Analysis of xx-top500-460-base.sdk
Contents
Original Sudoku
level: medium
position: 5...8.2..74..................2.5.......6....78......4..6.7.......1...5.....3.4... initial
Autosolve
position: 5...8.2..74..................2.5.......6....78......4..6.7.5.....1...5.....3.4... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A7: 2,9 => CTR => A7: 3,4 * DIS # A8: 2,9 => CTR => A8: 3,4 * PRF # B8: 2,9 => SOL * DIS # B8: 3,7 => CTR => B8: 2,9 * DIS # B9: 2,9 => CTR => B9: 5,7,8 * PRF # A3: 2,9 => SOL * DIS # A3: 1,3,6 => CTR => A3: 2,9 * CNT 7 HDP CHAINS / 13 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A7: 2,9 => CTR => A7: 3,4 * DIS A7: 3,4 # A8: 2,9 => CTR => A8: 3,4 * PRF A7: 3,4 + A8: 3,4 => SOL * STA A7: 3,4 + A8: 3,4 * CNT 3 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 5...8.2..74..................2.5.......6....78......4..6.7.......1...5.....3.4... | initial |
| 5...8.2..74..................2.5.......6....78......4..6.7.5.....1...5.....3.4... | autosolve |
| 516987234743261985289543716672458391194632857835179642368715429421896573957324168 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (3) H5: 2,5 I6: 2,5 A9: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E7,E9: 1.. / E7 = 1 => 3 pairs (_) / E9 = 1 => 4 pairs (_) A3,B3: 2.. / A3 = 2 => 0 pairs (*) / B3 = 2 => 0 pairs (X) H5,I6: 2.. / H5 = 2 => 1 pairs (_) / I6 = 2 => 0 pairs (*) D4,E5: 4.. / D4 = 4 => 0 pairs (*) / E5 = 4 => 0 pairs (X) D1,I1: 4.. / D1 = 4 => 0 pairs (X) / I1 = 4 => 0 pairs (_) A4,D4: 4.. / A4 = 4 => 0 pairs (X) / D4 = 4 => 0 pairs (_) A8,I8: 4.. / A8 = 4 => 0 pairs (*) / I8 = 4 => 0 pairs (X) C5,C7: 4.. / C5 = 4 => 0 pairs (*) / C7 = 4 => 0 pairs (X) E3,E5: 4.. / E3 = 4 => 0 pairs (*) / E5 = 4 => 0 pairs (X) G3,G7: 4.. / G3 = 4 => 0 pairs (X) / G7 = 4 => 0 pairs (_) D2,D3: 5.. / D2 = 5 => 3 pairs (_) / D3 = 5 => 3 pairs (_) H5,I6: 5.. / H5 = 5 => 0 pairs (*) / I6 = 5 => 0 pairs (X) B9,C9: 5.. / B9 = 5 => 0 pairs (*) / C9 = 5 => 0 pairs (X) A4,C6: 6.. / A4 = 6 => 0 pairs (*) / C6 = 6 => 0 pairs (X) C6,G6: 6.. / C6 = 6 => 0 pairs (X) / G6 = 6 => 0 pairs (_) A3,A4: 6.. / A3 = 6 => 0 pairs (X) / A4 = 6 => 0 pairs (_) F1,H1: 7.. / F1 = 7 => 0 pairs (*) / H1 = 7 => 0 pairs (X) B4,F4: 7.. / B4 = 7 => 0 pairs (*) / F4 = 7 => 0 pairs (X) B8,H8: 7.. / B8 = 7 => 0 pairs (X) / H8 = 7 => 0 pairs (_) C6,C9: 7.. / C6 = 7 => 0 pairs (X) / C9 = 7 => 0 pairs (_) E3,E6: 7.. / E3 = 7 => 0 pairs (X) / E6 = 7 => 0 pairs (_) G3,G9: 7.. / G3 = 7 => 0 pairs (*) / G9 = 7 => 0 pairs (X) D8,F8: 8.. / D8 = 8 => 3 pairs (_) / F8 = 8 => 0 pairs (X) F5,G5: 8.. / F5 = 8 => 3 pairs (_) / G5 = 8 => 3 pairs (_) B3,B9: 8.. / B3 = 8 => 0 pairs (*) / B9 = 8 => 0 pairs (X) D4,D8: 8.. / D4 = 8 => 0 pairs (X) / D8 = 8 => 3 pairs (_) * DURATION: 0:00:41.017159 START: 18:27:15.608401 END: 18:27:56.625560 2017-05-04 * CP COUNT: (26) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,H5,I6) * 5...8.2..74..................2.5.......6....78......4..6.7.5.....1...5.....3.4... * PAIR A9: 2,9 BLK 7 A7: 2,9,3,4 # reduction candidate for 2,9 A7: 2,9 => CTR * 5...8.2..74........2..7....6.2457......6.8..78.7...64..6.7.5....718..5...853.47.. A7: 3,4 # 4 pairs