0,7,6: 50:[100, 1776] Operation: 37*48=1776\n\nThought : Expand Node #0,7,6’s 1st child to build next frontier.\nAction : Exploring operation 1776-100=1676. \nResulting numbers: [1676].\n1676,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,7 with lowest heuristic value 21.666666666666668\nCurrent State #0,7: 50:[37, 48, 100]. Operations so far : ['26+74=100'].\n\nThought : Expand Node #0,7’s 8th child to build next frontier.\nAction : Exploring operation 37*100=3700. \nResulting numbers: [48, 3700].\nHeuristic score : (|48-50| + |3700-50|)/2 = (2 + 3650)/2 = 1826.00\nGenerated Node #0,7,7: 50:[48, 3700] Operation: 37*100=3700\n\nThought : Expand Node #0,7,7’s 1st child to build next frontier.\nAction : Exploring operation 3700-48=3652. \nResulting numbers: [3652].\n3652,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,7 with lowest heuristic value 21.666666666666668\nCurrent State #0,7: 50:[37, 48, 100]. Operations so far : ['26+74=100'].\n\nThought : Expand Node #0,7’s 9th child to build next frontier.\nAction : Exploring operation 48*100=4800. \nResulting numbers: [37, 4800].\nHeuristic score : (|37-50| + |4800-50|)/2 = (13 + 4750)/2 = 2381.50\nGenerated Node #0,7,8: 50:[37, 4800] Operation: 48*100=4800\n\nThought : Expand Node #0,7,8’s 1st child to build next frontier.\nAction : Exploring operation 4800-37=4763. \nResulting numbers: [4763].\n4763,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0 with lowest heuristic value 15.75\nCurrent State #0: 50:[37, 48, 26, 74]. Operations so far : [].\n\nThought : Expand Node #0’s 9th child to build next frontier.\nAction : Exploring operation 74/37=2. \nResulting numbers: [48, 26, 2].\nHeuristic score : (|48-50| + |26-50| + |2-50|)/3 = (2 + 24 + 48)/3 = 24.67\nGenerated Node #0,8: 50:[48, 26, 2] Operation: 74/37=2\n\nThought : Expand Node #0,8’s 1st child to build next frontier.\nAction : Exploring operation 26*2=52. \nResulting numbers: [48, 52].\nHeuristic score : (|48-50| + |52-50|)/2 = (2 + 2)/2 = 2.00\nGenerated Node #0,8,0: 50:[48, 52] Operation: 26*2=52\n\nThought : Expand Node #0,8,0’s 1st child to build next frontier.\nAction : Exploring operation 52-48=4. \nResulting numbers: [4].\n4,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,8 with lowest heuristic value 24.666666666666668\nCurrent State #0,8: 50:[48, 26, 2]. Operations so far : ['74/37=2'].\n\nThought : Expand Node #0,8’s 2nd child to build next frontier.\nAction : Exploring operation 48+2=50. \nResulting numbers: [26, 50].\nHeuristic score : (|26-50| + |50-50|)/2 = (24 + 0)/2 = 12.00\nGenerated Node #0,8,1: 50:[26, 50] Operation: 48+2=50\n\nThought : Expand Node #0,8,1’s 1st child to build next frontier.\nAction : Exploring operation 26+50=76. \nResulting numbers: [76].\n76,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,8 with lowest heuristic value 24.666666666666668\nCurrent State #0,8: 50:[48, 26, 2]. Operations so far : ['74/37=2'].\n\nThought : Expand Node #0,8’s 3rd child to build next frontier.\nAction : Exploring operation 26+2=28. \nResulting numbers: [48, 28].\nHeuristic score : (|48-50| + |28-50|)/2 = (2 + 22)/2 = 12.00\nGenerated Node #0,8,2: 50:[48, 28] Operation: 26+2=28\n\nThought : Expand Node #0,8,2’s 1st child to build next frontier.\nAction : Exploring operation 48+28=76. \nResulting numbers: [76].\n76,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,8 with lowest heuristic value 24.666666666666668\nCurrent State #0,8: 50:[48, 26, 2]. Operations so far : ['74/37=2'].