Analysis of xx-top95-040-base.sdk
Contents
Original Sudoku
level: medium
position: ...8....9.873...4.6..7.......85..97...........43..75.......3....3...145.4....2..1 initial
Autosolve
position: 3..8..7.9.873...4.6..7.......85..97......8....43..75.....4.3....3...145.4....2..1 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B4: 1,2 => CTR => B4: 6 * PRF # A2: 1,2 => SOL * DIS # A7: 1,2 => CTR => A7: 5,7,8,9 * DIS # A5: 2,9 => CTR => A5: 5,7 * DIS # C5: 2,9 => CTR => C5: 5,6 * DIS # A7: 2,9 => CTR => A7: 1,5,7,8 * DIS # A8: 2,9 => CTR => A8: 7,8 * DIS # E4: 4,6 => CTR => E4: 3 * DIS # E5: 4,6 => CTR => E5: 3,9 * DIS # I4: 4,6 => CTR => I4: 2,3 * PRF # H6: 1,2 => SOL * DIS # E5: 3,4 => CTR => E5: 6,9 * DIS # I8: 7,8 => CTR => I8: 2,6 * DIS # H9: 6,9 => CTR => H9: 3,8 * CNT 14 HDP CHAINS / 41 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B4: 1,2 => CTR => B4: 6 * DIS B4: 6 # B5: 7 => CTR => B5: 2,9 * DIS B4: 6 + B5: 2,9 # E1: 2 => CTR => E1: 1,4 * DIS B4: 6 + B5: 2,9 + E1: 1,4 # E3: 1,4 => CTR => E3: 2 * PRF B4: 6 + B5: 2,9 + E1: 1,4 + E3: 2 => SOL * STA B4: 6 + B5: 2,9 + E1: 1,4 + E3: 2 * CNT 5 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...8....9.873...4.6..7.......85..97...........43..75.......3....3...145.4....2..1 | initial |
| 3..8..7.9.873...4.6..7.......85..97......8....43..75.....4.3....3...145.4....2..1 | autosolve |
| 351846729287319645694725183168534972725198364943267518516483297832971456479652831 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) A4: 1,2 A6: 2,9 F4: 4,6 D5: 1,2 D6: 1,2 E6: 6,9 D8: 6,9 E8: 7,8 D9: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A4,B4: 1.. / A4 = 1 => 9 pairs (_) / B4 = 1 => 0 pairs (X) D5,D6: 1.. / D5 = 1 => 0 pairs (*) / D6 = 1 => 0 pairs (X) D6,H6: 1.. / D6 = 1 => 7 pairs (_) / H6 = 1 => 0 pairs (*) D5,D6: 2.. / D5 = 2 => 7 pairs (_) / D6 = 2 => 0 pairs (*) E4,E5: 3.. / E4 = 3 => 9 pairs (_) / E5 = 3 => 0 pairs (X) G9,H9: 3.. / G9 = 3 => 9 pairs (_) / H9 = 3 => 10 pairs (_) E4,I4: 3.. / E4 = 3 => 9 pairs (_) / I4 = 3 => 0 pairs (X) C1,C3: 4.. / C1 = 4 => 10 pairs (_) / C3 = 4 => 11 pairs (_) I4,I5: 4.. / I4 = 4 => 0 pairs (X) / I5 = 4 => 9 pairs (_) E5,I5: 4.. / E5 = 4 => 0 pairs (X) / I5 = 4 => 9 pairs (_) I2,I3: 5.. / I2 = 5 => 19 pairs (_) / I3 = 5 => 0 pairs (X) E7,E9: 5.. / E7 = 5 => 10 pairs (_) / E9 = 5 => 14 pairs (_) D8,D9: 6.. / D8 = 6 => 9 pairs (_) / D9 = 6 => 10 pairs (_) A5,B5: 7.. / A5 = 7 => 9 pairs (_) / B5 = 7 => 12 pairs (_) I7,I8: 7.. / I7 = 7 => 10 pairs (_) / I8 = 7 => 0 pairs (X) B9,E9: 7.. / B9 = 7 => 10 pairs (_) / E9 = 7 => 11 pairs (_) H6,I6: 8.. / H6 = 8 => 9 