Analysis of xx-top95-035-base.sdk
Contents
Original Sudoku
level: medium
position: ..8.9.1...6.5...2......6....3.1.7.5.........9..4...3...5....2...7...3.8.2..7....4 initial
Autosolve
position: ..839.1...6.5...2......6....3.1.7.5.....3...9..4...3...5....2...7...3.8.2..7....4 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 5,7 => CTR => A3: 1,3,9 * DIS # A5: 5,7 => CTR => A5: 1,6,8 * DIS # E3: 2,4 => CTR => E3: 1,7,8 * PRF # I1: 5 => SOL * DIS # H5: 6,7 => CTR => H5: 1,4 * CNT 5 HDP CHAINS / 21 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A3: 5,7 => CTR => A3: 1,3,9 * DIS A3: 1,3,9 # A5: 5,7 => CTR => A5: 1,6,8 * DIS A3: 1,3,9 + A5: 1,6,8 # E3: 2,4 => CTR => E3: 1,7,8 * PRF A3: 1,3,9 + A5: 1,6,8 + E3: 1,7,8 # I1: 5 => SOL * STA A3: 1,3,9 + A5: 1,6,8 + E3: 1,7,8 + I1: 5 * CNT 4 HDP CHAINS / 21 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..8.9.1...6.5...2......6....3.1.7.5.........9..4...3...5....2...7...3.8.2..7....4 | initial |
| ..839.1...6.5...2......6....3.1.7.5.....3...9..4...3...5....2...7...3.8.2..7....4 | autosolve |
| 748392165369514728125876943932147856687235419514689372853461297476923581291758634 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (4) A1: 5,7 B1: 2,4 F1: 2,4 H1: 6,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I4,I6: 2.. / I4 = 2 => 10 pairs (_) / I6 = 2 => 6 pairs (_) D8,E8: 2.. / D8 = 2 => 5 pairs (_) / E8 = 2 => 5 pairs (_) B1,F1: 2.. / B1 = 2 => 0 pairs (X) / F1 = 2 => 3 pairs (_) C9,H9: 3.. / C9 = 3 => 6 pairs (_) / H9 = 3 => 4 pairs (_) B1,B3: 4.. / B1 = 4 => 3 pairs (_) / B3 = 4 => 0 pairs (X) A7,A8: 4.. / A7 = 4 => 0 pairs (X) / A8 = 4 => 4 pairs (_) B1,F1: 4.. / B1 = 4 => 3 pairs (_) / F1 = 4 => 0 pairs (X) E4,G4: 4.. / E4 = 4 => 5 pairs (_) / G4 = 4 => 14 pairs (_) H3,H5: 4.. / H3 = 4 => 14 pairs (_) / H5 = 4 => 6 pairs (_) A1,I1: 5.. / A1 = 5 => 6 pairs (_) / I1 = 5 => 0 pairs (*) C3,C5: 5.. / C3 = 5 => 0 pairs (*) / C5 = 5 => 0 pairs (X) H1,I1: 6.. / H1 = 6 => 5 pairs (_) / I1 = 6 => 7 pairs (_) E2,E3: 7.. / E2 = 7 => 17 pairs (_) / E3 = 7 => 4 pairs (_) H7,I7: 7.. / H7 = 7 => 8 pairs (_) / I7 = 7 => 6 pairs (_) A7,B9: 8.. / A7 = 8 => 7 pairs (_) / B9 = 8 => 0 pairs (X) A4,C4: 9.. / A4 = 9 => 5 pairs (_) / C4 = 9 => 12 pairs (_) D6,F6: 9.. / D6 = 9 => 4 pairs (_) / F6 = 9 => 4 pairs (_) B3,B9: 9.. / B3 = 9 => 0 pairs (X) / B9 = 9 => 9 pairs (_) * DURATION: 0:00:23.559405 START: 23:30:58.286088 END: 23:31:21.845493 2017-05-03 * CP COUNT: (18) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B1,F1,H1) * ..839.1...6.5...2......6....3.1.7.5.....3...9..4...3...5....2...7...3.8.2..7....4 * PAIR A1: 5,7 BLK 1 A3: 5,7,1,3,9 # reduction candidate for 5,7 A3: 5,7 => CTR * ..839.1...6.5...2......6....3.1.7.5.....3...9..4...3...5....2...7...3.8.2..7....4 A3: 1,3,9 # 4 pairs C3: 