Analysis of xx-top95-086-base.sdk
Contents
Original Sudoku
level: medium
position: .32.....58..3.....9.428...1...4...39...6...5.....1.....2...67.8.....4....95....6. initial
Autosolve
position: .32.....585.3..9..964285371...4...39...6...5.....1....42...67.8.....45...95....6. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A4: 1,7 => CTR => A4: 2,5,6 * DIS # A5: 1,7 => CTR => A5: 2,3 * DIS # A8: 1,7 => CTR => A8: 3,6 * DIS # A8: 1,3 => CTR => A8: 6,7 * PRF # C8: 1,3 => SOL * DIS # D8: 7 => CTR => D8: 1,9 * PRF # E8: 7,9 => SOL * CNT 7 HDP CHAINS / 47 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A4: 1,7 => CTR => A4: 2,5,6 * DIS A4: 2,5,6 # A5: 1,7 => CTR => A5: 2,3 * DIS A4: 2,5,6 + A5: 2,3 # A8: 1,7 => CTR => A8: 3,6 * DIS A4: 2,5,6 + A5: 2,3 + A8: 3,6 # A9: 3 => CTR => A9: 1,7 * PRF A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # C8: 1,3 => SOL * STA A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 + C8: 1,3 * CNT 5 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .32.....58..3.....9.428...1...4...39...6...5.....1.....2...67.8.....4....95....6. | initial |
| .32.....585.3..9..964285371...4...39...6...5.....1....42...67.8.....45...95....6. | autosolve |
| 132749685857361924964285371216457839348692157579813246421536798683974512795128463 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) A1: 1,7 C2: 1,7 E1: 4,6 E2: 4,6 F2: 1,7 H1: 4,8 H2: 2,4 C7: 1,3 H7: 1,9 H8: 1,9 I8: 2,3 G9: 2,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,C2: 1.. / A1 = 1 => 23 pairs (_) / C2 = 1 => 0 pairs (X) G4,G5: 1.. / G4 = 1 => 13 pairs (_) / G5 = 1 => 12 pairs (_) H7,H8: 1.. / H7 = 1 => 16 pairs (_) / H8 = 1 => 14 pairs (_) C2,F2: 1.. / C2 = 1 => 0 pairs (X) / F2 = 1 => 23 pairs (_) H2,I2: 2.. / H2 = 2 => 13 pairs (_) / I2 = 2 => 11 pairs (_) E8,I8: 2.. / E8 = 2 => 14 pairs (_) / I8 = 2 => 17 pairs (_) H2,H6: 2.. / H2 = 2 => 13 pairs (_) / H6 = 2 => 11 pairs (_) I8,I9: 3.. / I8 = 3 => 14 pairs (_) / I9 = 3 => 17 pairs (_) C7,E7: 3.. / C7 = 3 => 16 pairs (_) / E7 = 3 => 22 pairs (_) E1,E2: 4.. / E1 = 4 => 11 pairs (_) / E2 = 4 => 11 pairs (_) B5,B6: 4.. / B5 = 4 => 14 pairs (_) / B6 = 4 => 15 pairs (_) G9,I9: 4.. / G9 = 4 => 15 pairs (_) / I9 = 4 => 14 pairs (_) A4,A6: 5.. / A4 = 5 => 18 pairs (_) / A6 = 5 => 13 pairs (_) E4,D6: 5.. / E4 = 5 => 13 pairs (_) / D6 = 5 => 18 pairs (_) D7,E7: 5.. / D7 = 5 => 13 pairs (_) / E7 = 5 => 18 pairs (_) A4,E4: 5.. / A4 = 5 => 18 pairs (_) / E4 = 5 => 13 pairs (_) A6,D6: 5.. / A6 = 5 => 13 pairs (_) / D6 = 5 => 18 pairs (_) D6,D7: 5.. / D6 = 5 => 18 pairs (_) / D7 = 5 => 13 pairs (_) E4,E7: 5.. / E4 = 5 => 13 pairs (_) / E7 = 5 => 18 pairs (_) E1,E2: 6.. / E1 = 6 => 11 pairs (_) / E2 = 6 => 11 pairs (_) G1,I2: 6.. / G1 = 6 => 11 pairs (_) / I2 = 6 => 11 pairs (_) A8,C8: 6.. / A8 = 6 => 12 pairs (_) / C8 = 6 => 0 pairs (X) E1,G1: 6.. / E1 = 6 => 11 pairs (_) / G1 = 6 => 11 pairs (_) E2,I2: 6.. / E2 = 6 => 11 pairs (_) / I2 = 6 => 11 pairs (_) I2,I6: 6.. / I2 = 6 => 11 pairs (_) / I6 = 6 => 11 pairs (_) A1,C2: 7.. / A1 = 7 => 0 pairs (X) / C2 = 7 => 23 pairs (_) I5,I6: 7.. / I5 = 7 => 12 pairs (_) / I6 = 7 => 15 pairs (_) C2,F2: 7.. / C2 = 7 => 23 pairs (_) / F2 = 7 => 0 pairs (X) G1,H1: 8.. / G1 = 8 => 9 pairs (_) / H1 = 8 => 13 pairs (_) B8,C8: 8.. / B8 = 8 => 16 pairs (_) / C8 = 8 => 14 pairs (_) D9,F9: 8.. / D9 = 8 => 12 pairs (_) / F9 = 8 => 24 pairs (_) D6,D9: 8.. / D6 = 8 => 24 pairs (_) / D9 = 8 => 12 pairs (_) H1,H6: 8.. / H1 = 8 => 13 pairs (_) / H6 = 8 => 9 pairs (_) D1,F1: 9.. / D1 = 9 => 16 pairs (_) / F1 = 9 => 13 pairs (_) C5,C6: 9.. / C5 = 9 => 14 pairs (_) / C6 = 9 => 12 pairs (_) H7,H8: 9.. / H7 = 9 => 14 pairs (_) / H8 = 9 => 16 pairs (_) * DURATION: 0:00:52.761292 START: 00:55:48.657675 END: 00:56:41.418967 2017-05-04 * CP COUNT: (36) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,C2,C7,E1,E2,F2,G9,H1,H2,H7,H8,I8) * .32.....585.3..9..964285371...4...39...6...5.....1....42...67.8.....45...95....6. * PAIR A1: 1,7 ROW 1 D1: 1,7,9 # reduction candidate for 1,7 D1: 1,7 # 13 pairs F1: 1,7,9 # reduction candidate for 1,7 F1: 1,7 # 16 pairs * PAIR A1: 1,7 COL A A4: 1,7,2,5,6 # reduction candidate for 1,7 A4: 1,7 => CTR * 1327.9.858573.19.69642853717.6452.392.3697.54549813627421536798678924513395178.6. A4: 2,5,6 # 12 pairs A5: 1,7,2,3 # reduction candidate for 1,7 A5: 1,7 => CTR * 132769.858573419269642853712.6457.397..69..5.54.81.6.7421536798678924513395178.6. A5: 2,3 # 13 pairs A8: 1,7,3,6 # reduction candidate for 1,7 A8: 1,7 => CTR * 1327.9.858573.19..9642853716.845.13921.69.854549813.27421536798786924513395178.6. A8: 3,6 # 13 pairs A9: 1,7,3 # reduction candidate for 1,7 A9: 1,7 # 15 pairs * PAIR C2: 1,7 COL C C4: 1,7,6,8 # reduction candidate for 1,7 C4: 1,7 # 18 pairs C5: 1,7,3,8,9 # reduction candidate for 1,7 C5: 1,7 # 18 pairs C8: 1,7,3,6,8 # reduction candidate for 1,7 C8: 1,7 # 21 pairs * PAIR E1: 4,6 ROW 1 G1: 4,6,8 # reduction candidate for 4,6 G1: 4,6 # 13 pairs G1: 8 # 9 pairs * PAIR E2: 4,6 ROW 2 I2: 4,6,2 # reduction candidate for 4,6 I2: 4,6 # 13 pairs I2: 2 # 11 pairs * PAIR F2: 1,7 BLK 2 D1: 1,7,9 # reduction candidate for 1,7 D1: 1,7 # 13 pairs F1: 1,7,9 # reduction candidate for 1,7 F1: 1,7 # 16 pairs * PAIR F2: 1,7 COL F F9: 1,7,2,3,8 # reduction candidate for 1,7 F9: 1,7 # 17 pairs F9: 2,3,8 # 13 pairs * PAIR H1: 4,8 BLK 3 G1: 4,8,6 # reduction candidate for 4,8 G1: 6 # 11 pairs G1: 4,8 # 11 pairs * PAIR H1: 4,8 COL H H6: 4,8,2 # reduction candidate for 4,8 H6: 4,8 # 13 pairs H6: 2 # 11 