pairs (_) / I6 = 8 => 9 pairs (_) A7,A8: 8.. / A7 = 8 => 11 pairs (_) / A8 = 8 => 11 pairs (_) F2,F3: 9.. / F2 = 9 => 10 pairs (_) / F3 = 9 => 0 pairs (X) E5,E6: 9.. / E5 = 9 => 0 pairs (*) / E6 = 9 => 0 pairs (X) D8,D9: 9.. / D8 = 9 => 10 pairs (_) / D9 = 9 => 9 pairs (_) H7,H9: 9.. / H7 = 9 => 9 pairs (_) / H9 = 9 => 0 pairs (X) A2,F2: 9.. / A2 = 9 => 0 pairs (X) / F2 = 9 => 10 pairs (_) A6,E6: 9.. / A6 = 9 => 0 pairs (*) / E6 = 9 => 0 pairs (X) * DURATION: 0:00:37.610941 START: 23:36:33.841497 END: 23:37:11.452438 2017-05-03 * CP COUNT: (24) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,D5,D6,D8,D9,E6,E8,F4) * 3..8..7.9.873...4.6..7.......85..97......8....43..75.....4.3....3...145.4....2..1 * PAIR A4: 1,2 BLK 4 B4: 1,2,6 # reduction candidate for 1,2 B4: 1,2 => CTR * 35.8.67.9.873.964569.7.5..3..8534976....98.34943.675.....4.3.9..396.1452475982361 B4: 6 # 28 pairs * PAIR A4: 1,2 COL A A2: 1,2,5,9 # reduction candidate for 1,2 A2: 1,2 => SOLVED * 351846729287319645694725183168534972725198364943267518516483297832971456479652831 A2: 5,9 # 10 pairs A7: 1,2,5,7,8,9 # reduction candidate for 1,2 A7: 1,2 => CTR * 3..8..7.95873.9.4.6..7....5..85..97.7....8...943.675.8...4.3..783..7145.47...2..1 A7: 5,7,8,9 # 9 pairs * PAIR A6: 2,9 BLK 4 A5: 2,9,5,7 # reduction candidate for 2,9 A5: 2,9 => CTR * 3..8.57.95873...4.6..7......685.497..75..8..4.43..75.....453....3..8145.45..72..1 A5: 5,7 # 10 pairs B5: 2,9,5,6,7 # reduction candidate for 2,9 B5: 2,9 # 20 pairs C5: 2,9,5,6 # reduction candidate for 2,9 C5: 2,9 => CTR * 3..8..7.99873.6.456..7.9..3168534972..9268..42431975.....4.3....329.14564..6.2..1 C5: 5,6 # 10 pairs * PAIR A6: 2,9 COL A A2: 2,9,1,5 # reduction candidate for 2,9 A2: 2,9 # 19 pairs A7: 2,9,1,5,7,8 # reduction candidate for 2,9 A7: 2,9 => CTR * 3..8.57.95873.9.4.6..7.4..51.85.697.7....8....43.975689..4.3..783.97145.47.6.2.91 A7: 1,5,7,8 # 9 pairs A8: 2,9,7,8 # reduction candidate for 2,9 A8: 2,9 => CTR * 3..8.57.95873.9.4.6..7.4..51.85.697.7....8....43.975..8..4.3...93.6.145.4..9.2..1 A8: 7,8 # 12 pairs * PAIR F4: 4,6 BLK 5 E4: 4,6,3 # reduction candidate for 4,6 E4: 4,6 => CTR * 3..8..7.9.873...4.6..7.......85..973....38..42431975.....4.3....3...145.4....2..1 E4: 3 # 9 pairs E5: 4,6,3,9 # reduction candidate for 4,6 E5: 4,6 => CTR * 3..8..7.99873.6.456..7.9..3168534972...268..42431975.....4.3....329.14564..6.2..1 E5: 3,9 # 10 pairs * PAIR F4: 4,6 ROW 4 I4: 4,6,2,3 # reduction candidate for 4,6 I4: 4,6 => CTR * 35.8.67.9.873.964569.7.5..3..8534976....98.34943.675.....4.3.9..396.1452475982361 I4: 2,3 # 10 pairs * PAIR F4: 4,6 COL F F1: 4,6,5 # reduction candidate for 4,6 F1: 4,6 # 21 pairs F1: 5 # 12 pairs * PAIR D5: 1,2 ROW 5 G5: 1,2,3,6 # reduction candidate for 1,2 G5: 1,2 # 11 pairs H5: 1,2,3,6 # reduction candidate for 1,2 H5: 1,2 # 12 pairs * PAIR D6: 1,2 ROW 6 H6: 1,2,6,8 # reduction candidate for 1,2 H6: 1,2 => SOLVED * 351846729287319645694725183168534972725198364943267518516483297832971456479652831 H6: 6,8 # 9 pairs * PAIR E6: 6,9 BLK 5 E5: 6,9,3,4 # reduction candidate for 6,9 E5: 3,4 => CTR * 3..8..7.9.873...4.6..7.....1685.4972...238...2431975.....4.3....3...145.4....2..1 E5: 6,9 # 23 pairs * PAIR D8: 6,9 ROW 8 C8: 6,9,2 # reduction candidate for 6,9 C8: 6,9 # 10 pairs C8: 2 # 9 pairs * PAIR E8: 7,8 BLK 8 E7: 7,8,5 # reduction candidate for 7,8 E7: 7,8 # 14 pairs E9: 7,8,5 # reduction candidate for 7,8 E9: 7,8 # 10 pairs * PAIR E8: 7,8 ROW 8 A8: 7,8,2,9 # reduction candidate for 7,8 A8: 7,8 # 12 pairs I8: 7,8,2,6 # reduction candidate for 7,8 I8: 7,8 => CTR * 3..8.57.95873.9.4.6..7.4..51.85.697.7....8....43.975..8..4.3...9326.145.4..9.2..1 I8: 2,6 # 12 pairs * PAIR D9: 6,9 ROW 9 B9: 6,9,5,7 # reduction candidate for 6,9 B9: 6,9 # 14 pairs C9: 6,9,5 # reduction candidate for 6,9 C9: 6,9 # 15 pairs H9: 6,9,3,8 # reduction candidate for 6,9 H9: 6,9 => CTR * 3..8.57.95873.9.4.6..7.4..5..85.697.756.98....43..75.....453..7.3..7145.475.823.1 H9: 3,8 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-040-base-pr-000.dot * REASONING * DIS # B4: 1,2 => CTR => B4: 6 * PRF # A2: 1,2 => SOL * DIS # A7: 1,2 => CTR => A7: 5,7,8,9 * DIS # A5: 2,9 => CTR => A5: 5,7 * DIS # C5: 2,9 => CTR => C5: 5,6 * DIS # A7: 2,9 => CTR => A7: 1,5,7,8 * DIS # A8: 2,9 => CTR => A8: 7,8 * DIS # E4: 4,6 => CTR => E4: 3 * DIS # E5: 4,6 => CTR => E5: 3,9 * DIS # I4: 4,6 => CTR => I4: 2,3 * PRF # H6: 1,2 => SOL * DIS # E5: 3,4 => CTR => E5: 6,9 * DIS # I8: 7,8 => CTR => I8: 2,6 * DIS # H9: 6,9 => CTR => H9: 3,8 * CNT 14 HDP CHAINS / 41 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,D5,D6,D8,D9,E6,E8,F4) * 3..8..7.9.873...4.6..7.......85..97......8....43..75.....4.3....3...145.4....2..1 * PAIR A4: 1,2 BLK 4 B4: 1,2,6 # reduction candidate for 1,2 B4: 1,2 => CTR * 35.8.67.9.873.964569.7.5..3..8534976....98.34943.675.....4.3.9..396.1452475982361 * PAIR A6: 2,9 BLK 4 B5: 2,9,7 # reduction candidate for 2,9 B5: 7 => CTR * 32.8.576998732..456..7....3168534972.....8..4.43..75.8.164.3297.329.14564..6.2..1 * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A2,A6,B1,B3,B5,C1,C3,D5,D6,E2,E5,E6,F1,F2,F3,G2,G3,G9,H6,H9) * 3..8..7.9.873...456..7....31685349727.5..8..4.43..75.8516483297832971456479652..1 * PAIR C1: 1,4 ROW 1 