5,7,1,2,3,9 # reduction candidate for 5,7 C3: 5,7 # 15 pairs * PAIR A1: 5,7 ROW 1 I1: 5,7,6 # reduction candidate for 5,7 I1: 6 # 7 pairs I1: 5,7 # 5 pairs * PAIR A1: 5,7 COL A A5: 5,7,1,6,8 # reduction candidate for 5,7 A5: 5,7 => CTR * 728394165.6.5..42..45..679.9321.7.565.7632..96.4...37285....2.747...3.812..7....4 A5: 1,6,8 # 6 pairs A6: 5,7,1,6,8 # reduction candidate for 5,7 A6: 5,7 # 6 pairs * PAIR B1: 2,4 BLK 1 B3: 2,4,1,9 # reduction candidate for 2,4 B3: 2,4 # 15 pairs B3: 1,9 # 10 pairs * PAIR F1: 2,4 BLK 2 D3: 2,4,8 # reduction candidate for 2,4 D3: 2,4 # 16 pairs E3: 2,4,1,7,8 # reduction candidate for 2,4 E3: 2,4 => CTR * 5283941..36957142814.826.93.3.14785....63.7497.49..3..85.4.92..47.2.398.29.7..6.4 E3: 1,7,8 # 4 pairs * PAIR F1: 2,4 COL F F5: 2,4,5,8 # reduction candidate for 2,4 F5: 2,4 # 6 pairs F5: 5,8 # 5 pairs * PAIR H1: 6,7 BLK 3 I1: 6,7,5 # reduction candidate for 6,7 I1: 5 => SOLVED * 748392165369514728125876943932147856687235419514689372853461297476923581291758634 I1: 6,7 # 6 pairs * PAIR H1: 6,7 COL H H5: 6,7,1,4 # reduction candidate for 6,7 H5: 6,7 => CTR * 548392176.6.5..8233..8.694563918745218523476972465.31.853...2974769235812917..634 H5: 1,4 # 5 pairs H6: 6,7,1 # reduction candidate for 6,7 H6: 6,7 # 9 pairs H7: 6,7,1,3,9 # reduction candidate for 6,7 H7: 6,7 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-035-base-pr-000.dot * REASONING * DIS # A3: 5,7 => CTR => A3: 1,3,9 * DIS # A5: 5,7 => CTR => A5: 1,6,8 * DIS # E3: 2,4 => CTR => E3: 1,7,8 * PRF # I1: 5 => SOL * DIS # H5: 6,7 => CTR => H5: 1,4 * CNT 5 HDP CHAINS / 21 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B1,F1,H1) * ..839.1...6.5...2......6....3.1.7.5.....3...9..4...3...5....2...7...3.8.2..7....4 * PAIR A1: 5,7 BLK 1 A3: 5,7,1,3,9 # reduction candidate for 5,7 A3: 5,7 => CTR * ..839.1...6.5...2......6....3.1.7.5.....3...9..4...3...5....2...7...3.8.2..7....4 C3: 5,7,1,2,3,9 # reduction candidate for 5,7 C3: 5,7 # 15 pairs * RESTART * PAIR A1: 5,7 BLK 1 C3: 5,7,1,2,3,9 # reduction candidate for 5,7 C3: 5,7 # 15 pairs C3: 1,2,3,9 # 7 pairs * PAIR A1: 5,7 ROW 1 I1: 5,7,6 # reduction candidate for 5,7 I1: 6 # 7 pairs I1: 5,7 # 5 pairs * PAIR A1: 5,7 COL A A5: 5,7,1,6,8 # reduction candidate for 5,7 A5: 5,7 => CTR * 728394165.6.5..42..45..679.9321.7.565.7632..96.4...37285....2.747...3.812..7....4 * RESTART * PAIR RESTART * PAIR A1: 5,7 BLK 1 C3: 5,7,1,2,3,9 # reduction candidate for 5,7 C3: 5,7 # 16 pairs C3: 1,2,3,9 # 7 pairs * PAIR A1: 5,7 ROW 1 I1: 5,7,6 # reduction candidate for 5,7 I1: 6 # 7 pairs I1: 5,7 # 7 pairs * PAIR B1: 2,4 BLK 1 B3: 2,4,1,9 # reduction candidate for 2,4 B3: 2,4 # 16 pairs B3: 1,9 # 10 pairs * PAIR F1: 2,4 BLK 2 D3: 2,4,8 # reduction candidate for 2,4 D3: 2,4 # 20 pairs E3: 2,4,1,7,8 # reduction candidate