Analysis of xx-top500-189-base.sdk
Contents
Original Sudoku
level: medium
position: .....1.8..6....7......4.......7..2.94.86.....1............3..4...79......2....... initial
Autosolve
position: 2.9.71.8.8642..7.171.84692....784219498612.7.172....6.98.137.42.4792.1...2146..97 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C4: 3,5 => SOL * DIS # C4: 6 => CTR => C4: 3,5 * DIS # C4: 5,6 => CTR => C4: 3 * PRF # C4: 3 => SOL * PRF # A8: 5,6 => SOL * DIS # A8: 3 => CTR => A8: 5,6 * PRF # C4: 3,5 => SOL * DIS # C4: 6 => CTR => C4: 3,5 * DIS # G9: 3,5 => CTR => G9: 8 * PRF # G9: 8 => SOL * PRF # A8: 5,6 => SOL * DIS # A8: 3 => CTR => A8: 5,6 * DIS # C4: 5,6 => CTR => C4: 3 * PRF # C4: 3 => SOL * PRF # A8: 3,5 => SOL * DIS # A8: 6 => CTR => A8: 3,5 * DIS # G9: 3,5 => CTR => G9: 8 * PRF # G9: 8 => SOL * PRF # G9: 5,8 => SOL * DIS # G9: 3 => CTR => G9: 5,8 * DIS # G9: 3,5 => CTR => G9: 8 * PRF # G9: 8 => SOL * PRF # A8: 3,5 => SOL * DIS # A8: 6 => CTR => A8: 3,5 * CNT 24 HDP CHAINS / 24 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C4: 3,5 => SOL * STA C4: 3,5 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .....1.8..6....7......4.......7..2.94.86.....1............3..4...79......2....... | initial |
| 2.9.71.8.8642..7.171.84692....784219498612.7.172....6.98.137.42.4792.1...2146..97 | autosolve |
| 239571684864293751715846923653784219498612375172359468986137542547928136321465897 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (25) B1: 3,5 C3: 3,5 D1: 3,5 E2: 5,9 F2: 3,9 G1: 4,6 I1: 4,6 H2: 3,5 I3: 3,5 A4: 5,6 B4: 3,5 D6: 3,5 E6: 5,9 F6: 3,9 G5: 3,5 I5: 3,5 G6: 4,8 I6: 4,8 C7: 5,6 A9: 3,5 F8: 5,8 F9: 5,8 G7: 5,6 H8: 3,5 I8: 6,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,C3: 3.. / B1 = 3 => 0 pairs (*) / C3 = 3 => 0 pairs (X) D1,F2: 3.. / D1 = 3 => 0 pairs (X) / F2 = 3 => 0 pairs (_) H2,I3: 3.. / H2 = 3 => 0 pairs (X) / I3 = 3 => 0 pairs (_) B4,C4: 3.. / B4 = 3 => 0 pairs (X) / C4 = 3 => 0 pairs (_) D6,F6: 3.. / D6 = 3 => 0 pairs (*) / F6 = 3 => 0 pairs (X) G5,I5: 3.. / G5 = 3 => 0 pairs (*) / I5 = 3 => 0 pairs (X) A8,A9: 3.. / A8 = 3 => 0 pairs (X) / A9 = 3 => 0 pairs (_) H8,G9: 3.. / H8 = 3 => 0 pairs (*) / G9 = 3 => 0 pairs (X) B1,D1: 3.. / B1 = 3 => 0 pairs (*) / D1 = 3 => 0 pairs (X) F2,H2: 3.. / F2 = 3 => 0 pairs (*) / H2 = 3 => 0 pairs (X) C3,I3: 3.. / C3 = 3 => 0 pairs (X) / I3 = 3 => 0 pairs (_) A8,H8: 3.. / A8 = 3 => 0 pairs (X) / H8 = 3 => 0 pairs (_) A9,G9: 3.. / A9 = 3 => 0 pairs (*) / G9 = 3 => 0 pairs (X) B1,B4: 3.. / B1 = 3 => 0 pairs (*) / B4 = 3 => 0 pairs (X) C3,C4: 3.. / C3 = 3 => 0 pairs (X) / C4 = 3 => 0 pairs (_) D1,D6: 3.. / D1 = 3 => 0 pairs (X) / D6 = 3 => 0 pairs (_) F2,F6: 3.. / F2 = 3 => 0 pairs (*) / F6 = 3 => 0 pairs (X) G5,G9: 3.. / G5 = 3 => 0 pairs (*) / G9 = 3 => 0 pairs (X) H2,H8: 3.. / H2 = 3 => 0 pairs (X) / H8 = 3 => 0 pairs (_) I3,I5: 3.. / I3 = 3 => 0 pairs (*) / I5 = 3 => 0 pairs (X) G1,I1: 4.. / G1 = 4 => 0 pairs (X) / I1 = 4 => 0 pairs (_) G6,I6: 4.. / G6 = 4 => 0 pairs (*) / I6 = 4 => 0 pairs (X) G1,G6: 4.. / G1 = 4 => 0 pairs (X) / G6 = 4 => 0 pairs (_) I1,I6: 4.. / I1 = 4 => 0 pairs (*) / I6 = 4 => 0 pairs (X) B1,C3: 5.. / B1 = 5 => 0 pairs (X) / C3 = 5 => 0 pairs (_) D1,E2: 5.. / D1 = 5 => 0 pairs (*) / E2 = 5 => 0 pairs (X) H2,I3: 5.. / H2 = 5 => 0 pairs (*) / I3 = 5 => 0 pairs (X) D6,E6: 5.. / D6 = 5 => 0 pairs (X) / E6 = 5 => 0 pairs (_) G5,I5: 5.. / G5 = 5 => 0 pairs (X) / I5 = 5 => 0 pairs (_) F8,F9: 5.. / F8 = 5 => 0 pairs (X) / F9 = 5 => 0 pairs (_) B1,D1: 5.. / B1 = 5 => 0 pairs (X) / D1 = 5 => 0 pairs (_) E2,H2: 5.. / E2 = 5 => 0 pairs (X) / H2 = 5 => 0 pairs (_) C3,I3: 5.. / C3 = 5 => 0 pairs (*) / I3 = 5 => 0 pairs (X) C7,G7: 5.. / C7 = 5 => 0 pairs (X) / G7 = 5 => 0 pairs (_) B1,B4: 5.. / B1 = 5 => 0 pairs (X) / B4 = 5 => 0 pairs (_) D1,D6: 5.. / D1 = 5 => 0 pairs (*) / D6 = 5 => 0 pairs (X) E2,E6: 5.. / E2 = 5 => 0 pairs (X) / E6 = 5 => 0 pairs (_) H2,H8: 5.. / H2 = 5 => 0 pairs (*) / H8 = 5 => 0 pairs (X) I3,I5: 5.. / I3 = 5 => 0 pairs (X) / I5 = 5 => 0 pairs (_) G1,I1: 6.. / G1 = 6 => 0 pairs (*) / I1 = 6 => 0 pairs (X) A4,C4: 6.. / A4 = 6 => 0 pairs (*) / C4 = 6 => 0 pairs (X) C7,A8: 6.. / C7 = 6 => 0 pairs (*) / A8 = 6 => 0 pairs (X) G7,I8: 6.. / G7 = 6 => 0 pairs (X) / I8 = 6 => 0 pairs (_) C7,G7: 6.. / C7 = 6 => 0 pairs (*) / G7 = 6 => 0 pairs (X) A8,I8: 6.. / A8 = 6 => 0 pairs (X) / I8 = 6 => 0 pairs (_) A4,A8: 6.. / A4 = 6 => 0 pairs (*) / A8 = 6 => 0 pairs (X) C4,C7: 6.. / C4 = 6 => 0 pairs (X) / C7 = 6 => 0 pairs (_) G1,G7: 6.. / G1 = 6 => 0 pairs (*) / G7 = 6 => 0 pairs (X) I1,I8: 6.. / I1 = 6 => 0 pairs (X) / I8 = 6 => 0 pairs (_) G6,I6: 8.. / G6 = 8 => 0 pairs (X) / I6 = 8 => 0 pairs (_) F8,F9: 8.. / F8 = 8 => 0 pairs (*) / F9 = 8 => 0 pairs (X) I8,G9: 8.. / I8 = 8 => 0 pairs (X) / G9 = 8 => 0 pairs (_) F8,I8: 8.. / F8 = 8 => 0 pairs (*) / I8 = 8 => 0 pairs (X) F9,G9: 8.. / F9 = 8 => 0 pairs (X) / G9 = 8 => 0 pairs (_) G6,G9: 8.. / G6 = 8 => 0 pairs (X) / G9 = 8 => 0 pairs (_) I6,I8: 8.. / I6 = 8 => 0 pairs (*) / I8 = 8 => 0 pairs (X) E2,F2: 9.. / E2 = 9 => 0 pairs (*) / F2 = 9 => 0 pairs (X) E6,F6: 9.. / E6 = 9 => 0 pairs (X) / F6 = 9 => 0 pairs (_) E2,E6: 9.. / E2 = 9 => 0 pairs (*) / E6 = 9 => 0 pairs (X) F2,F6: 9.. / F2 = 9 => 0 pairs (X) / F6 = 9 => 0 pairs (_) * DURATION: 0:02:05.592195 START: 09:09:10.095460 END: 09:11:15.687655 2017-05-04 * CP COUNT: (60) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A9,B1,B4,C3,C7,D1,D6,E2,E6,F2,F6,F8,F9,G1,G5,G6,G7,H2,H8,I1,I3,I5,I6,I8) * 2.9.71.8.8642..7.171.84692....784219498612.7.172....6.98.137.42.4792.1...2146..97 * PAIR C3: 3,5 COL C