E1: 1,4,2 # reduction candidate for 1,4 E1: 2 => CTR * 3.482.7192873196456917458231685349727251.8..4.43..75.8516483297832971456479652..1 * PAIR RESTART * PAIR C3: 1,4 ROW 3 E3: 1,4,2 # reduction candidate for 1,4 E3: 1,4 => CTR * 3..8..7.9.8732.1456..7..8231685349727.5..86342431.75.8516483297832971456479652..1 E3: 2 => SOLVED * 351846729287319645694725183168534972725198364943267518516483297832971456479652831 * DURATION: 0:00:12.946065 START: 23:37:48.816409 END: 23:38:01.762474 2017-05-03 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-040-base-pr-001.dot * REASONING * DIS # B4: 1,2 => CTR => B4: 6 * DIS B4: 6 # B5: 7 => CTR => B5: 2,9 * DIS B4: 6 + B5: 2,9 # E1: 2 => CTR => E1: 1,4 * DIS B4: 6 + B5: 2,9 + E1: 1,4 # E3: 1,4 => CTR => E3: 2 * PRF B4: 6 + B5: 2,9 + E1: 1,4 + E3: 2 => SOL * STA B4: 6 + B5: 2,9 + E1: 1,4 + E3: 2 * CNT 5 HDP CHAINS / 6 HYP OPENED
Header Info
Top 95 Sudokus 040 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 351846729287319645694725183168534972725198364943267518516483297832971456479652831 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 # B4: 1,2 => CTR => B4: 6 * INC # B4: 6 => UNS * PRF # A2: 1,2 => SOL * INC # A2: 5,9 => UNS * DIS # A7: 1,2 => CTR => A7: 5,7,8,9 * INC # A7: 5,7,8,9 => UNS * DIS # A5: 2,9 => CTR => A5: 5,7 * INC # A5: 5,7 => UNS * INC # B5: 2,9 => UNS * DIS # C5: 2,9 => CTR => C5: 5,6 * INC # C5: 5,6 => UNS * INC # A2: 2,9 => UNS * DIS # A7: 2,9 => CTR => A7: 1,5,7,8 * INC # A7: 1,5,7,8 => UNS * DIS # A8: 2,9 => CTR => A8: 7,8 * INC # A8: 7,8 => UNS * DIS # E4: 4,6 => CTR => E4: 3 * INC # E4: 3 => UNS * DIS # E5: 4,6 => CTR => E5: 3,9 * INC # E5: 3,9 => UNS * DIS # I4: 4,6 => CTR => I4: 2,3 * INC # I4: 2,3 => UNS * INC # F1: 4,6 => UNS * INC # F1: 5 => UNS * INC # G5: 1,2 => UNS * INC # H5: 1,2 => UNS * PRF # H6: 1,2 => SOL * INC # H6: 6,8 => UNS * INC # E5: 6,9 => UNS * DIS # E5: 3,4 => CTR => E5: 6,9 * INC # C8: 6,9 => UNS * INC # C8: 2 => UNS * INC # E7: 7,8 => UNS * INC # E9: 7,8 => UNS * INC # A8: 7,8 => UNS * DIS # I8: 7,8 => CTR => I8: 2,6 * INC # I8: 2,6 => UNS * INC # B9: 6,9 => UNS * INC # C9: 6,9 => UNS * DIS # H9: 6,9 => CTR => H9: 3,8 * INC # H9: 3,8 => UNS * CNT 41 HDP CHAINS / 41 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B4: 1,2 => CTR => B4: 6 * INC B4: 6 # B5: 2,9 => UNS * DIS B4: 6 # B5: 7 => CTR => B5: 2,9 * INC B4: 6 + B5: 2,9 # E1: 1,4 => UNS * DIS B4: 6 + B5: 2,9 # E1: 2 => CTR => E1: 1,4 * DIS B4: 6 + B5: 2,9 + E1: 1,4 # E3: 1,4 => CTR => E3: 2 * PRF B4: 6 + B5: 2,9 + E1: 1,4 + E3: 2 => SOL * STA B4: 6 + B5: 2,9 + E1: 1,4 + E3: 2 * CNT 7 HDP CHAINS / 6 HYP OPENED