Analysis of xx-top95-053-base.sdk
Contents
Original Sudoku
level: medium
position: .2....5938..5..46.94..6...8..2.3.....6..8.73.7..2.........4.38..7....6..........5 initial
Autosolve
position: .2....5938..5..46.945.6...8..2.3.....6..8.7327..2.........4.38..7....6..........5 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 7 => CTR => C1: 1,6 * DIS # C2: 1,3 => CTR => C2: 7 * PRF # C1: 6 => SOL * DIS # H3: 2 => CTR => H3: 1,7 * DIS # C2: 3 => CTR => C2: 1,7 * DIS # I7: 9 => CTR => I7: 1,7 * DIS # H3: 1,2 => CTR => H3: 7 * CNT 7 HDP CHAINS / 29 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 7 => CTR => C1: 1,6 * PRF C1: 1,6 # D8: 8 => SOL * STA C1: 1,6 + D8: 8 * CNT 2 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .2....5938..5..46.94..6...8..2.3.....6..8.73.7..2.........4.38..7....6..........5 | initial |
| .2....5938..5..46.945.6...8..2.3.....6..8.7327..2.........4.38..7....6..........5 | autosolve |
| 126478593837592461945361278412937856569184732783256914251649387374815629698723145 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) A1: 1,6 B2: 1,3 D1: 4,8 E1: 1,7 F1: 4,8 E2: 2,9 F2: 2,9 I2: 1,7 G3: 1,2 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,F2: 2.. / E2 = 2 => 7 pairs (_) / F2 = 2 => 8 pairs (_) G3,H3: 2.. / G3 = 2 => 10 pairs (_) / H3 = 2 => 0 pairs (X) A7,F7: 2.. / A7 = 2 => 9 pairs (_) / F7 = 2 => 10 pairs (_) G3,G9: 2.. / G3 = 2 => 10 pairs (_) / G9 = 2 => 0 pairs (X) B2,C2: 3.. / B2 = 3 => 10 pairs (_) / C2 = 3 => 0 pairs (X) D3,F3: 3.. / D3 = 3 => 10 pairs (_) / F3 = 3 => 10 pairs (_) B6,C6: 3.. / B6 = 3 => 0 pairs (X) / C6 = 3 => 10 pairs (_) A8,A9: 3.. / A8 = 3 => 9 pairs (_) / A9 = 3 => 9 pairs (_) B2,B6: 3.. / B2 = 3 => 10 pairs (_) / B6 = 3 => 0 pairs (X) C2,C6: 3.. / C2 = 3 => 0 pairs (X) / C6 = 3 => 10 pairs (_) D1,F1: 4.. / D1 = 4 => 8 pairs (_) / F1 = 4 => 7 pairs (_) H4,H6: 5.. / H4 = 5 => 11 pairs (_) / H6 = 5 => 11 pairs (_) A5,F5: 5.. / A5 = 5 => 10 pairs (_) / F5 = 5 => 11 pairs (_) E6,E8: 5.. / E6 = 5 => 11 pairs (_) / E8 = 5 => 10 pairs (_) A1,C1: 6.. / A1 = 6 => 9 pairs (_) / C1 = 6 => 0 pairs (*) I4,I6: 6.. / I4 = 6 => 9 pairs (_) / I6 = 6 => 11 pairs (_) F6,I6: 6.. / F6 = 6 => 9 pairs (_) / I6 = 6 => 11 pairs (_) C1,C2: 7.. / C1 = 7 => 0 pairs (X) / C2 = 7 => 21 pairs (_) I2,H3: 7.. / I2 = 7 => 0 pairs (X) / H3 = 7 => 21 pairs (_) D4,F4: 7.. / D4 = 7 => 10 pairs (_) / F4 = 7 => 10 pairs (_) I7,H9: 7.. / I7 = 7 => 21 pairs (_) / H9 = 7 => 0 pairs (X) C1,E1: 7.. / C1 = 7 => 0 pairs (X) / E1 = 7 => 21 pairs (_) C2,I2: 7.. / C2 = 7 => 21 pairs (_) / I2 = 7 => 0 pairs (X) E1,E9: 7.. / E1 = 7 => 21 pairs (_) / E9 = 7 => 0 