Analysis of xx-top500-172-base.sdk
Contents
Original Sudoku
level: medium
position: 2.....1.3...5.7...............83...2.71.............6.3...2.4...6....75.......... initial
Autosolve
position: 257.4.1.313.5.76246.43125.75468319728712693459234758613.572.41.4621.375.71..5423. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I7: 8,9 => CTR => I7: 6 * PRF # I7: 6 => SOL * PRF # I9: 8,9 => SOL * DIS # I9: 6 => CTR => I9: 8,9 * PRF # I7: 6,8 => SOL * DIS # I7: 9 => CTR => I7: 6,8 * PRF # I9: 6,9 => SOL * DIS # I9: 8 => CTR => I9: 6,9 * DIS # I7: 8,9 => CTR => I7: 6 * PRF # I7: 6 => SOL * PRF # I9: 8,9 => SOL * DIS # I9: 6 => CTR => I9: 8,9 * CNT 12 HDP CHAINS / 12 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I7: 8,9 => CTR => I7: 6 * PRF I7: 6 => SOL * STA I7: 6 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 2.....1.3...5.7...............83...2.71.............6.3...2.4...6....75.......... | initial |
| 257.4.1.313.5.76246.43125.75468319728712693459234758613.572.41.4621.375.71..5423. | autosolve |
| 257946183139587624684312597546831972871269345923475861395728416462193758718654239 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) C2: 8,9 B3: 8,9 D1: 6,9 F1: 6,8 E2: 8,9 H1: 8,9 H3: 8,9 B7: 8,9 C9: 8,9 F7: 6,8 E8: 8,9 D9: 6,9 I8: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,F1: 6.. / D1 = 6 => 0 pairs (X) / F1 = 6 => 0 pairs (_) F7,D9: 6.. / F7 = 6 => 0 pairs (X) / D9 = 6 => 0 pairs (_) I7,I9: 6.. / I7 = 6 => 0 pairs (*) / I9 = 6 => 0 pairs (X) F7,I7: 6.. / F7 = 6 => 0 pairs (X) / I7 = 6 => 0 pairs (_) D9,I9: 6.. / D9 = 6 => 0 pairs (*) / I9 = 6 => 0 pairs (X) D1,D9: 6.. / D1 = 6 => 0 pairs (X) / D9 = 6 => 0 pairs (_) F1,F7: 6.. / F1 = 6 => 0 pairs (*) / F7 = 6 => 0 pairs (X) C2,B3: 8.. / C2 = 8 => 0 pairs (X) / B3 = 8 => 0 pairs (_) F1,E2: 8.. / F1 = 8 => 0 pairs (X) / E2 = 8 => 0 pairs (_) H1,H3: 8.. / H1 = 8 => 0 pairs (*) / H3 = 8 => 0 pairs (X) B7,C9: 8.. / B7 = 8 => 0 pairs (X) / C9 = 8 => 0 pairs (_) F7,E8: 8.. / F7 = 8 => 0 pairs (*) / E8 = 8 => 0 pairs (X) F1,H1: 8.. / F1 = 8 => 0 pairs (X) / H1 = 8 => 0 pairs (_) C2,E2: 8.. / C2 = 8 => 0 pairs (X) / E2 = 8 => 0 pairs (_) B3,H3: 8.. / B3 = 8 => 0 pairs (*) / H3 = 8 => 0 pairs (X) E8,I8: 8.. / E8 = 8 => 0 pairs (X) / I8 = 8 => 0 pairs (_) C9,I9: 8.. / C9 = 8 => 0 pairs (*) / I9 = 8 => 0 pairs (X) B3,B7: 8.. / B3 = 8 => 0 pairs (*) / B7 = 8 => 0 pairs (X) C2,C9: 8.. / C2 = 8 => 0 pairs (X) / C9 = 8 => 0 pairs (_) E2,E8: 8.. / E2 = 8 => 0 pairs (*) / E8 = 8 => 0 pairs (X) F1,F7: 8.. / F1 = 8 => 0 pairs (X) / F7 = 8 => 0 pairs (_) C2,B3: 9.. / C2 = 9 => 0 pairs (*) / B3 = 9 => 0 pairs (X) D1,E2: 9.. / D1 = 9 => 0 pairs (*) / E2 = 9 => 0 pairs (X) H1,H3: 9.. / H1 = 9 => 0 pairs (X) / H3 = 9 => 0 pairs (_) B7,C9: 9.. / B7 = 9 => 0 pairs (*) / C9 = 9 => 0 pairs (X) E8,D9: 9.. / E8 = 9 => 0 pairs (*) / D9 = 9 => 0 pairs (X) D1,H1: 9.. / D1 = 9 => 0 pairs (*) / H1 = 9 => 0 pairs (X) C2,E2: 9.. / C2 = 9 => 0 pairs (*) / E2 = 9 => 0 pairs (X) B3,H3: 9.. / B3 = 9 => 0 pairs (X) / H3 = 9 => 0 pairs (_) B7,I7: 9.. / B7 = 9 => 0 pairs (*) / I7 = 9 => 0 pairs (X) E8,I8: 9.. / E8 = 9 => 0 pairs (*) / I8 = 9 => 0 pairs (X) B3,B7: 9.. / B3 = 9 => 0 pairs (X) / B7 = 9 => 0 pairs (_) C2,C9: 9.. / C2 = 9 => 0 pairs (*) / C9 = 9 => 0 pairs (X) D1,D9: 9.. / D1 = 9 => 0 pairs (*) / D9 = 9 => 0 pairs (X) E2,E8: 9.. / E2 = 9 => 0 pairs (X) / E8 = 9 => 0 pairs (_) * DURATION: 0:01:02.336017 START: 08:36:26.156401 END: 08:37:28.492418 2017-05-04 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B7,C2,C9,D1,D9,E2,E8,F1,F7,H1,H3,I8) * 