pairs * PAIR H2: 2,4 BLK 3 I2: 2,4,6 # reduction candidate for 2,4 I2: 6 # 11 pairs I2: 2,4 # 11 pairs * PAIR H2: 2,4 COL H H6: 2,4,8 # reduction candidate for 2,4 H6: 2,4 # 13 pairs H6: 8 # 9 pairs * PAIR C7: 1,3 BLK 7 A8: 1,3,6,7 # reduction candidate for 1,3 A8: 1,3 => CTR * 132.....58573.192.964285371..845..392..6..85.5..81..4.421536798386..4512795128463 A8: 6,7 # 13 pairs C8: 1,3,6,7,8 # reduction candidate for 1,3 C8: 1,3 => SOLVED * 132749685857361924964285371216457839348692157579813246421536798683974512795128463 C8: 6,7,8 # 12 pairs A9: 1,3,7 # reduction candidate for 1,3 A9: 1,3 # 17 pairs * PAIR C7: 1,3 COL C C5: 1,3,7,8,9 # reduction candidate for 1,3 C5: 1,3 # 24 pairs C5: 7,8,9 # 12 pairs * PAIR H7: 1,9 ROW 7 D7: 1,9,5 # reduction candidate for 1,9 D7: 1,9 # 18 pairs D7: 5 # 13 pairs * PAIR H8: 1,9 ROW 8 D8: 1,9,7 # reduction candidate for 1,9 D8: 7 => CTR * 1329.7.858573.19.696428537167.452.392..67..5454.81.62742.5.67.8...7.45..7951.8.6. D8: 1,9 # 14 pairs * PAIR I8: 2,3 BLK 9 I9: 2,3,4 # reduction candidate for 2,3 I9: 2,3 # 15 pairs I9: 4 # 14 pairs * PAIR I8: 2,3 ROW 8 E8: 2,3,7,9 # reduction candidate for 2,3 E8: 7,9 => SOLVED * 132749685857361924964285371216457839348692157579813246421536798683974512795128463 E8: 2,3 # 13 pairs * PAIR G9: 2,4 BLK 9 I9: 2,4,3 # reduction candidate for 2,4 I9: 3 # 17 pairs I9: 2,4 # 14 pairs * PAIR G9: 2,4 COL G G5: 2,4,1,8 # reduction candidate for 2,4 G5: 2,4 # 17 pairs G6: 2,4,6,8 # reduction candidate for 2,4 G6: 2,4 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-086-base-pr-000.dot * REASONING * DIS # A4: 1,7 => CTR => A4: 2,5,6 * DIS # A5: 1,7 => CTR => A5: 2,3 * DIS # A8: 1,7 => CTR => A8: 3,6 * DIS # A8: 1,3 => CTR => A8: 6,7 * PRF # C8: 1,3 => SOL * DIS # D8: 7 => CTR => D8: 1,9 * PRF # E8: 7,9 => SOL * CNT 7 HDP CHAINS / 47 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,C2,C7,E1,E2,F2,G9,H1,H2,H7,H8,I8) * .32.....585.3..9..964285371...4...39...6...5.....1....42...67.8.....45...95....6. * PAIR A1: 1,7 ROW 1 D1: 1,7,9 # reduction candidate for 1,7 D1: 1,7 # 13 pairs F1: 1,7,9 # reduction candidate for 1,7 F1: 1,7 # 16 pairs * PAIR A1: 1,7 COL A A4: 1,7,2,5,6 # reduction candidate for 1,7 A4: 1,7 => CTR * 1327.9.858573.19.69642853717.6452.392.3697.54549813627421536798678924513395178.6. A5: 1,7,2,3 # reduction candidate for 1,7 A5: 1,7 => CTR * 132769.858573419269642853712.6457.397..69..5.54.81.6.7421536798678924513395178.6. A8: 1,7,3,6 # reduction candidate for 1,7 A8: 1,7 => CTR * 1327.9.858573.19..9642853716.845.13921.69.854549813.27421536798786924513395178.6. A9: 1,7,3 # reduction candidate for 1,7 A9: 1,7 # 15 pairs * RESTART * PAIR A1: 1,7 COL A A9: 1,7,3 # reduction candidate for 1,7 A9: 3 => CTR * 