Analysis of xx-top95-022-base.sdk
Contents
Original Sudoku
level: medium
position: ..247..58..............1.4.....2...9528.9.4....9...1.........3.3....75..685..2... initial
Autosolve
position: ..247..58..............1.4.....2...952819.4....9...1252......3.3....75.2685..2... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B6: 4,7 => CTR => B6: 3,6 * DIS # D4: 3,6 => CTR => D4: 5,7 * DIS # F4: 3,6 => CTR => F4: 4,5 * DIS # I5: 7 => CTR => I5: 3,6 * PRF # G4: 6,8 => SOL * DIS # G4: 3 => CTR => G4: 6,8 * DIS # I5: 6,7 => CTR => I5: 3 * PRF # I5: 3 => SOL * CNT 8 HDP CHAINS / 39 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B6: 4,7 => CTR => B6: 3,6 * DIS B6: 3,6 # D4: 3,6 => CTR => D4: 5,7 * DIS B6: 3,6 + D4: 5,7 # F4: 3,6 => CTR => F4: 4,5 * DIS B6: 3,6 + D4: 5,7 + F4: 4,5 # I5: 7 => CTR => I5: 3,6 * PRF B6: 3,6 + D4: 5,7 + F4: 4,5 + I5: 3,6 # G4: 6,8 => SOL * STA B6: 3,6 + D4: 5,7 + F4: 4,5 + I5: 3,6 + G4: 6,8 * CNT 5 HDP CHAINS / 26 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..247..58..............1.4.....2...9528.9.4....9...1.........3.3....75..685..2... | initial |
| ..247..58..............1.4.....2...952819.4....9...1252......3.3....75.2685..2... | autosolve |
| 132479658847563291956281347413725869528196473769348125271854936394617582685932714 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) A1: 1,9 A6: 4,7 F5: 3,6 H4: 6,8 H5: 6,7 C8: 1,4 D9: 3,9 G9: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,B1: 1.. / A1 = 1 => 17 pairs (_) / B1 = 1 => 15 pairs (_) H2,I2: 1.. / H2 = 1 => 11 pairs (_) / I2 = 1 => 10 pairs (_) A1,A4: 1.. / A1 = 1 => 17 pairs (_) / A4 = 1 => 15 pairs (_) D2,D3: 2.. / D2 = 2 => 8 pairs (_) / D3 = 2 => 8 pairs (_) G2,G3: 2.. / G2 = 2 => 8 pairs (_) / G3 = 2 => 8 pairs (_) D2,G2: 2.. / D2 = 2 => 8 pairs (_) / G2 = 2 => 8 pairs (_) D3,G3: 2.. / D3 = 2 => 8 pairs (_) / G3 = 2 => 8 pairs (_) G4,I5: 3.. / G4 = 3 => 0 pairs (X) / I5 = 3 => 0 pairs (_) D9,E9: 3.. / D9 = 3 => 9 pairs (_) / E9 = 3 => 12 pairs (_) F5,I5: 3.. / F5 = 3 => 0 pairs (X) / I5 = 3 => 0 pairs (_) I7,I9: 4.. / I7 = 4 => 13 pairs (_) / I9 = 4 => 10 pairs (_) E9,I9: 4.. / E9 = 4 => 13 pairs (_) / I9 = 4 => 10 pairs (_) B2,B3: 5.. / B2 = 5 => 11 pairs (_) / B3 = 5 => 8 pairs (_) D4,F4: 5.. / D4 = 5 => 9 pairs (_) / F4 = 5 => 10 pairs (_) D4,D6: 7.. / D4 = 7 => 10 pairs (_) / D6 = 7 => 9 pairs (_) H5,I5: 7.. / H5 = 7 => 9 pairs (_) / I5 = 7 => 0 pairs (X) B7,C7: 7.. / B7 = 7 => 10 pairs (_) / C7 = 7 => 9 pairs (_) A2,A3: 8.. / A2 = 8 => 9 pairs (_) / A3 = 8 => 10 pairs (_) G4,H4: 8.. / G4 = 8 => 0 pairs (*) / H4 = 8 => 0 pairs (X) G7,H8: 8.. / G7 = 8 => 8 pairs (_) / H8 = 8 => 0 pairs (*) G4,G7: 8.. / G4 = 8 => 0 pairs (*) / G7 = 8 => 0 pairs (X) H4,H8: 8.. / H4 = 8 => 8 pairs (_) / H8 = 8 => 0 pairs (*) B7,B8: 9.. / B7 = 9 => 12 pairs (_) / B8 = 9 => 9 pairs (_) * DURATION: 0:00:30.335791 START: 23:19:19.479560 END: 23:19:49.815351 2017-05-03 * CP