Analysis of xx-top95-038-base.sdk
Contents
Original Sudoku
level: medium
position: 1....6.8..64..........4...7....9.6...7.4..5..5...7.1...5....32.3....8...4........ initial
Autosolve
position: 1....648..64..........4..67....9.67..7.4..5..5...7.1...5...432.3....87..4.....8.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 3,5 => CTR => C1: 2,7,9 * DIS # D1: 3,5 => CTR => D1: 2,7,9 * PRF # A2: 2,9 => SOL * DIS # F2: 2,9 => CTR => F2: 3,5,7 * DIS # C3: 2,9 => CTR => C3: 3,5,8 * DIS # A5: 2,8 => CTR => A5: 6,9 * DIS # A2: 2,8 => CTR => A2: 7,9 * DIS # D6: 2,3 => CTR => D6: 6,8 * DIS # F2: 2,3 => CTR => F2: 5,7,9 * DIS # F9: 2,3 => CTR => F9: 1,5,7,9 * PRF # D7: 1,6 => SOL * DIS # C7: 1,6 => CTR => C7: 7,8,9 * CNT 12 HDP CHAINS / 60 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 3,5 => CTR => C1: 2,7,9 * DIS C1: 2,7,9 # D1: 3,5 => CTR => D1: 2,7,9 * PRF C1: 2,7,9 + D1: 2,7,9 # A2: 2,9 => SOL * STA C1: 2,7,9 + D1: 2,7,9 + A2: 2,9 * CNT 3 HDP CHAINS / 12 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1....6.8..64..........4...7....9.6...7.4..5..5...7.1...5....32.3....8...4........ | initial |
| 1....648..64..........4..67....9.67..7.4..5..5...7.1...5...432.3....87..4.....8.. | autosolve |
| 137926485964587231825341967241895673673412598589673142758164329396258714412739856 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) I1: 3,5 G2: 2,9 G3: 2,9 A4: 2,8 F6: 2,3 H5: 3,9 E7: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D3,F3: 1.. / D3 = 1 => 7 pairs (_) / F3 = 1 => 12 pairs (_) H2,I2: 1.. / H2 = 1 => 9 pairs (_) / I2 = 1 => 9 pairs (_) G2,G3: 2.. / G2 = 2 => 11 pairs (_) / G3 = 2 => 6 pairs (_) B4,B6: 4.. / B4 = 4 => 7 pairs (_) / B6 = 4 => 12 pairs (_) H8,I8: 4.. / H8 = 4 => 11 pairs (_) / I8 = 4 => 7 pairs (_) B4,I4: 4.. / B4 = 4 => 7 pairs (_) / I4 = 4 => 12 pairs (_) H6,H8: 4.. / H6 = 4 => 7 pairs (_) / H8 = 4 => 11 pairs (_) C1,C3: 5.. / C1 = 5 => 0 pairs (X) / C3 = 5 => 7 pairs (_) D4,F4: 5.. / D4 = 5 => 12 pairs (_) / F4 = 5 => 7 pairs (_) E5,D6: 6.. / E5 = 6 => 0 pairs (X) / D6 = 6 => 7 pairs (_) C6,D6: 6.. / C6 = 6 => 0 pairs (X) / D6 = 6 => 7 pairs (_) A5,A7: 6.. / A5 = 6 => 7 pairs (_) / A7 = 6 => 0 pairs (X) C1,A2: 7.. / C1 = 7 => 0 pairs (*) / A2 = 7 => 0 pairs (X) C1,D1: 7.. / C1 = 7 => 0 pairs (*) / D1 = 7 => 0 pairs (X) A2,A7: 7.. / A2 = 7 => 0 pairs (X) / A7 = 7 => 0 pairs (_) F2,F9: 7.. / F2 = 7 => 0 pairs (*) / F9 = 7 => 0 pairs (X) A7,C7: 8.. / A7 = 8 => 0 pairs (X) / C7 = 8 => 7 pairs (_) E2,E5: 8.. / E2 = 8 => 7 pairs (_) / E5 = 8 => 8 pairs (_) G2,G3: 9.. / G2 = 9 => 6 pairs (_) / G3 = 9 => 11 pairs (_) * DURATION: 0:00:22.346687 START: 23:32:34.976692 END: 23:32:57.323379 2017-05-03 * CP COUNT: (19) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,E7,F6,G2,G3,H5,I1) * 1....648..64..........4..67....9.67..7.4..5..5...7.1...5...432.3....87..4.....8.. * PAIR I1: 3,5 BLK 3 H2: 3,5,1 # reduction candidate for 3,5 H2: 3,5 # 9 