pairs (X) H3,H9: 7.. / H3 = 7 => 21 pairs (_) / H9 = 7 => 0 pairs (X) I2,I7: 7.. / I2 = 7 => 0 pairs (X) / I7 = 7 => 21 pairs (_) D1,F1: 8.. / D1 = 8 => 7 pairs (_) / F1 = 8 => 8 pairs (_) G4,G6: 8.. / G4 = 8 => 12 pairs (_) / G6 = 8 => 11 pairs (_) B4,G4: 8.. / B4 = 8 => 11 pairs (_) / G4 = 8 => 12 pairs (_) E2,F2: 9.. / E2 = 9 => 8 pairs (_) / F2 = 9 => 7 pairs (_) * DURATION: 0:00:38.952729 START: 23:57:40.444244 END: 23:58:19.396973 2017-05-03 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B2,D1,E1,E2,F1,F2,G3,I2) * .2....5938..5..46.945.6...8..2.3.....6..8.7327..2.........4.38..7....6..........5 * PAIR A1: 1,6 BLK 1 C1: 1,6,7 # reduction candidate for 1,6 C1: 7 => CTR * 627.1.5938..5..467945.6...8..2.3.....6..8.7327..2.........4.38..7....6......7...5 C1: 1,6 # 21 pairs * PAIR A1: 1,6 COL A A7: 1,6,2,5 # reduction candidate for 1,6 A7: 1,6 # 13 pairs A9: 1,6,2,3,4 # reduction candidate for 1,6 A9: 1,6 # 13 pairs * PAIR B2: 1,3 BLK 1 C2: 1,3,7 # reduction candidate for 1,3 C2: 1,3 => CTR * .27.1.5938..5..467945.6...8..2.3.....6..8.7327..2.........4.38..7....6......7...5 C2: 7 # 21 pairs * PAIR B2: 1,3 COL B B6: 1,3,5,8,9 # reduction candidate for 1,3 B6: 1,3 # 12 pairs B6: 5,8,9 # 10 pairs * PAIR E1: 1,7 BLK 2 D3: 1,7,3 # reduction candidate for 1,7 D3: 1,7 # 10 pairs F3: 1,7,3 # reduction candidate for 1,7 F3: 1,7 # 10 pairs * PAIR E1: 1,7 ROW 1 C1: 1,7,6 # reduction candidate for 1,7 C1: 6 => SOLVED * 126478593837592461945361278412937856569184732783256914251649387374815629698723145 C1: 1,7 # 9 pairs * PAIR E1: 1,7 COL E E9: 1,7,2,9 # reduction candidate for 1,7 E9: 2,9 # 21 pairs E9: 1,7 # 11 pairs * PAIR E2: 2,9 COL E E8: 2,9,1,5 # reduction candidate for 2,9 E8: 2,9 # 13 pairs E9: 2,9,1,7 # reduction candidate for 2,9 E9: 2,9 # 21 pairs * PAIR F2: 2,9 COL F F7: 2,9,1,5,6,7 # reduction candidate for 2,9 F7: 2,9 # 10 pairs F8: 2,9,1,3,5,8 # reduction candidate for 2,9 F8: 2,9 # 10 pairs F9: 2,9,1,3,6,7,8 # reduction candidate for 2,9 F9: 2,9 # 10 pairs * PAIR I2: 1,7 BLK 3 H3: 1,7,2 # reduction candidate for 1,7 H3: 2 => CTR * .2....5938..5..467945.6.128..2.3.....6..8.7327..2.........4.38..7....6........275 H3: 1,7 # 10 pairs * PAIR I2: 1,7 ROW 2 C2: 1,7,3 # reduction candidate for 1,7 C2: 3 => CTR * .27.1.5938135..467945.6...8..2.3.....6..8.73273.2.........4.38..7....6......7...5 C2: 1,7 # 10 pairs * PAIR I2: 1,7 COL I I7: 1,7,9 # reduction candidate for 1,7 I7: 9 => CTR * .27.1.5938..5..467945.6...8..2.3.....6..8.7327..2.........4.389.7....6.........75 I7: 1,7 # 11 pairs * PAIR G3: 1,2 BLK 3 H3: 1,2,7 # reduction candidate for 1,2 H3: 1,2 => CTR * .27.1.5938..5..467945.6...8..2.3.....6..8.7327..2.........4.38..7....6.........75 H3: 7 # 21 pairs * PAIR G3: 1,2 COL G G9: 1,2,9 # reduction candidate for 1,2 G9: 9 # 18 pairs G9: 1,2 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-053-base-pr-000.dot * REASONING * DIS # C1: 7 => CTR => C1: 1,6 * DIS # C2: 1,3 => CTR => C2: 7 * PRF # C1: 6 => SOL * DIS # H3: 2 => CTR => H3: 1,7 * DIS # C2: 3 => CTR => C2: 1,7 * DIS # I7: 9 => CTR => I7: 1,7 * DIS # H3: 1,2 => CTR => H3: 7 * CNT 7 HDP CHAINS / 29 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B2,D1,E1,E2,F1,F2,G3,I2) * .2....5938..5..46.945.6...8..2.3.....6..8.7327..2.........4.38..7....6..........5 * PAIR A1: 1,6 BLK 1 C1: 1,6,7 # reduction candidate for 1,6 C1: 7 => CTR * 627.1.5938..5..467945.6...8..2.3.....6..8.7327..2.........4.38..7....6......7...5 * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A1,A5,A9,B4,B7,C1,C7,D1,D3,D4,D5,D7,D9,E6,E8,F1,F3,F4,F9,H4,H6) * .2..7.593837592461945.6.2784.2.3.8.6.69.8.7327832.69.42...4.387.74...629.98.2.145 * PAIR D3: 1,3 COL D D8: 1,3,8 # reduction candidate for 1,3 D8: 8 => SOLVED * 126478593837592461945361278412937856569184732783256914251649387374815629698723145 * DURATION: 0:00:06.488794 START: 23:58:41.983021 END: 23:58:48.471815 2017-05-03 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-053-base-pr-001.dot * REASONING * DIS # C1: 7 => CTR => C1: 1,6 * PRF C1: 1,6 # D8: 8 => SOL * STA C1: 1,6 + D8: 8 * CNT 2 HDP CHAINS / 4 HYP OPENED
Header Info
Top 95 Sudokus 053 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 126478593837592461945361278412937856569184732783256914251649387374815629698723145 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 # C1: 1,6 => UNS * DIS # C1: 7 => CTR => C1: 1,6 * INC # A7: 1,6 => UNS * INC # A9: 1,6 => UNS * DIS # C2: 1,3 => CTR => C2: 7 * INC # C2: 7 => UNS * INC # B6: 1,3 => UNS * INC # B6: 5,8,9 => UNS * INC # D3: 1,7 => UNS * INC # F3: 1,7 => UNS * INC # C1: 1,7 => UNS * PRF # C1: 6 => SOL * INC # E9: 1,7 => UNS * INC # E9: 2,9 => UNS * INC # E8: 2,9 => UNS * INC # E9: 2,9 => UNS * INC # F7: 2,9 => UNS * INC # F8: 2,9 => UNS * INC # F9: 2,9 => UNS * INC # H3: 1,7 => UNS * DIS # H3: 2 => CTR => H3: 1,7 * INC # C2: 1,7 => UNS * DIS # C2: 3 => CTR => C2: 1,7 * INC # I7: 1,7 => UNS * DIS # I7: 9 => CTR => I7: 1,7 * DIS # H3: 1,2 => CTR => H3: 7 * INC # H3: 7 => UNS * INC # G9: 1,2 => UNS * INC # G9: 9 => UNS * CNT 29 HDP CHAINS / 29 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 1,6 => UNS * DIS # C1: 7 => CTR => C1: 1,6 * INC C1: 1,6 # D8: 1,3 => UNS * PRF C1: 1,6 # D8: 8 => SOL * STA C1: 1,6 + D8: 8 * CNT 4 HDP CHAINS / 4 HYP OPENED