132.....58573.19..964285371...4...39...6...5.7..51....42..567.8.....45...95....6. * PAIR RESTART * PAIR A1: 1,7 ROW 1 D1: 1,7,9 # reduction candidate for 1,7 D1: 1,7 # 16 pairs F1: 1,7,9 # reduction candidate for 1,7 F1: 1,7 # 19 pairs * PAIR C2: 1,7 COL C C4: 1,7,6,8 # reduction candidate for 1,7 C4: 1,7 # 18 pairs C5: 1,7,3,8,9 # reduction candidate for 1,7 C5: 1,7 # 18 pairs C8: 1,7,3,6,8 # reduction candidate for 1,7 C8: 1,7 # 21 pairs * PAIR E1: 4,6 ROW 1 G1: 4,6,8 # reduction candidate for 4,6 G1: 4,6 # 16 pairs G1: 8 # 12 pairs * PAIR E2: 4,6 ROW 2 I2: 4,6,2 # reduction candidate for 4,6 I2: 4,6 # 16 pairs I2: 2 # 15 pairs * PAIR F2: 1,7 BLK 2 D1: 1,7,9 # reduction candidate for 1,7 D1: 1,7 # 16 pairs F1: 1,7,9 # reduction candidate for 1,7 F1: 1,7 # 19 pairs * PAIR F2: 1,7 COL F F9: 1,7,2,3,8 # reduction candidate for 1,7 F9: 1,7 # 21 pairs F9: 2,3,8 # 16 pairs * PAIR H1: 4,8 BLK 3 G1: 4,8,6 # reduction candidate for 4,8 G1: 6 # 14 pairs G1: 4,8 # 14 pairs * PAIR H1: 4,8 COL H H6: 4,8,2 # reduction candidate for 4,8 H6: 4,8 # 16 pairs H6: 2 # 15 pairs * PAIR H2: 2,4 BLK 3 I2: 2,4,6 # reduction candidate for 2,4 I2: 6 # 14 pairs I2: 2,4 # 14 pairs * PAIR H2: 2,4 COL H H6: 2,4,8 # reduction candidate for 2,4 H6: 2,4 # 16 pairs H6: 8 # 12 pairs * PAIR C7: 1,3 BLK 7 C8: 1,3,6,7,8 # reduction candidate for 1,3 C8: 1,3 => SOLVED * 132749685857361924964285371216457839348692157579813246421536798683974512795128463 * DURATION: 0:00:27.635091 START: 00:57:20.405120 END: 00:57:48.040211 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-086-base-pr-001.dot * REASONING * DIS # A4: 1,7 => CTR => A4: 2,5,6 * DIS A4: 2,5,6 # A5: 1,7 => CTR => A5: 2,3 * DIS A4: 2,5,6 + A5: 2,3 # A8: 1,7 => CTR => A8: 3,6 * DIS A4: 2,5,6 + A5: 2,3 + A8: 3,6 # A9: 3 => CTR => A9: 1,7 * PRF A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # C8: 1,3 => SOL * STA A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 + C8: 1,3 * CNT 5 HDP CHAINS / 30 HYP OPENED
Header Info
Top 95 Sudokus 086 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 132749685857361924964285371216457839348692157579813246421536798683974512795128463 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:
* INC # D1: 1,7 => UNS * INC # F1: 1,7 => UNS * DIS # A4: 1,7 => CTR => A4: 2,5,6 * INC # A4: 2,5,6 => UNS * DIS # A5: 1,7 => CTR => A5: 2,3 * INC # A5: 2,3 => UNS * DIS # A8: 1,7 => CTR => A8: 3,6 * INC # A8: 3,6 => UNS * INC # A9: 1,7 => UNS * INC # C4: 1,7 => UNS * INC # C5: 1,7 => UNS * INC # C8: 1,7 => UNS * INC # G1: 4,6 => UNS * INC # G1: 8 => UNS * INC # I2: 4,6 => UNS * INC # I2: 2 => UNS * INC # D1: 1,7 => UNS * INC # F1: 1,7 => UNS * INC # F9: 1,7 => UNS * INC # F9: 2,3,8 => UNS * INC # G1: 4,8 => UNS * INC # G1: 6 => UNS * INC # H6: 4,8 => UNS * INC # H6: 2 => UNS * INC # I2: 2,4 => UNS * INC # I2: 6 => UNS * INC # H6: 2,4 => UNS * INC # H6: 8 => UNS * DIS # A8: 1,3 => CTR => A8: 6,7 * INC # A8: 6,7 => UNS * PRF # C8: 1,3 => SOL * INC # C8: 6,7,8 => UNS * INC # A9: 1,3 => UNS * INC # C5: 1,3 => UNS * INC # C5: 7,8,9 => UNS * INC # D7: 1,9 => UNS * INC # D7: 5 => UNS * INC # D8: 1,9 => UNS * DIS # D8: 7 => CTR => D8: 1,9 * INC # I9: 2,3 => UNS * INC # I9: 4 => UNS * INC # E8: 2,3 => UNS * PRF # E8: 7,9 => SOL * INC # I9: 2,4 => UNS * INC # I9: 3 => UNS * INC # G5: 2,4 => UNS * INC # G6: 2,4 => UNS * CNT 47 HDP CHAINS / 47 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D1: 1,7 => UNS * INC # F1: 1,7 => UNS * DIS # A4: 1,7 => CTR => A4: 2,5,6 * DIS A4: 2,5,6 # A5: 1,7 => CTR => A5: 2,3 * DIS A4: 2,5,6 + A5: 2,3 # A8: 1,7 => CTR => A8: 3,6 * INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 # A9: 1,7 => UNS * INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 # A9: 1,7 => UNS * DIS A4: 2,5,6 + A5: 2,3 + A8: 3,6 # A9: 3 => CTR => A9: 1,7 * INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # D1: 1,7 => UNS * INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # F1: 1,7 => UNS * INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # C4: 1,7 => UNS * INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # C5: 1,7 => UNS * INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # C8: 1,7 => UNS * INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # G1: 4,6 => UNS * INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # G1: 8 => UNS * INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # I2: 4,6 => UNS * INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # I2: 2 => UNS * INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # D1: 1,7 => UNS * INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # F1: 1,7 => UNS * INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # F9: 1,7 => UNS * INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # F9: 2,3,8 => UNS * INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # G1: 4,8 => UNS * INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # G1: 6 => UNS * INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # H6: 4,8 => UNS * INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # H6: 2 => UNS * INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # I2: 2,4 => UNS * INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # I2: 6 => UNS * INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # H6: 2,4 => UNS * INC A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # H6: 8 => UNS * PRF A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 # C8: 1,3 => SOL * STA A4: 2,5,6 + A5: 2,3 + A8: 3,6 + A9: 1,7 + C8: 1,3 * CNT 30 HDP CHAINS / 30 HYP OPENED