COUNT: (23) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,C8,D9,F5,G9,H4,H5) * ..247..58..............1.4.....2...952819.4....9...1252......3.3....75.2685..2... * PAIR A6: 4,7 BLK 4 A4: 4,7,1 # reduction candidate for 4,7 A4: 4,7 # 17 pairs B4: 4,7,1,3,6 # reduction candidate for 4,7 B4: 4,7 # 19 pairs C4: 4,7,1,3,6 # reduction candidate for 4,7 C4: 4,7 # 22 pairs B6: 4,7,3,6 # reduction candidate for 4,7 B6: 4,7 => CTR * ..247..58..............1.4.....2...952819.4....9...1252......3.3....75.2685..2... B6: 3,6 # 9 pairs * PAIR A6: 4,7 COL A A2: 4,7,8,9 # reduction candidate for 4,7 A2: 4,7 # 15 pairs A2: 8,9 # 9 pairs * PAIR F5: 3,6 BLK 5 D4: 3,6,5,7 # reduction candidate for 3,6 D4: 3,6 => CTR * ..247..58..............1.4.....25..952819.4..4.97..1252....4.3.3....75.2685..2..4 D4: 5,7 # 9 pairs F4: 3,6,4,5 # reduction candidate for 3,6 F4: 3,6 => CTR * ..247..58..............1.4....52...952819.4..4.97..1252....4.3.3....75.2685..2..4 F4: 4,5 # 9 pairs D6: 3,6,7,8 # reduction candidate for 3,6 D6: 3,6 # 13 pairs E6: 3,6,4,8 # reduction candidate for 3,6 E6: 3,6 # 14 pairs F6: 3,6,4,8 # reduction candidate for 3,6 F6: 3,6 # 22 pairs * PAIR F5: 3,6 ROW 5 I5: 3,6,7 # reduction candidate for 3,6 I5: 7 => CTR * ..247..58..............1.4.....2.389528193467.39...1252.....8363....75.2685..2..4 I5: 3,6 # 9 pairs * PAIR F5: 3,6 COL F F1: 3,6,9 # reduction candidate for 3,6 F1: 3,6 # 11 pairs F2: 3,6,5,8,9 # reduction candidate for 3,6 F2: 3,6 # 20 pairs * PAIR H4: 6,8 BLK 6 G4: 6,8,3 # reduction candidate for 6,8 G4: 6,8 => SOLVED * 132479658847563291956281347413725869528196473769348125271854936394617582685932714 G4: 3 => CTR * ..247..58..............1.4.....2.3895281934...39...1252.....83.3....75.2685..2... * PAIR H4: 6,8 COL H H8: 6,8,1,9 # reduction candidate for 6,8 H8: 1,9 # 16 pairs H8: 6,8 # 11 pairs * PAIR H5: 6,7 BLK 6 I5: 6,7,3 # reduction candidate for 6,7 I5: 6,7 => CTR * ..247..58..............1.4.....2.3895281934...39...1252.....83.3....75.2685..2... I5: 3 => SOLVED * 132479658847563291956281347413725869528196473769348125271854936394617582685932714 * PAIR H5: 6,7 COL H H2: 6,7,1,9 # reduction candidate for 6,7 H2: 6,7 # 17 pairs H2: 1,9 # 9 pairs * PAIR C8: 1,4 BLK 7 B7: 1,4,7,9 # reduction candidate for 1,4 B7: 1,4 # 11 pairs C7: 1,4,7 # reduction candidate for 1,4 C7: 1,4 # 10 pairs B8: 1,4,9 # reduction candidate for 1,4 B8: 1,4 # 12 pairs * PAIR C8: 1,4 ROW 8 E8: 1,4,6,8 # reduction candidate for 1,4 E8: 1,4 # 13 pairs E8: 6,8 # 10 pairs * PAIR C8: 1,4 COL C C4: 1,4,3,6,7 # reduction candidate for 1,4 C4: 1,4 # 19 pairs C4: 3,6,7 # 9 pairs * PAIR D9: 3,9 COL D D2: 3,9,2,5,6,8 # reduction candidate for 3,9 D2: 3,9 # 10 pairs D3: 3,9,2,5,6,8 # reduction candidate for 3,9 D3: 3,9 # 10 pairs * PAIR G9: 7,9 BLK 9 H9: 7,9,1 # reduction candidate for 7,9 H9: 7,9 # 11 pairs H9: 1 # 11 pairs * PAIR G9: 7,9 COL G G2: 7,9,2,3,6 # reduction candidate for 7,9 G2: 