for 2,4 E3: 2,4 => CTR * ..83941...6.571428.4.826....32147.5661.23..49.84...3.285.4.92..47.6.3.8.29.785..4 * RESTART * PAIR F1: 2,4 BLK 2 D3: 2,4,8 # reduction candidate for 2,4 D3: 2,4 # 20 pairs D3: 8 # 6 pairs * PAIR F1: 2,4 COL F F5: 2,4,5,8 # reduction candidate for 2,4 F5: 2,4 # 8 pairs F5: 5,8 # 7 pairs * PAIR H1: 6,7 BLK 3 I1: 6,7,5 # reduction candidate for 6,7 I1: 5 => SOLVED * 748392165369514728125876943932147856687235419514689372853461297476923581291758634 * DURATION: 0:00:17.542048 START: 23:31:37.692018 END: 23:31:55.234066 2017-05-03 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-035-base-pr-001.dot * REASONING * DIS # A3: 5,7 => CTR => A3: 1,3,9 * DIS A3: 1,3,9 # A5: 5,7 => CTR => A5: 1,6,8 * DIS A3: 1,3,9 + A5: 1,6,8 # E3: 2,4 => CTR => E3: 1,7,8 * PRF A3: 1,3,9 + A5: 1,6,8 + E3: 1,7,8 # I1: 5 => SOL * STA A3: 1,3,9 + A5: 1,6,8 + E3: 1,7,8 + I1: 5 * CNT 4 HDP CHAINS / 21 HYP OPENED
Header Info
Top 95 Sudokus 035 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 748392165369514728125876943932147856687235419514689372853461297476923581291758634 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 # A3: 5,7 => CTR => A3: 1,3,9 * INC # A3: 1,3,9 => UNS * INC # C3: 5,7 => UNS * INC # I1: 5,7 => UNS * INC # I1: 6 => UNS * DIS # A5: 5,7 => CTR => A5: 1,6,8 * INC # A5: 1,6,8 => UNS * INC # A6: 5,7 => UNS * INC # B3: 2,4 => UNS * INC # B3: 1,9 => UNS * INC # D3: 2,4 => UNS * DIS # E3: 2,4 => CTR => E3: 1,7,8 * INC # E3: 1,7,8 => UNS * INC # F5: 2,4 => UNS * INC # F5: 5,8 => UNS * INC # I1: 6,7 => UNS * PRF # I1: 5 => SOL * DIS # H5: 6,7 => CTR => H5: 1,4 * INC # H5: 1,4 => UNS * INC # H6: 6,7 => UNS * INC # H7: 6,7 => UNS * CNT 21 HDP CHAINS / 21 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A3: 5,7 => CTR => A3: 1,3,9 * INC A3: 1,3,9 # C3: 5,7 => UNS * INC A3: 1,3,9 # C3: 5,7 => UNS * INC A3: 1,3,9 # C3: 1,2,3,9 => UNS * INC A3: 1,3,9 # I1: 5,7 => UNS * INC A3: 1,3,9 # I1: 6 => UNS * DIS A3: 1,3,9 # A5: 5,7 => CTR => A5: 1,6,8 * INC A3: 1,3,9 + A5: 1,6,8 # C3: 5,7 => UNS * INC A3: 1,3,9 + A5: 1,6,8 # C3: 1,2,3,9 => UNS * INC A3: 1,3,9 + A5: 1,6,8 # I1: 5,7 => UNS * INC A3: 1,3,9 + A5: 1,6,8 # I1: 6 => UNS * INC A3: 1,3,9 + A5: 1,6,8 # B3: 2,4 => UNS * INC A3: 1,3,9 + A5: 1,6,8 # B3: 1,9 => UNS * INC A3: 1,3,9 + A5: 1,6,8 # D3: 2,4 => UNS * DIS A3: 1,3,9 + A5: 1,6,8 # E3: 2,4 => CTR => E3: 1,7,8 * INC A3: 1,3,9 + A5: 1,6,8 + E3: 1,7,8 # D3: 2,4 => UNS * INC A3: 1,3,9 + A5: 1,6,8 + E3: 1,7,8 # D3: 8 => UNS * INC A3: 1,3,9 + A5: 1,6,8 + E3: 1,7,8 # F5: 2,4 => UNS * INC A3: 1,3,9 + A5: 1,6,8 + E3: 1,7,8 # F5: 5,8 => UNS * INC A3: 1,3,9 + A5: 1,6,8 + E3: 1,7,8 # I1: 6,7 => UNS * PRF A3: 1,3,9 + A5: 1,6,8 + E3: 1,7,8 # I1: 5 => SOL * STA A3: 1,3,9 + A5: 1,6,8 + E3: 1,7,8 + I1: 5 * CNT 21 HDP CHAINS / 21 HYP OPENED