C4: 3,5,6 # reduction candidate for 3,5 C4: 3,5 => SOLVED * 239571684864293751715846923653784219498612375172359468986137542547928136321465897 C4: 6 => CTR * 2.9.71.8.8642..7.1713846925.36784219498612573172....6.98513764264792.1...2146..97 * PAIR A4: 5,6 BLK 4 C4: 5,6,3 # reduction candidate for 5,6 C4: 5,6 => CTR * 2.9.71.8.8642..7.1713846925.3.784219498612573172....6.98513764264792.1...2146..97 C4: 3 => SOLVED * 239571684864293751715846923653784219498612375172359468986137542547928136321465897 * PAIR A4: 5,6 COL A A8: 5,6,3 # reduction candidate for 5,6 A8: 5,6 => SOLVED * 239571684864293751715846923653784219498612375172359468986137542547928136321465897 A8: 3 => CTR * 2.9.71.8.8642..7.171.84692.6..784219498612.7.172....6.98613754234792.1...2146..97 * PAIR B4: 3,5 BLK 4 C4: 3,5,6 # reduction candidate for 3,5 C4: 3,5 => SOLVED * 239571684864293751715846923653784219498612375172359468986137542547928136321465897 C4: 6 => CTR * 2.9.71.8.8642..7.1713846925.36784219498612573172....6.98513764264792.1...2146..97 * PAIR G5: 3,5 COL G G9: 3,5,8 # reduction candidate for 3,5 G9: 3,5 => CTR * 2.9.714868642.375171584692....784219498612.7.172...86498.137642647925138321468597 G9: 8 => SOLVED * 239571684864293751715846923653784219498612375172359468986137542547928136321465897 * PAIR C7: 5,6 BLK 7 A8: 5,6,3 # reduction candidate for 5,6 A8: 5,6 => SOLVED * 239571684864293751715846923653784219498612375172359468986137542547928136321465897 A8: 3 => CTR * 2.9.71.8.8642..7.171.84692.6..784219498612.7.172....6.98613754234792.1...2146..97 * PAIR C7: 5,6 COL C C4: 5,6,3 # reduction candidate for 5,6 C4: 5,6 => CTR * 2.9.71.8.8642..7.1713846925.3.784219498612573172....6.98513764264792.1...2146..97 C4: 3 => SOLVED * 239571684864293751715846923653784219498612375172359468986137542547928136321465897 * PAIR A9: 3,5 BLK 7 A8: 3,5,6 # reduction candidate for 3,5 A8: 3,5 => SOLVED * 239571684864293751715846923653784219498612375172359468986137542547928136321465897 A8: 6 => CTR * 2.9.71.868642.375171584692....784219498612.7.172....6.98.137.4264792.138321468597 * PAIR A9: 3,5 ROW 9 G9: 3,5,8 # reduction candidate for 3,5 G9: 3,5 => CTR * 2.9.714868642.375171584692....784219498612.7.172...86498.137642647925138321468597 G9: 8 => SOLVED * 239571684864293751715846923653784219498612375172359468986137542547928136321465897 * PAIR F9: 5,8 ROW 9 G9: 5,8,3 # reduction candidate for 5,8 G9: 5,8 => SOLVED * 239571684864293751715846923653784219498612375172359468986137542547928136321465897 G9: 3 => CTR * 2.9.71.8.8642..7.171.84692....784219498612.7.172...86498.137.42.4792.1.8.21468397 * PAIR H8: 3,5 BLK 9 G9: 3,5,8 # reduction candidate for 3,5 G9: 3,5 => CTR * 2.9.714868642.375171584692....784219498612.7.172...86498.137642647925138321468597 G9: 8 => SOLVED * 