A8: 2,9,3,4 # reduction candidate for 2,9 A8: 2,9 => CTR * 5..48.2..74.............4..4.2.5.......64...78.6....4..647.5.....1...5.4..73.4... A8: 3,4 # 4 pairs B8: 2,9,3,7 # reduction candidate for 2,9 B8: 2,9 => SOLVED * 516987234743261985289543716672458391194632857835179642368715429421896573957324168 B8: 3,7 => CTR * 5...8.2..74...........7....6.2457......6.8..78.7...64..6.7.5....718..5....53.47.. B9: 2,9,5,7,8 # reduction candidate for 2,9 B9: 2,9 => CTR * 5...8.2..74.......28.......6.245....1.46....78.7...64..687.5....718..5..9253.4... B9: 5,7,8 # 3 pairs * PAIR A9: 2,9 ROW 9 E9: 2,9,1,6 # reduction candidate for 2,9 E9: 2,9 # 4 pairs H9: 2,9,1,6,7,8 # reduction candidate for 2,9 H9: 2,9 # 5 pairs I9: 2,9,1,6,8 # reduction candidate for 2,9 I9: 2,9 # 5 pairs * PAIR A9: 2,9 COL A A3: 2,9,1,3,6 # reduction candidate for 2,9 A3: 2,9 => SOLVED * 516987234743261985289543716672458391194632857835179642368715429421896573957324168 A3: 1,3,6 => CTR * 5...8.2..74........2..7....6.2457......6.8..78.7...64..6.7.5....718..5...853.47.. * INCONCLUSIVE * SAVE PR GRAPH xx-top500-460-base-pr-000.dot * REASONING * DIS # A7: 2,9 => CTR => A7: 3,4 * DIS # A8: 2,9 => CTR => A8: 3,4 * PRF # B8: 2,9 => SOL * DIS # B8: 3,7 => CTR => B8: 2,9 * DIS # B9: 2,9 => CTR => B9: 5,7,8 * PRF # A3: 2,9 => SOL * DIS # A3: 1,3,6 => CTR => A3: 2,9 * CNT 7 HDP CHAINS / 13 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,H5,I6) * 5...8.2..74..................2.5.......6....78......4..6.7.5.....1...5.....3.4... * PAIR A9: 2,9 BLK 7 A7: 2,9,3,4 # reduction candidate for 2,9 A7: 2,9 => CTR * 5...8.2..74........2..7....6.2457......6.8..78.7...64..6.7.5....718..5...853.47.. A8: 2,9,3,4 # reduction candidate for 2,9 A8: 2,9 => CTR * 5..48.2..74.............4..4.2.5.......64...78.6....4.3647.5.....1...534..73.4... A8: 3,4 => SOLVED * 516987234743261985289543716672458391194632857835179642368715429421896573957324168 * DURATION: 0:00:02.815790 START: 18:28:06.916673 END: 18:28:09.732463 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-460-base-pr-001.dot * REASONING * DIS # A7: 2,9 => CTR => A7: 3,4 * DIS A7: 3,4 # A8: 2,9 => CTR => A8: 3,4 * PRF A7: 3,4 + A8: 3,4 => SOL * STA A7: 3,4 + A8: 3,4 * CNT 3 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 460 solution: 516987234743261985289543716672458391194632857835179642368715429421896573957324168 info: 95529 FNBHWYK S8.f 32602 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 516987234743261985289543716672458391194632857835179642368715429421896573957324168 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 # A7: 2,9 => CTR => A7: 3,4 * INC # A7: 3,4 => UNS * DIS # A8: 2,9 => CTR => A8: 3,4 * INC # A8: 3,4 => UNS * PRF # B8: 2,9 => SOL * DIS # B8: 3,7 => CTR => B8: 2,9 * DIS # B9: 2,9 => CTR => B9: 5,7,8 * INC # B9: 5,7,8 => UNS * INC # E9: 2,9 => UNS * INC # H9: 2,9 => UNS * INC # I9: 2,9 => UNS * PRF # A3: 2,9 => SOL * DIS # A3: 1,3,6 => CTR => A3: 2,9 * CNT 13 HDP CHAINS / 13 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A7: 2,9 => CTR => A7: 3,4 * DIS A7: 3,4 # A8: 2,9 => CTR => A8: 3,4 * PRF A7: 3,4 + A8: 3,4 => SOL * STA A7: 3,4 + A8: 3,4 * CNT 3 HDP CHAINS / 2 HYP OPENED