Analysis of xx-top500-343-base.sdk
Contents
Original Sudoku
level: hard
position: ..1....5....2..6......3.......5.1.2.34.......7...2.....8....7.....4.5.........3.. initial
Autosolve
position: .31.4725.49725863152.13..74.6.5714233428..517715324...28..137.5.734.51.215.7.23.. autosolve
Pair Reduction Variants
Deep Pair Reduction
Time used: 0:00:29.056110
The following important HDP chains were detected:
* DIS # I6: 8,9 # E8: 8 => CTR => E8: 6,9 * DIS # I6: 8,9 + E8: 6,9 # C7: 4 => CTR => C7: 6,9 * DIS # I9: 8,9 # E8: 6,9 => CTR => E8: 8 * DIS # I9: 8,9 + E8: 8 # H9: 8,9 => CTR => H9: 4,6 * PRF # I9: 8,9 + E8: 8 + H9: 4,6 => SOL * STA I9: 8,9 * CNT 5 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..1....5....2..6......3.......5.1.2.34.......7...2.....8....7.....4.5.........3.. | initial |
| .31.4725.49725863152.13..74.6.5714233428..517715324...28..137.5.734.51.215.7.23.. | autosolve |
| 831647259497258631526139874968571423342896517715324986284913765673485192159762348 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (13) A1: 6,8 C3: 6,8 D1: 6,9 F3: 6,9 I1: 8,9 G3: 8,9 A4: 8,9 C4: 8,9 E5: 6,9 F5: 6,9 G6: 8,9 A8: 6,9 D7: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C7,C9: 4.. / C7 = 4 => 15 pairs (_) / C9 = 4 => 14 pairs (_) H7,H9: 4.. / H7 = 4 => 14 pairs (_) / H9 = 4 => 15 pairs (_) C7,H7: 4.. / C7 = 4 => 15 pairs (_) / H7 = 4 => 14 pairs (_) C9,H9: 4.. / C9 = 4 => 14 pairs (_) / H9 = 4 => 15 pairs (_) A1,C3: 6.. / A1 = 6 => 0 pairs (X) / C3 = 6 => 0 pairs (_) D1,F3: 6.. / D1 = 6 => 0 pairs (*) / F3 = 6 => 0 pairs (X) E5,F5: 6.. / E5 = 6 => 0 pairs (X) / F5 = 6 => 0 pairs (_) H6,I6: 6.. / H6 = 6 => 18 pairs (_) / I6 = 6 => 15 pairs (_) A1,D1: 6.. / A1 = 6 => 0 pairs (X) / D1 = 6 => 0 pairs (_) C3,F3: 6.. / C3 = 6 => 0 pairs (*) / F3 = 6 => 0 pairs (X) A1,A8: 6.. / A1 = 6 => 0 pairs (X) / A8 = 6 => 0 pairs (_) D1,D7: 6.. / D1 = 6 => 0 pairs (*) / D7 = 6 => 0 pairs (X) F3,F5: 6.. / F3 = 6 => 0 pairs (X) / F5 = 6 => 0 pairs (_) I6,I9: 6.. / I6 = 6 => 15 pairs (_) / I9 = 6 => 18 pairs (_) A1,C3: 8.. / A1 = 8 => 0 pairs (*) / C3 = 8 => 0 pairs (X) I1,G3: 8.. / I1 = 8 => 0 pairs (X) / G3 = 8 => 0 pairs (_) A4,C4: 8.. / A4 = 8 => 0 pairs (X) / C4 = 8 => 0 pairs (_) E8,E9: 8.. / E8 = 8 => 15 pairs (_) / E9 = 8 => 16 pairs (_) A1,I1: 8.. / A1 = 8 => 0 pairs (*) / I1 = 8 => 0 pairs (X) C3,G3: 8.. / C3 = 8 => 0 pairs (X) / G3 = 8 => 0 pairs (_) E8,H8: 8.. / E8 = 8 => 15 pairs (_) / H8 = 8 => 16 pairs (_) A1,A4: 8.. / A1 = 8 => 0 pairs (*) / A4 = 8 => 0 pairs (X) C3,C4: 8.. / C3 = 8 => 0 pairs (X) / C4 = 8 => 0 pairs (_) G3,G6: 8.. / G3 = 8 => 0 pairs (*) / G6 = 8 => 0 pairs (X) D1,F3: 9.. / D1 = 9 => 0 pairs (X) / F3 = 9 => 0 pairs (_) I1,G3: 9.. / I1 = 9 => 0 pairs (*) / G3 = 9 => 0 pairs (X) A4,C4: 9.. / A4 = 9 => 0 pairs (*) / C4 = 9 => 0 pairs (X) E5,F5: 9.. / E5 = 9 => 0 pairs (*) / F5 = 9 => 0 pairs (X) D1,I1: 9.. / D1 = 9 => 0 pairs (X) / I1 = 9 => 0 pairs (_) F3,G3: 9.. / F3 = 9 => 0 pairs (*) / G3 = 9 => 0 pairs (X) A4,A8: 9.. / A4 = 9 => 0 pairs (*) / A8 = 9 => 0 pairs (X) D1,D7: 9.. / D1 = 9 => 0 pairs (X) / D7 = 9 => 0 pairs (_) F3,F5: 9.. / F3 = 9 => 0 pairs (*) / F5 = 9 => 0 pairs (X) G3,G6: 9.. / G3 = 9 => 0 pairs (X) / G6 = 9 => 0 pairs (_) * DURATION: 0:00:59.191821 START: 14:26:59.503607 END: 14:27:58.695428 2017-05-04 * CP COUNT: (34) * SOLUTION FOUND * DEEP PAIR REDUCTION * DURATION: 0:00:28.790859 START: 14:28:26.105294 END: 14:28:54.896153 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-343-base-pr-002.dot * REASONING * DIS # I6: 8,9 # E8: 8 => CTR => E8: 6,9 * DIS # I6: 8,9 + E8: 6,9 # C7: 4 => CTR => C7: 6,9 * DIS # I9: 8,9 # E8: 6,9 => CTR => E8: 8 * DIS # I9: 8,9 + E8: 8 # H9: 8,9 => CTR => H9: 4,6 * PRF # I9: 8,9 + E8: 8 + H9: 4,6 => SOL * STA I9: 8,9 * CNT 5 HDP CHAINS / 22 HYP OPENED
Header Info
Top 500 Minimum 17 343 solution: 831647259497258631526139874968571423342896517715324986284913765673485192159762348 info: 3345 FNWXY S8.f 44529 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 831647259497258631526139874968571423342896517715324986284913765673485192159762348 solved
See section Deep Pair Reduction for the HDP chains leading to this result.
Appendix: Full HDP Chains
A1. Pair Reduction Analysis
Full list of HDP chains traversed:
* INC # I6: 8,9 => UNS * INC # I9: 8,9 => UNS * INC # E8: 6,9 => UNS * INC # E9: 6,9 => UNS * INC # H6: 8,9 => UNS * INC # I6: 8,9 => UNS * INC # C7: 6,9 => UNS * INC # C9: 6,9 => UNS * INC # E8: 6,9 => UNS * INC # H8: 6,9 => UNS * INC # E8: 6,9 => UNS * INC # E9: 6,9 => UNS * INC # C7: 6,9 => UNS * INC # H7: 6,9 => UNS * CNT 14 HDP CHAINS / 14 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # I6: 8,9 => UNS * INC # I9: 8,9 => UNS * INC # E8: 6,9 => UNS * INC # E9: 6,9 => UNS * INC # H6: 8,9 => UNS * INC # I6: 8,9 => UNS * INC # C7: 6,9 => UNS * INC # C9: 6,9 => UNS * INC # E8: 6,9 => UNS * INC # H8: 6,9 => UNS * INC # E8: 6,9 => UNS * INC # E9: 6,9 => UNS * INC # C7: 6,9 => UNS * INC # H7: 6,9 => UNS * CNT 14 HDP CHAINS / 14 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # I6: 8,9 => UNS * INC # I9: 8,9 => UNS * INC # E8: 6,9 => UNS * INC # E9: 6,9 => UNS * INC # H6: 8,9 => UNS * INC # I6: 8,9 => UNS * INC # C7: 6,9 => UNS * INC # C9: 6,9 => UNS * INC # E8: 6,9 => UNS * INC # H8: 6,9 => UNS * INC # E8: 6,9 => UNS * INC # E9: 6,9 => UNS * INC # C7: 6,9 => UNS * INC # H7: 6,9 => UNS * INC # I6: 8,9 # E8: 6,9 => UNS * DIS # I6: 8,9 # E8: 8 => CTR => E8: 6,9 * INC # I6: 8,9 + E8: 6,9 # C7: 6,9 => UNS * DIS # I6: 8,9 + E8: 6,9 # C7: 4 => CTR => C7: 6,9 * INC # I6: 8,9 + E8: 6,9 + C7: 6,9 => UNS * DIS # I9: 8,9 # E8: 6,9 => CTR => E8: 8 * DIS # I9: 8,9 + E8: 8 # H9: 8,9 => CTR => H9: 4,6 * PRF # I9: 8,9 + E8: 8 + H9: 4,6 => SOL * STA I9: 8,9 * CNT 22 HDP CHAINS / 22 HYP OPENED