257.4.1.313.5.76246.43125.75468319728712693459234758613.572.41.4621.375.71..5423. * PAIR B7: 8,9 ROW 7 I7: 8,9,6 # reduction candidate for 8,9 I7: 8,9 => CTR * 257.4.1.313.5.76246.43125.75468319728712693459234758613.572641.46218375971.954236 I7: 6 => SOLVED * 257946183139587624684312597546831972871269345923475861395728416462193758718654239 * PAIR C9: 8,9 ROW 9 I9: 8,9,6 # reduction candidate for 8,9 I9: 8,9 => SOLVED * 257946183139587624684312597546831972871269345923475861395728416462193758718654239 I9: 6 => CTR * 257.4.1.313.5.76246.43125.75468319728712693459234758613.572.41.4621.375.718954236 * PAIR F7: 6,8 ROW 7 I7: 6,8,9 # reduction candidate for 6,8 I7: 6,8 => SOLVED * 257946183139587624684312597546831972871269345923475861395728416462193758718654239 I7: 9 => CTR * 257.4.1.313.5.76246.43125.75468319728712693459234758613.57264194621.375.71..5423. * PAIR D9: 6,9 ROW 9 I9: 6,9,8 # reduction candidate for 6,9 I9: 6,9 => SOLVED * 257946183139587624684312597546831972871269345923475861395728416462193758718654239 I9: 8 => CTR * 257.4.1.313.5.76246.43125.75468319728712693459234758613.572.4164621.375971..5423. * PAIR I8: 8,9 BLK 9 I7: 8,9,6 # reduction candidate for 8,9 I7: 8,9 => CTR * 257.4.1.313.5.76246.43125.75468319728712693459234758613.572641.46218375971.954236 I7: 6 => SOLVED * 257946183139587624684312597546831972871269345923475861395728416462193758718654239 I9: 8,9,6 # reduction candidate for 8,9 I9: 8,9 => SOLVED * 257946183139587624684312597546831972871269345923475861395728416462193758718654239 I9: 6 => CTR * 257.4.1.313.5.76246.43125.75468319728712693459234758613.572.41.4621.375.718954236 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-172-base-pr-000.dot * REASONING * DIS # I7: 8,9 => CTR => I7: 6 * PRF # I7: 6 => SOL * PRF # I9: 8,9 => SOL * DIS # I9: 6 => CTR => I9: 8,9 * PRF # I7: 6,8 => SOL * DIS # I7: 9 => CTR => I7: 6,8 * PRF # I9: 6,9 => SOL * DIS # I9: 8 => CTR => I9: 6,9 * DIS # I7: 8,9 => CTR => I7: 6 * PRF # I7: 6 => SOL * PRF # I9: 8,9 => SOL * DIS # I9: 6 => CTR => I9: 8,9 * CNT 12 HDP CHAINS / 12 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B7,C2,C9,D1,D9,E2,E8,F1,F7,H1,H3,I8) * 257.4.1.313.5.76246.43125.75468319728712693459234758613.572.41.4621.375.71..5423. * PAIR B7: 8,9 ROW 7 I7: 8,9,6 # reduction candidate for 8,9 I7: 8,9 => CTR * 257.4.1.313.5.76246.43125.75468319728712693459234758613.572641.46218375971.954236 I7: 6 => SOLVED * 257946183139587624684312597546831972871269345923475861395728416462193758718654239 * DURATION: 0:00:03.148229 START: 08:37:44.880379 END: 08:37:48.028608 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-172-base-pr-001.dot * REASONING * DIS # I7: 8,9 => CTR => I7: 6 * PRF I7: 6 => SOL * STA I7: 6 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 172 solution: 257946183139587624684312597546831972871269345923475861395728416462193758718654239 info: 1826 FNTWX S8.f 26887 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 257946183139587624684312597546831972871269345923475861395728416462193758718654239 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 # I7: 8,9 => CTR => I7: 6 * PRF # I7: 6 => SOL * PRF # I9: 8,9 => SOL * DIS # I9: 6 => CTR => I9: 8,9 * PRF # I7: 6,8 => SOL * DIS # I7: 9 => CTR => I7: 6,8 * PRF # I9: 6,9 => SOL * DIS # I9: 8 => CTR => I9: 6,9 * DIS # I7: 8,9 => CTR => I7: 6 * PRF # I7: 6 => SOL * PRF # I9: 8,9 => SOL * DIS # I9: 6 => CTR => I9: 8,9 * CNT 12 HDP CHAINS / 12 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # I7: 8,9 => CTR => I7: 6 * PRF I7: 6 => SOL * STA I7: 6 * CNT 2 HDP CHAINS / 1 HYP OPENED