pairs I2: 3,5,1 # reduction candidate for 3,5 I2: 3,5 # 9 pairs * PAIR I1: 3,5 ROW 1 C1: 3,5,2,7,9 # reduction candidate for 3,5 C1: 3,5 => CTR * 19.72648.764...2......4.967....9.67..7.4..5..5...7.1..857..432.3....87..4....78.. C1: 2,7,9 # 7 pairs D1: 3,5,2,7,9 # reduction candidate for 3,5 D1: 3,5 => CTR * 197.2648..64.......35.4..67....9.67..7.4..5..5...7.1..758..432.3....87..4.....8.. D1: 2,7,9 # 7 pairs E1: 3,5,2 # reduction candidate for 3,5 E1: 3,5 # 14 pairs * PAIR G2: 2,9 ROW 2 A2: 2,9,7,8 # reduction candidate for 2,9 A2: 2,9 => SOLVED * 137926485964587231825341967241895673673412598589673142758164329396258714412739856 A2: 7,8 # 8 pairs D2: 2,9,3,5,7,8 # reduction candidate for 2,9 D2: 2,9 # 9 pairs F2: 2,9,3,5,7 # reduction candidate for 2,9 F2: 2,9 => CTR * 1....648..64..........4..67....9.67..7.4..5..5...7.1...5...432.3....87..4....78.. F2: 3,5,7 # 7 pairs * PAIR G3: 2,9 ROW 3 A3: 2,9,8 # reduction candidate for 2,9 A3: 2,9 # 11 pairs B3: 2,9,3,8 # reduction candidate for 2,9 B3: 2,9 # 22 pairs C3: 2,9,3,5,8 # reduction candidate for 2,9 C3: 2,9 => CTR * 195726483764...2..832.4.9672...9.67..7.4..5..5...7.1...57..432.3....87..4....78.. C3: 3,5,8 # 7 pairs D3: 2,9,1,3,5,8 # reduction candidate for 2,9 D3: 2,9 # 17 pairs F3: 2,9,1,3,5 # reduction candidate for 2,9 F3: 2,9 # 15 pairs * PAIR A4: 2,8 BLK 4 B4: 2,8,1,3,4 # reduction candidate for 2,8 B4: 2,8 # 17 pairs C4: 2,8,1,3 # reduction candidate for 2,8 C4: 2,8 # 19 pairs A5: 2,8,6,9 # reduction candidate for 2,8 A5: 2,8 => CTR * 1....648..64..........4..67....9.67..7.4..5..5...7.1..6587143293....87..4.7...8.. A5: 6,9 # 8 pairs C5: 2,8,1,3,6,9 # reduction candidate for 2,8 C5: 2,8 # 14 pairs B6: 2,8,3,4,9 # reduction candidate for 2,8 B6: 2,8 # 10 pairs C6: 2,8,3,6,9 # reduction candidate for 2,8 C6: 2,8 # 14 pairs * PAIR A4: 2,8 ROW 4 D4: 2,8,1,3,5 # reduction candidate for 2,8 D4: 2,8 # 13 pairs I4: 2,8,3,4 # reduction candidate for 2,8 I4: 2,8 # 11 pairs * PAIR A4: 2,8 COL A A2: 2,8,7,9 # reduction candidate for 2,8 A2: 2,8 => CTR * 1.79.648.864..79..93584126724139567.67.41.5.858.67.1..75816432939...87..4..7398.. A2: 7,9 # 8 pairs A3: 2,8,9 # reduction candidate for 2,8 A3: 2,8 # 10 pairs * PAIR F6: 2,3 BLK 5 D4: 2,3,1,5,8 # reduction candidate for 2,3 D4: 2,3 # 10 pairs F4: 2,3,1,5 # reduction candidate for 2,3 F4: 2,3 # 13 pairs E5: 2,3,1,6,8 # reduction candidate for 2,3 E5: 2,3 # 15 pairs F5: 2,3,1 # reduction candidate for 2,3 F5: 2,3 # 10 pairs D6: 2,3,6,8 # reduction candidate for 2,3 D6: 2,3 => CTR * 1....648..64..........4..67....9.67..7.46.5..5.6.7.1..6587143293....87..4.7...8.. D6: 6,8 # 8 pairs * PAIR F6: 2,3 ROW 6 B6: 2,3,4,8,9 # reduction candidate for 2,3 B6: 2,3 # 14 pairs C6: 2,3,6,8,9 # reduction candidate for 2,3 C6: 2,3 # 9 pairs I6: 2,3,4,8,9 # reduction candidate for 2,3 I6: 2,3 # 10 pairs * PAIR F6: 2,3 COL F F2: 2,3,5,7,9 # reduction candidate for 2,3 F2: 2,3 => CTR * 