Analysis of xx-top500-023-base.sdk
Contents
Original Sudoku
level: medium
position: ....5..6.4.2...........1......3..2.4.18............7...5..6..1.7..2..4........... initial
Autosolve
position: 1..457.624.2...175....21.4....31.2.4.187426...245..7.125..64.177.12.54.6.4617.52. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 3,9 => CTR => B1: 8 * PRF # B1: 8 => SOL * PRF # B3: 3,9 => SOL * PRF # G1: 3,9 => SOL * DIS # G1: 8 => CTR => G1: 3,9 * DIS # E2: 8,9 => CTR => E2: 3 * DIS # I3: 3,9 => CTR => I3: 8 * PRF # I3: 8 => SOL * PRF # I9: 3,9 => SOL * DIS # I9: 8 => CTR => I9: 3,9 * PRF # B8: 3,9 => SOL * DIS # B8: 8 => CTR => B8: 3,9 * DIS # G7: 3,9 => CTR => G7: 8 * PRF # G7: 8 => SOL * DIS # B8: 3 => CTR => B8: 8,9 * DIS # F9: 8,9 => CTR => F9: 3 * PRF # A3: 5,6 => SOL * DIS # F9: 8,9 => CTR => F9: 3 * DIS # G7: 3 => CTR => G7: 8,9 * DIS # D3: 8,9 => CTR => D3: 6 * DIS # G7: 3,9 => CTR => G7: 8 * PRF # G7: 8 => SOL * PRF # I9: 3,9 => SOL * DIS # I9: 8 => CTR => I9: 3,9 * PRF # B8: 3,9 => SOL * DIS # B8: 8 => CTR => B8: 3,9 * DIS # E8: 3,9 => CTR => E8: 8 * PRF # E8: 8 => SOL * CNT 28 HDP CHAINS / 50 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B1: 3,9 => CTR => B1: 8 * PRF B1: 8 => SOL * STA B1: 8 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....5..6.4.2...........1......3..2.4.18............7...5..6..1.7..2..4........... | initial |
| 1..457.624.2...175....21.4....31.2.4.187426...245..7.125..64.177.12.54.6.4617.52. | autosolve |
| 189457362462839175537621948675318294918742653324596781253964817791285436846173529 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) C1: 3,9 C3: 5,7 C4: 5,7 E6: 8,9 I5: 3,9 C7: 3,9 A9: 8,9 D7: 8,9 H8: 3,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,F2: 3.. / E2 = 3 => 12 pairs (_) / F2 = 3 => 0 pairs (X) A5,A6: 3.. / A5 = 3 => 14 pairs (_) / A6 = 3 => 12 pairs (_) C7,B8: 3.. / C7 = 3 => 14 pairs (_) / B8 = 3 => 0 pairs (X) E8,F9: 3.. / E8 = 3 => 0 pairs (X) / F9 = 3 => 12 pairs (_) A6,H6: 3.. / A6 = 3 => 12 pairs (_) / H6 = 3 => 14 pairs (_) C7,G7: 3.. / C7 = 3 => 14 pairs (_) / G7 = 3 => 0 pairs (X) F9,I9: 3.. / F9 = 3 => 12 pairs (_) / I9 = 3 => 0 pairs (X) C1,C7: 3.. / C1 = 3 => 0 pairs (X) / C7 = 3 => 14 pairs (_) E2,E8: 3.. / E2 = 3 => 12 pairs (_) / E8 = 3 => 0 pairs (X) F2,F9: 3.. / F2 = 3 => 0 pairs (X) / F9 = 3 => 12 pairs (_) A3,C3: 5.. / A3 = 5 => 0 pairs (*) / C3 = 5 => 0 pairs (X) H4,H5: 5.. / H4 = 5 => 14 pairs (_) / H5 = 5 => 11 pairs (_) A5,H5: 5.. / A5 = 5 => 14 pairs (_) / H5 = 5 => 11 pairs (_) C3,C4: 5.. / C3 = 5 => 9 pairs (_) / C4 = 5 => 0 pairs (*) D2,D3: 6.. / D2 = 6 => 0 pairs (X) / D3 = 6 => 11 pairs (_) F4,F6: 6.. / F4 = 6 => 15 pairs (_) / F6 = 6 => 11 pairs (_) B2,D2: 6.. / B2 = 6 => 11 pairs (_) / D2 = 6 => 0 pairs (X) A6,F6: 6.. / A6 = 6 => 15 pairs (_) / F6 = 6 => 11 pairs (_) B3,C3: 7.. / B3 = 7 => 9 pairs (_) / C3 = 7 => 0 pairs (*) B4,C4: 7.. / B4 = 7 => 0 pairs (*) / C4 = 7 => 0 pairs (X) B3,B4: 7.. / B3 = 7 => 9 pairs (_) / B4 = 7 => 0 pairs (*) C3,C4: 7.. / C3 = 7 => 0 pairs (*) / C4 = 7 => 0 pairs (X) H4,H6: 8.. / H4 = 8 => 12 pairs (_) / H6 = 8 => 14 pairs (_) B8,A9: 8.. / B8 = 8 => 0 pairs (X) / A9 = 8 => 0 pairs (_) G7,I9: 8.. / G7 = 8 => 0 pairs (*) / I9 = 8 => 0 pairs (X) B1,G1: 8.. / B1 = 8 => 0 pairs (*) / G1 = 8 => 0 pairs (X) F4,H4: 8.. / F4 = 8 => 14 pairs (_) / H4 = 8 => 12 pairs (_) D7,G7: 8.. / D7 = 8 => 0 pairs (X) / G7 = 8 => 0 pairs (_) B8,E8: 8.. / B8 = 8 => 0 pairs (X) / E8 = 8 => 0 pairs (_) A3,A9: 8.. / A3 = 8 => 0 pairs (X) / A9 = 8 => 0 pairs (_) I3,I9: 8.. / I3 = 8 => 0 pairs (*) / I9 = 8 => 0 pairs (X) C1,C7: 9.. / C1 = 9 => 14 pairs (_) / C7 = 9 => 0 pairs (X) * DURATION: 0:00:59.427146 START: 03:22:11.218350 END: 03:23:10.645496 2017-05-04 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,C1,C3,C4,C7,D7,E6,H8,I5) * 1..457.624.2...175....21.4....31.2.4.187426...245..7.125..64.177.12.54.6.4617.52. * PAIR C1: 3,9 BLK 1 B1: 3,9,8 # reduction candidate for 3,9 B1: 3,9 => CTR * 1.94578624629381758.5621.4..97316284.1874265962458973125.864.177812.54.6946173528 B1: 8 => SOLVED * 189457362462839175537621948675318294918742653324596781253964817791285436846173529 B3: 3,9,6,7,8 # reduction candidate for 3,9 B3: 3,9 => SOLVED * 189457362462839175537621948675318294918742653324596781253964817791285436846173529 B3: 6,7,8 # 10 pairs * PAIR C1: 3,9 ROW 1 G1: 3,9,8 # reduction candidate for 3,9 G1: 3,9 => SOLVED * 189457362462839175537621948675318294918742653324596781253964817791285436846173529 G1: 8 => CTR * 1.94578624629381758.5621.4..97316284.1874265962458973125.864.177812.54.6946173528 * PAIR E6: 8,9 BLK 5 F4: 8,9,6 # reduction candidate for 8,9 F4: 8,9 # 11 pairs F6: 8,9,6 # reduction candidate for 8,9 F6: 8,9 # 15 pairs * PAIR E6: 8,9 ROW 6 H6: 8,9,3 # reduction candidate for 8,9 H6: 3 # 14 pairs H6: 8,9 # 12 pairs * PAIR E6: 8,9 COL E E2: 8,9,3 # reduction candidate for 8,9 E2: 8,9 => CTR * 1..457.624.2..3175....21.48...31.2.4.187426.9.245..7.1253964817781235496.4617.523 E2: 3 # 12 pairs E8: 8,9,3 # reduction candidate for 8,9 E8: 8,9 # 12 pairs * PAIR I5: 3,9 BLK 6 H5: 3,9,5 # reduction candidate for 3,9 H5: 3,9 # 14 pairs H6: 3,9,8 # reduction candidate for 3,9 H6: 3,9 # 12 pairs * PAIR I5: 3,9 ROW 5 A5: 3,9,5 # reduction candidate for 3,9 A5: 5 # 14 pairs A5: 3,9 # 11 pairs * PAIR I5: 3,9 COL I I3: 3,9,8 # reduction candidate for 3,9 I3: 3,9 => CTR * 1.9457862462938175875621.4..97316284.1874265962458973125.864.177812.54.6946173528 I3: 8 => SOLVED * 189457362462839175537621948675318294918742653324596781253964817791285436846173529 I9: 3,9,8 # reduction candidate for 3,9 I9: 3,9 => SOLVED * 189457362462839175537621948675318294918742653324596781253964817791285436846173529 I9: 8 => CTR * 1.9457862462938175875621349.97316284.187426...245..7.125.864.17781295436946173528 * PAIR C7: 3,9 BLK 7 B8: 3,9,8 # reduction candidate for 3,9 B8: 3,9 => SOLVED * 189457362462839175537621948675318294918742653324596781253964817791285436846173529 B8: 8 => CTR * 1.9457862462...1758.5621349.9731.2.4.187426933245.67812538649177812954.694617.52. * PAIR C7: 3,9 ROW 