Analysis of xx-top95-019-base.sdk
Contents
Original Sudoku
level: medium
position: .237....68...6.59.9.....7......4.97.3.7.96..2.........5..47.........2....8....... initial
Autosolve
position: .23759..687.26.59.9.....72.....4.97.3.7.96..2....27...5..47.........2....8...5... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C6: 1,4 => CTR => C6: 5,8,9 * PRF # B4: 1 => SOL * DIS # B6: 1,4 => CTR => B6: 5,9 * DIS # C6: 1,4 => CTR => C6: 5,8,9 * PRF # I6: 5,8 => SOL * DIS # B8: 6,9 => CTR => B8: 1,3,4 * CNT 6 HDP CHAINS / 42 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C6: 1,4 => CTR => C6: 5,8,9 * PRF C6: 5,8,9 # B4: 1 => SOL * STA C6: 5,8,9 + B4: 1 * CNT 2 HDP CHAINS / 13 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .237....68...6.59.9.....7......4.97.3.7.96..2.........5..47.........2....8....... | initial |
| .23759..687.26.59.9.....72.....4.97.3.7.96..2....27...5..47.........2....8...5... | autosolve |
| 123759486874261593965384721216543978357896142498127365532478619641932857789615234 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) A1: 1,4 C2: 1,4 B3: 5,6 C3: 5,6 A4: 2,6 A6: 1,4 G6: 3,6 H6: 3,6 A8: 6,7 D8: 6,9 D9: 6,9 E9: 1,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,C2: 1.. / A1 = 1 => 0 pairs (*) / C2 = 1 => 0 pairs (X) A1,A6: 1.. / A1 = 1 => 0 pairs (*) / A6 = 1 => 0 pairs (X) A4,C4: 2.. / A4 = 2 => 14 pairs (_) / C4 = 2 => 11 pairs (_) G7,G9: 2.. / G7 = 2 => 12 pairs (_) / G9 = 2 => 14 pairs (_) C7,G7: 2.. / C7 = 2 => 14 pairs (_) / G7 = 2 => 12 pairs (_) A4,A9: 2.. / A4 = 2 => 14 pairs (_) / A9 = 2 => 11 pairs (_) I2,I3: 3.. / I2 = 3 => 14 pairs (_) / I3 = 3 => 17 pairs (_) D4,F4: 3.. / D4 = 3 => 14 pairs (_) / F4 = 3 => 16 pairs (_) G6,H6: 3.. / G6 = 3 => 10 pairs (_) / H6 = 3 => 10 pairs (_) B7,B8: 3.. / B7 = 3 => 14 pairs (_) / B8 = 3 => 0 pairs (X) F2,I2: 3.. / F2 = 3 => 17 pairs (_) / I2 = 3 => 14 pairs (_) D3,D4: 3.. / D3 = 3 => 16 pairs (_) / D4 = 3 => 14 pairs (_) A1,C2: 4.. / A1 = 4 => 0 pairs (X) / C2 = 4 => 0 pairs (_) F2,F3: 4.. / F2 = 4 => 0 pairs (X) / F3 = 4 => 14 pairs (_) F3,I3: 4.. / F3 = 4 => 14 pairs (_) / I3 = 4 => 0 pairs (X) A1,A6: 4.. / A1 = 4 => 0 pairs (X) / A6 = 4 => 0 pairs (_) B3,C3: 5.. / B3 = 5 => 14 pairs (_) / C3 = 5 => 14 pairs (_) H8,I8: 5.. / H8 = 5 => 12 pairs (_) / I8 = 5 => 21 pairs (_) H5,H8: 5.. / H5 = 5 => 21 pairs (_) / H8 = 5 => 12 pairs (_) B3,C3: 6.. / B3 = 6 => 14 pairs (_) / C3 = 6 => 14 pairs (_) G6,H6: 6.. / G6 = 6 => 10 pairs (_) / H6 = 6 => 10 pairs (_) D8,D9: 6.. / D8 = 6 => 10 pairs (_) / D9 = 6 => 11 pairs (_) A8,A9: 7.. / A8 = 7 => 12 pairs (_) / A9 = 7 => 13 pairs (_) I8,I9: 7.. / I8 = 7 => 13 pairs (_) / I9 = 7 => 12 pairs (_) A8,I8: 7.. / A8 = 7 => 12 pairs (_) / I8 = 7 => 13 pairs (_) A9,I9: 7.. / A9 = 7 => 13 pairs (_) / I9 = 7 => 12 pairs (_) G1,H1: 8.. / G1 = 8 => 14 pairs (_) / H1 = 8 => 13 pairs (_) C4,C6: 8.. / C4 = 8 => 16 pairs (_) / C6 = 8 => 13 pairs (_) F7,E8: 8.. / F7 = 8 => 16 pairs (_) / E8 = 8 => 14 pairs (_) E3,E8: 8.. / E3 = 8 => 16 pairs (_) / E8 = 8 => 14 pairs (_) B6,C6: 9.. / B6 = 9 => 12 pairs (_) / C6 = 9 => 0 pairs (X) D8,D9: 9.. / D8 = 9 => 11 pairs (_) / D9 = 9 => 10 pairs (_) * DURATION: 0:00:57.405478 START: 23:15:05.077818 END: 23:16:02.483296 2017-05-03 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,A6,A8,B3,C2,C3,D8,D9,E9,G6,H6) * .23759..687.26.59.9.....72.....4.97.3.7.96..2....27...5..47.........2....8...5... * PAIR A1: 1,4 ROW 1 G1: 1,4,8 # reduction candidate for 1,4 G1: 1,4 # 13 pairs H1: 1,4,8 # reduction candidate for 1,4 H1: 1,4 # 14 pairs * PAIR C2: 1,4 ROW 2 F2: 1,4,3 # reduction candidate for 1,4 F2: 1,4 # 14 pairs I2: 1,4,3 # reduction candidate for 1,4 I2: 1,4 # 17 pairs * PAIR C2: 1,4 COL C C6: 1,4,5,8,9 # reduction candidate for 1,4 C6: 1,4 => CTR * .23759..687.26.59.9.5...72.268.4.97.3.7.96..2.9..27...5..47.........2....8...5... C6: 5,8,9 # 12 pairs C8: 1,4,6,9 # reduction candidate for 1,4 C8: 1,4 # 15 pairs C9: 1,4,2,6,9 # reduction candidate for 1,4 C9: 1,4 # 14 pairs * PAIR B3: 5,6 COL B B4: 5,6,1 # reduction candidate for 5,6 B4: 1 => SOLVED * 123759486874261593965384721216543978357896142498127365532478619641932857789615234 B4: 5,6 # 16 pairs * PAIR C3: 5,6 COL C C4: 5,6,1,2,8 # reduction candidate for 5,6 C4: 5,6 # 15 pairs C4: 1,2,8 # 12 pairs * PAIR A4: 2,6 BLK 4 C4: 2,6,1,5,8 # reduction candidate for 2,6 C4: 2,6 # 14 pairs C4: 1,5,8 # 14 pairs * PAIR A4: 2,6 COL A A9: 2,6,7 # reduction candidate for 2,6 A9: 7 # 13 pairs A9: 2,6 # 12 pairs * PAIR A6: 1,4 BLK 4 B5: 1,4,5 # reduction candidate for 1,4 B5: 1,4 # 16 pairs B6: 1,4,5,9 # reduction candidate for 1,4 B6: 1,4 => CTR * .23759..687.26.59.9.5...72.268.4.97.3.7.96..2..9.27...5..47.........2....8...5... B6: 5,9 # 13 pairs C6: 1,4,5,8,9 # reduction candidate for 1,4 C6: 1,4 => CTR * .23759..687.26.59.9.5...72.268.4.97.3.7.96..2.9..27...5..47.........2....8...5... C6: 5,8,9 # 12 pairs * PAIR A6: 1,4 ROW 6 I6: 1,4,5,8 # reduction candidate for 1,4 I6: 5,8 => SOLVED * 123759486874261593965384721216543978357896142498127365532478619641932857789615234 I6: 1,4 # 18 pairs * PAIR G6: 3,6 COL G G7: 3,6,1,2,8 # reduction candidate for 3,6 G7: 3,6 # 15 pairs G8: 3,6,1,4,8 # reduction candidate for 3,6 G8: 3,6 # 13 pairs G9: 3,6,1,2,4 # reduction candidate for 3,6 G9: 3,6 # 13 pairs * PAIR H6: 3,6 COL H H7: 3,6,1,8 # reduction candidate for 3,6 H7: 3,6 # 14 pairs H8: 3,6,1,4,5,8 # reduction candidate for 3,6 H8: 3,6 # 26 pairs H9: 3,6,1,4 # reduction candidate for 3,6 H9: 3,6 # 14 pairs * PAIR A8: 6,7 BLK 7 A9: 6,7,2 # reduction candidate for 6,7 A9: 6,7 # 14 pairs A9: 2 # 11 pairs * PAIR D8: 6,9 ROW 8 B8: 6,9,1,3,4 # reduction candidate for 6,9 B8: 6,9 => CTR * .23759..687.26.59.9.....72.....4.97.3.7.96..2....27...53.47.........2....8...5... B8: 1,3,4 # 12 pairs C8: 6,9,1,4 # reduction candidate for 6,9 C8: 6,9 # 13 pairs * PAIR D9: 6,9 ROW 9 C9: 6,9,1,2,4 # reduction candidate for 6,9 C9: 6,9 # 14 pairs C9: 1,2,4 # 12 pairs * PAIR E9: 1,3 BLK 8 F7: 1,3,8 # reduction candidate for 1,3 F7: 1,3 # 14 pairs E8: 1,3,8 # reduction candidate for 1,3 E8: 1,3 # 16 pairs * PAIR E9: 1,3 ROW 9 G9: 1,3,2,4,6 # reduction candidate for 1,3 G9: 1,3 # 14 pairs H9: 1,3,4,6 # reduction candidate for 1,3 H9: 1,3 # 13 pairs * PAIR E9: 1,3 COL E E3: 1,3,8 # reduction candidate for 1,3 E3: 8 # 16 pairs E3: 1,3 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-019-base-pr-000.dot * REASONING * DIS # C6: 1,4 => CTR => C6: 5,8,9 * PRF # B4: 1 => SOL * DIS # B6: 1,4 => CTR => B6: 5,9 * DIS # C6: 1,4 => CTR => C6: 5,8,9 * PRF # I6: 5,8 => SOL * DIS # B8: 6,9 => CTR => B8: 1,3,4 * CNT 6 HDP CHAINS / 42 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,A6,A8,B3,C2,C3,D8,D9,E9,G6,H6) * .23759..687.26.59.9.....72.....4.97.3.7.96..2....27...5..47.........2....8...5... * PAIR A1: 1,4 ROW 1 G1: 1,4,8 # reduction candidate for 1,4 G1: 1,4 # 13 pairs H1: 1,4,8 # reduction candidate for 1,4 H1: 1,4 # 14 pairs * PAIR C2: 1,4 ROW 2 F2: 1,4,3 # reduction candidate for 1,4 F2: 1,4 # 14 pairs I2: 1,4,3 # reduction candidate for 1,4 I2: 1,4 # 17 pairs * PAIR C2: 1,4 COL C C6: 1,4,5,8,9 # reduction candidate for 1,4 C6: 1,4 => CTR * .23759..687.26.59.9.5...72.268.4.97.3.7.96..2.9..27...5..47.........2....8...5... C8: 1,4,6,9 # reduction candidate for 1,4 C8: 1,4 # 15 pairs C9: 1,4,2,6,9 # reduction candidate for 1,4 C9: 1,4 # 14 pairs * PAIR RESTART * PAIR C2: 1,4 ROW 2 F2: 1,4,3 # reduction candidate for 1,4 F2: 1,4 # 14 pairs I2: 1,4,3 # reduction candidate for 1,4 I2: 1,4 # 17 pairs * PAIR C2: 1,4 COL C C8: 1,4,6,9 # reduction candidate for 1,4 C8: 1,4 # 15 pairs C9: 1,4,2,6,9 # reduction candidate for 1,4 C9: 1,4 # 14 pairs * PAIR B3: 5,6 COL B B4: 5,6,1 # reduction candidate for 5,6 B4: 1 => SOLVED * 123759486874261593965384721216543978357896142498127365532478619641932857789615234 * DURATION: 0:00:13.607631 START: 23:16:42.678408 END: 23:16:56.286039 2017-05-03 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-019-base-pr-001.dot * REASONING * DIS # C6: 1,4 => CTR => C6: 5,8,9 * PRF C6: 5,8,9 # B4: 1 => SOL * STA C6: 5,8,9 + B4: 1 * CNT 2 HDP CHAINS / 13 HYP OPENED
Header Info
Top 95 Sudokus 019 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 123759486874261593965384721216543978357896142498127365532478619641932857789615234 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 # G1: 1,4 => UNS * INC # H1: 1,4 => UNS * INC # F2: 1,4 => UNS * INC # I2: 1,4 => UNS * DIS # C6: 1,4 => CTR => C6: 5,8,9 * INC # C6: 5,8,9 => UNS * INC # C8: 1,4 => UNS * INC # C9: 1,4 => UNS * INC # B4: 5,6 => UNS * PRF # B4: 1 => SOL * INC # C4: 5,6 => UNS * INC # C4: 1,2,8 => UNS * INC # C4: 2,6 => UNS * INC # C4: 1,5,8 => UNS * INC # A9: 2,6 => UNS * INC # A9: 7 => UNS * INC # B5: 1,4 => UNS * DIS # B6: 1,4 => CTR => B6: 5,9 * INC # B6: 5,9 => UNS * DIS # C6: 1,4 => CTR => C6: 5,8,9 * INC # C6: 5,8,9 => UNS * INC # I6: 1,4 => UNS * PRF # I6: 5,8 => SOL * INC # G7: 3,6 => UNS * INC # G8: 3,6 => UNS * INC # G9: 3,6 => UNS * INC # H7: 3,6 => UNS * INC # H8: 3,6 => UNS * INC # H9: 3,6 => UNS * INC # A9: 6,7 => UNS * INC # A9: 2 => UNS * DIS # B8: 6,9 => CTR => B8: 1,3,4 * INC # B8: 1,3,4 => UNS * INC # C8: 6,9 => UNS * INC # C9: 6,9 => UNS * INC # C9: 1,2,4 => UNS * INC # F7: 1,3 => UNS * INC # E8: 1,3 => UNS * INC # G9: 1,3 => UNS * INC # H9: 1,3 => UNS * INC # E3: 1,3 => UNS * INC # E3: 8 => UNS * CNT 42 HDP CHAINS / 42 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G1: 1,4 => UNS * INC # H1: 1,4 => UNS * INC # F2: 1,4 => UNS * INC # I2: 1,4 => UNS * DIS # C6: 1,4 => CTR => C6: 5,8,9 * INC C6: 5,8,9 # C8: 1,4 => UNS * INC C6: 5,8,9 # C9: 1,4 => UNS * INC C6: 5,8,9 # F2: 1,4 => UNS * INC C6: 5,8,9 # I2: 1,4 => UNS * INC C6: 5,8,9 # C8: 1,4 => UNS * INC C6: 5,8,9 # C9: 1,4 => UNS * INC C6: 5,8,9 # B4: 5,6 => UNS * PRF C6: 5,8,9 # B4: 1 => SOL * STA C6: 5,8,9 + B4: 1 * CNT 13 HDP CHAINS / 13 HYP OPENED