1.7..648..64...9..8351492672...9567..7.4.15..5...7.1...58..432.3....87..4....78.. F2: 5,7,9 # 7 pairs F3: 2,3,1,5,9 # reduction candidate for 2,3 F3: 2,3 # 10 pairs F9: 2,3,1,5,7,9 # reduction candidate for 2,3 F9: 2,3 => CTR * 1.7..648..64..79..8...49267....9567..7.4.15..5...7.1..758..432.3....87..4..7..8.. F9: 1,5,7,9 # 7 pairs * PAIR H5: 3,9 BLK 6 I5: 3,9,2,8 # reduction candidate for 3,9 I5: 3,9 # 14 pairs H6: 3,9,4 # reduction candidate for 3,9 H6: 3,9 # 11 pairs I6: 3,9,2,4,8 # reduction candidate for 3,9 I6: 3,9 # 13 pairs * PAIR H5: 3,9 ROW 5 C5: 3,9,1,2,6,8 # reduction candidate for 3,9 C5: 3,9 # 10 pairs C5: 1,2,6,8 # 7 pairs * PAIR E7: 1,6 BLK 8 D7: 1,6,7,9 # reduction candidate for 1,6 D7: 1,6 => SOLVED * 137926485964587231825341967241895673673412598589673142758164329396258714412739856 D7: 7,9 # 8 pairs D8: 1,6,2,5,9 # reduction candidate for 1,6 D8: 1,6 # 11 pairs E8: 1,6,2,5 # reduction candidate for 1,6 E8: 1,6 # 9 pairs D9: 1,6,2,3,5,7,9 # reduction candidate for 1,6 D9: 1,6 # 11 pairs E9: 1,6,2,3,5 # reduction candidate for 1,6 E9: 1,6 # 10 pairs * PAIR E7: 1,6 ROW 7 C7: 1,6,7,8,9 # reduction candidate for 1,6 C7: 1,6 => CTR * 1....648..64..........4..67....9.67..7.4..5..5...7.1..85.7.43293....87..4.7...8.. C7: 7,8,9 # 7 pairs I7: 1,6,9 # reduction candidate for 1,6 I7: 1,6 # 9 pairs * PAIR E7: 1,6 COL E E5: 1,6,2,3,8 # reduction candidate for 1,6 E5: 1,6 # 9 pairs E5: 2,3,8 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-038-base-pr-000.dot * REASONING * DIS # C1: 3,5 => CTR => C1: 2,7,9 * DIS # D1: 3,5 => CTR => D1: 2,7,9 * PRF # A2: 2,9 => SOL * DIS # F2: 2,9 => CTR => F2: 3,5,7 * DIS # C3: 2,9 => CTR => C3: 3,5,8 * DIS # A5: 2,8 => CTR => A5: 6,9 * DIS # A2: 2,8 => CTR => A2: 7,9 * DIS # D6: 2,3 => CTR => D6: 6,8 * DIS # F2: 2,3 => CTR => F2: 5,7,9 * DIS # F9: 2,3 => CTR => F9: 1,5,7,9 * PRF # D7: 1,6 => SOL * DIS # C7: 1,6 => CTR => C7: 7,8,9 * CNT 12 HDP CHAINS / 60 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,E7,F6,G2,G3,H5,I1) * 1....648..64..........4..67....9.67..7.4..5..5...7.1...5...432.3....87..4.....8.. * PAIR I1: 3,5 BLK 3 H2: 3,5,1 # reduction candidate for 3,5 H2: 3,5 # 9 pairs I2: 3,5,1 # reduction candidate for 3,5 I2: 3,5 # 9 pairs * PAIR I1: 3,5 ROW 1 C1: 3,5,2,7,9 # reduction candidate for 3,5 C1: 3,5 => CTR * 19.72648.764...2......4.967....9.67..7.4..5..5...7.1..857..432.3....87..4....78.. D1: 3,5,2,7,9 # reduction candidate for 3,5 D1: 3,5 => CTR * 197.2648..64.......35.4..67....9.67..7.4..5..5...7.1..758..432.3....87..4.....8.. E1: 3,5,2 # reduction candidate for 3,5 E1: 3,5 # 14 pairs * RESTART * PAIR I1: 3,5 ROW 1 E1: 3,5,2 # reduction candidate for 3,5 E1: 2 # 16 pairs E1: 3,5 # 14 pairs * PAIR RESTART * PAIR I1: 3,5 BLK 3 H2: 3,5,1 # reduction candidate for 3,5 H2: 3,5 # 9 pairs I2: 3,5,1 # reduction candidate for 3,5 I2: 3,5 # 9 pairs * PAIR I1: 3,5 ROW 1 E1: 3,5,2 # reduction candidate for 3,5 E1: 2 # 16 pairs E1: 