7 G7: 3,9,8 # reduction candidate for 3,9 G7: 3,9 => CTR * 1.94578624629381758.5621.4..97316284.1874265962458973125.864.177812.54.6946173528 G7: 8 => SOLVED * 189457362462839175537621948675318294918742653324596781253964817791285436846173529 * PAIR A9: 8,9 BLK 7 B8: 8,9,3 # reduction candidate for 8,9 B8: 3 => CTR * 1..457.624.2...175....21.4....31.2.4.187426...245..7.125..64.17731285496.4617.52. B8: 8,9 # 14 pairs * PAIR A9: 8,9 ROW 9 F9: 8,9,3 # reduction candidate for 8,9 F9: 8,9 => CTR * 1..457.624.2..3175....21.48...31.2.4.187426.9.245..7.1253964817781235496.4617.523 F9: 3 # 12 pairs I9: 8,9,3 # reduction candidate for 8,9 I9: 8,9 # 12 pairs * PAIR A9: 8,9 COL A A3: 8,9,5,6 # reduction candidate for 8,9 A3: 5,6 => SOLVED * 189457362462839175537621948675318294918742653324596781253964817791285436846173529 A3: 8,9 # 18 pairs * PAIR D7: 8,9 BLK 8 E8: 8,9,3 # reduction candidate for 8,9 E8: 8,9 # 12 pairs F9: 8,9,3 # reduction candidate for 8,9 F9: 8,9 => CTR * 1..457.624.2..3175....21.48...31.2.4.187426.9.245..7.1253964817781235496.4617.523 F9: 3 # 12 pairs * PAIR D7: 8,9 ROW 7 G7: 8,9,3 # reduction candidate for 8,9 G7: 3 => CTR * 1..457.624.2...175....21.4....31.2.4.187426...245..7.125.8643177.12.54.6.4617.52. G7: 8,9 # 14 pairs * PAIR D7: 8,9 COL D D2: 8,9,6 # reduction candidate for 8,9 D2: 8,9 # 11 pairs D3: 8,9,6 # reduction candidate for 8,9 D3: 8,9 => CTR * 1..457.624.26..175....21.48...31.2.4.187426...245..7.125.864.177.12.54.684617.52. D3: 6 # 11 pairs * PAIR H8: 3,9 BLK 9 G7: 3,9,8 # reduction candidate for 3,9 G7: 3,9 => CTR * 1.94578624629381758.5621.4..97316284.1874265962458973125.864.177812.54.6946173528 G7: 8 => SOLVED * 189457362462839175537621948675318294918742653324596781253964817791285436846173529 I9: 3,9,8 # reduction candidate for 3,9 I9: 3,9 => SOLVED * 189457362462839175537621948675318294918742653324596781253964817791285436846173529 I9: 8 => CTR * 1.9457862462938175875621349.97316284.187426...245..7.125.864.17781295436946173528 * PAIR H8: 3,9 ROW 8 B8: 3,9,8 # reduction candidate for 3,9 B8: 3,9 => SOLVED * 189457362462839175537621948675318294918742653324596781253964817791285436846173529 B8: 8 => CTR * 1.9457862462...1758.5621349.9731.2.4.187426933245.67812538649177812954.694617.52. E8: 3,9,8 # reduction candidate for 3,9 E8: 3,9 => CTR * 139457862462938175875621349.97316284.187426...245..7.1253864917781295436946173528 E8: 8 => SOLVED * 189457362462839175537621948675318294918742653324596781253964817791285436846173529 * PAIR H8: 3,9 COL H H5: 3,9,5 # reduction candidate for 3,9 H5: 3,9 # 14 pairs H6: 3,9,8 # reduction candidate for 3,9 H6: 3,9 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-023-base-pr-000.dot * REASONING * DIS # B1: 3,9 => CTR => B1: 8 * PRF # B1: 8 => SOL * PRF # B3: 3,9 => SOL * PRF # G1: 3,9 => SOL * DIS # G1: 8 => CTR => G1: 3,9 * DIS # E2: 8,9 => CTR => E2: 3 * DIS # I3: 3,9 => CTR => I3: 8 * PRF # I3: 8 => SOL * PRF # I9: 3,9 => SOL * DIS # I9: 8 => CTR => I9: 3,9 * PRF # B8: 3,9 => SOL * DIS # B8: 8 => CTR => B8: 3,9 * DIS # G7: 3,9 => CTR => G7: 8 * PRF # G7: 8 => SOL * DIS # B8: 3 => CTR => B8: 8,9 * DIS # F9: 8,9 => CTR => F9: 3 * PRF # A3: 5,6 => SOL * DIS # F9: 8,9 => CTR => F9: 3 * DIS # G7: 3 => CTR => G7: 8,9 * DIS # D3: 8,9 => CTR => D3: 6 * DIS # G7: 3,9 => CTR => G7: 8 * PRF # G7: 8 => SOL * PRF # I9: 3,9 => SOL * DIS # I9: 8 => CTR => I9: 3,9 * PRF # B8: 3,9 => SOL * DIS # B8: 8 => CTR => B8: 3,9 * DIS # E8: 3,9 => CTR => E8: 8 * PRF # E8: 8 => SOL * CNT 28 HDP CHAINS / 50 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,C1,C3,C4,C7,D7,E6,H8,I5) * 1..457.624.2...175....21.4....31.2.4.187426...245..7.125..64.177.12.54.6.4617.52. * PAIR C1: 3,9 BLK 1 B1: 3,9,8 # reduction candidate for 3,9 B1: 3,9 => CTR * 1.94578624629381758.5621.4..97316284.1874265962458973125.864.177812.54.6946173528 B1: 8 => SOLVED * 189457362462839175537621948675318294918742653324596781253964817791285436846173529 * DURATION: 0:00:02.011698 START: 03:24:07.030359 END: 03:24:09.042057 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-023-base-pr-001.dot * REASONING * DIS # B1: 3,9 => CTR => B1: 8 * PRF B1: 8 => SOL * STA B1: 8 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 023 solution: 189457362462839175537621948675318294918742653324596781253964817791285436846173529 info: 1319 FNBTWXY S8.f 4755 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 189457362462839175537621948675318294918742653324596781253964817791285436846173529 solved
See section Pair Reduction for the HDP chains leading to this result.
Appendix: Full HDP Chains
A1. Pair Reduction Analysis
Full list of HDP chains traversed:
* DIS # B1: 3,9 => CTR => B1: 8 * PRF # B1: 8 => SOL * PRF # B3: 3,9 => SOL * INC # B3: 6,7,8 => UNS * PRF # G1: 3,9 => SOL * DIS # G1: 8 => CTR => G1: 3,9 * INC # F4: 8,9 => UNS * INC # F6: 8,9 => UNS * INC # H6: 8,9 => UNS * INC # H6: 3 => UNS * DIS # E2: 8,9 => CTR => E2: 3 * INC # E2: 3 => UNS * INC # E8: 8,9 => UNS * INC # H5: 3,9 => UNS * INC # H6: 3,9 => UNS * INC # A5: 3,9 => UNS * INC # A5: 5 => UNS * DIS # I3: 3,9 => CTR => I3: 8 * PRF # I3: 8 => SOL * PRF # I9: 3,9 => SOL * DIS # I9: 8 => CTR => I9: 3,9 * PRF # B8: 3,9 => SOL * DIS # B8: 8 => CTR => B8: 3,9 * DIS # G7: 3,9 => CTR => G7: 8 * PRF # G7: 8 => SOL * INC # B8: 8,9 => UNS * DIS # B8: 3 => CTR => B8: 8,9 * DIS # F9: 8,9 => CTR => F9: 3 * INC # F9: 3 => UNS * INC # I9: 8,9 => UNS * INC # A3: 8,9 => UNS * PRF # A3: 5,6 => SOL * INC # E8: 8,9 => UNS * DIS # F9: 8,9 => CTR => F9: 3 * INC # F9: 3 => UNS * INC # G7: 8,9 => UNS * DIS # G7: 3 => CTR => G7: 8,9 * INC # D2: 8,9 => UNS * DIS # D3: 8,9 => CTR => D3: 6 * INC # D3: 6 => UNS * DIS # G7: 3,9 => CTR => G7: 8 * PRF # G7: 8 => SOL * PRF # I9: 3,9 => SOL * DIS # I9: 8 => CTR => I9: 3,9 * PRF # B8: 3,9 => SOL * DIS # B8: 8 => CTR => B8: 3,9 * DIS # E8: 3,9 => CTR => E8: 8 * PRF # E8: 8 => SOL * INC # H5: 3,9 => UNS * INC # H6: 3,9 => UNS * CNT 50 HDP CHAINS / 50 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B1: 3,9 => CTR => B1: 8 * PRF B1: 8 => SOL * STA B1: 8 * CNT 2 HDP CHAINS / 1 HYP OPENED