\n\nThought : Expand Node #0,8’s 4th child to build next frontier.\nAction : Exploring operation 48-2=46. \nResulting numbers: [26, 46].\nHeuristic score : (|26-50| + |46-50|)/2 = (24 + 4)/2 = 14.00\nGenerated Node #0,8,3: 50:[26, 46] Operation: 48-2=46\n\nThought : Expand Node #0,8,3’s 1st child to build next frontier.\nAction : Exploring operation 26+46=72. \nResulting numbers: [72].\n72,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,8 with lowest heuristic value 24.666666666666668\nCurrent State #0,8: 50:[48, 26, 2]. Operations so far : ['74/37=2'].\n\nThought : Expand Node #0,8’s 5th child to build next frontier.\nAction : Exploring operation 26-2=24. \nResulting numbers: [48, 24].\nHeuristic score : (|48-50| + |24-50|)/2 = (2 + 26)/2 = 14.00\nGenerated Node #0,8,4: 50:[48, 24] Operation: 26-2=24\n\nThought : Expand Node #0,8,4’s 1st child to build next frontier.\nAction : Exploring operation 48+24=72. \nResulting numbers: [72].\n72,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,8 with lowest heuristic value 24.666666666666668\nCurrent State #0,8: 50:[48, 26, 2]. Operations so far : ['74/37=2'].\n\nThought : Expand Node #0,8’s 6th child to build next frontier.\nAction : Exploring operation 26/2=13. \nResulting numbers: [48, 13].\nHeuristic score : (|48-50| + |13-50|)/2 = (2 + 37)/2 = 19.50\nGenerated Node #0,8,5: 50:[48, 13] Operation: 26/2=13\n\nThought : Expand Node #0,8,5’s 1st child to build next frontier.\nAction : Exploring operation 48+13=61. \nResulting numbers: [61].\n61,50 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,8 with lowest heuristic value 24.666666666666668\nCurrent State #0,8: 50:[48, 26, 2]. Operations so far : ['74/37=2'].\n\nThought : Expand Node #0,8’s 7th child to build next frontier.\nAction : Exploring operation 48/2=24. \nResulting numbers: [26, 24].\nHeuristic score : (|26-50| + |24-50|)/2 = (24 + 26)/2 = 25.00\nGenerated Node #0,8,6: 50:[26, 24] Operation: 48/2=24\n\nThought : Expand Node #0,8,6’s 1st child to build next frontier.\nAction : Exploring operation 26+24=50. \nResulting numbers: [50].\n50,50 equal: Goal Reached\n\n```\nSOLUTION: YES\nOPERATIONS: ['74/37=2', '48/2=24', '26+24=50']\nRESULT: 50\n```\n",
"role": "assistant"
}
]
| 19,899 |
[
83,
23,
43,
84
]
| 65 | bfs_5 | sum_heuristic | [{"content":"Combine these initial numbers [83, 23, 43, 84] using only arithmetic operations (+, -, (...TRUNCATED) | 6,232 |
[
20,
31,
9,
39
]
| 88 | dfs | sum_heuristic | [{"content":"Combine these initial numbers [20, 31, 9, 39] using only arithmetic operations (+, -, *(...TRUNCATED) | 14,142 |
[
83,
37,
79,
81
]
| 84 | dfs | sum_heuristic | [{"content":"Combine these initial numbers [83, 37, 79, 81] using only arithmetic operations (+, -, (...TRUNCATED) | 9,993 |
[
77,
95,
5,
81
]
| 68 | bfs_5 | sum_heuristic | [{"content":"Combine these initial numbers [77, 95, 5, 81] using only arithmetic operations (+, -, *(...TRUNCATED) | 5,945 |
[
98,
5,
24,
20
]
| 59 | dfs | sum_heuristic | [{"content":"Combine these initial numbers [98, 5, 24, 20] using only arithmetic operations (+, -, *(...TRUNCATED) | 3,158 |
[
87,
45,
50,
47
]
| 72 | dfs | sum_heuristic | [{"content":"Combine these initial numbers [87, 45, 50, 47] using only arithmetic operations (+, -, (...TRUNCATED) | 22,752 |
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