3,5 # 14 pairs * PAIR G2: 2,9 ROW 2 A2: 2,9,7,8 # reduction candidate for 2,9 A2: 2,9 => SOLVED * 137926485964587231825341967241895673673412598589673142758164329396258714412739856 * DURATION: 0:00:10.323933 START: 23:33:37.344789 END: 23:33:47.668722 2017-05-03 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-038-base-pr-001.dot * REASONING * DIS # C1: 3,5 => CTR => C1: 2,7,9 * DIS C1: 2,7,9 # D1: 3,5 => CTR => D1: 2,7,9 * PRF C1: 2,7,9 + D1: 2,7,9 # A2: 2,9 => SOL * STA C1: 2,7,9 + D1: 2,7,9 + A2: 2,9 * CNT 3 HDP CHAINS / 12 HYP OPENED
Header Info
Top 95 Sudokus 038 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 137926485964587231825341967241895673673412598589673142758164329396258714412739856 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 # H2: 3,5 => UNS * INC # I2: 3,5 => UNS * DIS # C1: 3,5 => CTR => C1: 2,7,9 * INC # C1: 2,7,9 => UNS * DIS # D1: 3,5 => CTR => D1: 2,7,9 * INC # D1: 2,7,9 => UNS * INC # E1: 3,5 => UNS * PRF # A2: 2,9 => SOL * INC # A2: 7,8 => UNS * INC # D2: 2,9 => UNS * DIS # F2: 2,9 => CTR => F2: 3,5,7 * INC # F2: 3,5,7 => UNS * INC # A3: 2,9 => UNS * INC # B3: 2,9 => UNS * DIS # C3: 2,9 => CTR => C3: 3,5,8 * INC # C3: 3,5,8 => UNS * INC # D3: 2,9 => UNS * INC # F3: 2,9 => UNS * INC # B4: 2,8 => UNS * INC # C4: 2,8 => UNS * DIS # A5: 2,8 => CTR => A5: 6,9 * INC # A5: 6,9 => UNS * INC # C5: 2,8 => UNS * INC # B6: 2,8 => UNS * INC # C6: 2,8 => UNS * INC # D4: 2,8 => UNS * INC # I4: 2,8 => UNS * DIS # A2: 2,8 => CTR => A2: 7,9 * INC # A2: 7,9 => UNS * INC # A3: 2,8 => UNS * INC # D4: 2,3 => UNS * INC # F4: 2,3 => UNS * INC # E5: 2,3 => UNS * INC # F5: 2,3 => UNS * DIS # D6: 2,3 => CTR => D6: 6,8 * INC # D6: 6,8 => UNS * INC # B6: 2,3 => UNS * INC # C6: 2,3 => UNS * INC # I6: 2,3 => UNS * DIS # F2: 2,3 => CTR => F2: 5,7,9 * INC # F2: 5,7,9 => UNS * INC # F3: 2,3 => UNS * DIS # F9: 2,3 => CTR => F9: 1,5,7,9 * INC # F9: 1,5,7,9 => UNS * INC # I5: 3,9 => UNS * INC # H6: 3,9 => UNS * INC # I6: 3,9 => UNS * INC # C5: 3,9 => UNS * INC # C5: 1,2,6,8 => UNS * PRF # D7: 1,6 => SOL * INC # D7: 7,9 => UNS * INC # D8: 1,6 => UNS * INC # E8: 1,6 => UNS * INC # D9: 1,6 => UNS * INC # E9: 1,6 => UNS * DIS # C7: 1,6 => CTR => C7: 7,8,9 * INC # C7: 7,8,9 => UNS * INC # I7: 1,6 => UNS * INC # E5: 1,6 => UNS * INC # E5: 2,3,8 => UNS * CNT 60 HDP CHAINS / 60 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # H2: 3,5 => UNS * INC # I2: 3,5 => UNS * DIS # C1: 3,5 => CTR => C1: 2,7,9 * DIS C1: 2,7,9 # D1: 3,5 => CTR => D1: 2,7,9 * INC C1: 2,7,9 + D1: 2,7,9 # E1: 3,5 => UNS * INC C1: 2,7,9 + D1: 2,7,9 # E1: 3,5 => UNS * INC C1: 2,7,9 + D1: 2,7,9 # E1: 2 => UNS * INC C1: 2,7,9 + D1: 2,7,9 # H2: 3,5 => UNS * INC C1: 2,7,9 + D1: 2,7,9 # I2: 3,5 => UNS * INC C1: 2,7,9 + D1: 2,7,9 # E1: 3,5 => UNS * INC C1: 2,7,9 + D1: 2,7,9 # E1: 2 => UNS * PRF C1: 2,7,9 + D1: 2,7,9 # A2: 2,9 => SOL * STA C1: 2,7,9 + D1: 2,7,9 + A2: 2,9 * CNT 12 HDP CHAINS / 12 HYP OPENED