239571684864293751715846923653784219498612375172359468986137542547928136321465897 * PAIR H8: 3,5 ROW 8 A8: 3,5,6 # reduction candidate for 3,5 A8: 3,5 => SOLVED * 239571684864293751715846923653784219498612375172359468986137542547928136321465897 A8: 6 => CTR * 2.9.71.868642.375171584692....784219498612.7.172....6.98.137.4264792.138321468597 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-189-base-pr-000.dot * REASONING * PRF # C4: 3,5 => SOL * DIS # C4: 6 => CTR => C4: 3,5 * DIS # C4: 5,6 => CTR => C4: 3 * PRF # C4: 3 => SOL * PRF # A8: 5,6 => SOL * DIS # A8: 3 => CTR => A8: 5,6 * PRF # C4: 3,5 => SOL * DIS # C4: 6 => CTR => C4: 3,5 * DIS # G9: 3,5 => CTR => G9: 8 * PRF # G9: 8 => SOL * PRF # A8: 5,6 => SOL * DIS # A8: 3 => CTR => A8: 5,6 * DIS # C4: 5,6 => CTR => C4: 3 * PRF # C4: 3 => SOL * PRF # A8: 3,5 => SOL * DIS # A8: 6 => CTR => A8: 3,5 * DIS # G9: 3,5 => CTR => G9: 8 * PRF # G9: 8 => SOL * PRF # G9: 5,8 => SOL * DIS # G9: 3 => CTR => G9: 5,8 * DIS # G9: 3,5 => CTR => G9: 8 * PRF # G9: 8 => SOL * PRF # A8: 3,5 => SOL * DIS # A8: 6 => CTR => A8: 3,5 * CNT 24 HDP CHAINS / 24 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A9,B1,B4,C3,C7,D1,D6,E2,E6,F2,F6,F8,F9,G1,G5,G6,G7,H2,H8,I1,I3,I5,I6,I8) * 2.9.71.8.8642..7.171.84692....784219498612.7.172....6.98.137.42.4792.1...2146..97 * PAIR C3: 3,5 COL C C4: 3,5,6 # reduction candidate for 3,5 C4: 3,5 => SOLVED * 239571684864293751715846923653784219498612375172359468986137542547928136321465897 * DURATION: 0:00:02.350970 START: 09:11:49.973294 END: 09:11:52.324264 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-189-base-pr-001.dot * REASONING * PRF # C4: 3,5 => SOL * STA C4: 3,5 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 189 solution: 239571684864293751715846923653784219498612375172359468986137542547928136321465897 info: 1836 FNBTWY S8.f 41070 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 239571684864293751715846923653784219498612375172359468986137542547928136321465897 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:
* PRF # C4: 3,5 => SOL * DIS # C4: 6 => CTR => C4: 3,5 * DIS # C4: 5,6 => CTR => C4: 3 * PRF # C4: 3 => SOL * PRF # A8: 5,6 => SOL * DIS # A8: 3 => CTR => A8: 5,6 * PRF # C4: 3,5 => SOL * DIS # C4: 6 => CTR => C4: 3,5 * DIS # G9: 3,5 => CTR => G9: 8 * PRF # G9: 8 => SOL * PRF # A8: 5,6 => SOL * DIS # A8: 3 => CTR => A8: 5,6 * DIS # C4: 5,6 => CTR => C4: 3 * PRF # C4: 3 => SOL * PRF # A8: 3,5 => SOL * DIS # A8: 6 => CTR => A8: 3,5 * DIS # G9: 3,5 => CTR => G9: 8 * PRF # G9: 8 => SOL * PRF # G9: 5,8 => SOL * DIS # G9: 3 => CTR => G9: 5,8 * DIS # G9: 3,5 => CTR => G9: 8 * PRF # G9: 8 => SOL * PRF # A8: 3,5 => SOL * DIS # A8: 6 => CTR => A8: 3,5 * CNT 24 HDP CHAINS / 24 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C4: 3,5 => SOL * STA C4: 3,5 * CNT 1 HDP CHAINS / 1 HYP OPENED