7,9 # 11 pairs G3: 7,9,2,3,6 # reduction candidate for 7,9 G3: 7,9 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-022-base-pr-000.dot * REASONING * DIS # B6: 4,7 => CTR => B6: 3,6 * DIS # D4: 3,6 => CTR => D4: 5,7 * DIS # F4: 3,6 => CTR => F4: 4,5 * DIS # I5: 7 => CTR => I5: 3,6 * PRF # G4: 6,8 => SOL * DIS # G4: 3 => CTR => G4: 6,8 * DIS # I5: 6,7 => CTR => I5: 3 * PRF # I5: 3 => SOL * CNT 8 HDP CHAINS / 39 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,C8,D9,F5,G9,H4,H5) * ..247..58..............1.4.....2...952819.4....9...1252......3.3....75.2685..2... * PAIR A6: 4,7 BLK 4 A4: 4,7,1 # reduction candidate for 4,7 A4: 4,7 # 17 pairs B4: 4,7,1,3,6 # reduction candidate for 4,7 B4: 4,7 # 19 pairs C4: 4,7,1,3,6 # reduction candidate for 4,7 C4: 4,7 # 22 pairs B6: 4,7,3,6 # reduction candidate for 4,7 B6: 4,7 => CTR * ..247..58..............1.4.....2...952819.4....9...1252......3.3....75.2685..2... * PAIR A6: 4,7 COL A A2: 4,7,8,9 # reduction candidate for 4,7 A2: 4,7 # 16 pairs A2: 8,9 # 10 pairs * PAIR RESTART * PAIR A6: 4,7 BLK 4 A4: 4,7,1 # reduction candidate for 4,7 A4: 4,7 # 17 pairs B4: 4,7,1,3,6 # reduction candidate for 4,7 B4: 4,7 # 19 pairs C4: 4,7,1,3,6 # reduction candidate for 4,7 C4: 4,7 # 22 pairs * PAIR A6: 4,7 COL A A2: 4,7,8,9 # reduction candidate for 4,7 A2: 4,7 # 16 pairs A2: 8,9 # 10 pairs * PAIR F5: 3,6 BLK 5 D4: 3,6,5,7 # reduction candidate for 3,6 D4: 3,6 => CTR * ..247..58..............1.4.....25..952819.4..4.97..1252....4.3.3....75.2685..2..4 F4: 3,6,4,5 # reduction candidate for 3,6 F4: 3,6 => CTR * ..247..58..............1.4....52...952819.4..4.97..1252....4.3.3....75.2685..2..4 D6: 3,6,7,8 # reduction candidate for 3,6 D6: 3,6 # 13 pairs E6: 3,6,4,8 # reduction candidate for 3,6 E6: 3,6 # 14 pairs F6: 3,6,4,8 # reduction candidate for 3,6 F6: 3,6 # 22 pairs * PAIR F5: 3,6 ROW 5 I5: 3,6,7 # reduction candidate for 3,6 I5: 7 => CTR * ..247..58..............1.4.....2.389528193467.39...1252.....8363....75.2685..2..4 * PAIR F5: 3,6 COL F F1: 3,6,9 # reduction candidate for 3,6 F1: 3,6 # 14 pairs F2: 3,6,5,8,9 # reduction candidate for 3,6 F2: 3,6 # 21 pairs * PAIR RESTART * PAIR F5: 3,6 BLK 5 D6: 3,6,7,8 # reduction candidate for 3,6 D6: 3,6 # 14 pairs E6: 3,6,4,8 # reduction candidate for 3,6 E6: 3,6 # 15 pairs F6: 3,6,4,8 # reduction candidate for 3,6 F6: 3,6 # 23 pairs * PAIR F5: 3,6 COL F F1: 3,6,9 # reduction candidate for 3,6 F1: 3,6 # 14 pairs F2: 3,6,5,8,9 # reduction candidate for 3,6 F2: 3,6 # 21 pairs * PAIR H4: 6,8 BLK 6 G4: 6,8,3 # reduction candidate for 6,8 G4: 6,8 => SOLVED * 132479658847563291956281347413725869528196473769348125271854936394617582685932714 * DURATION: 0:00:20.096715 START: 23:20:17.484800 END: 23:20:37.581515 2017-05-03 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-022-base-pr-001.dot * REASONING * DIS # B6: 4,7 => CTR => B6: 3,6 * DIS B6: 3,6 # D4: 3,6 => CTR => D4: 5,7 * DIS B6: 3,6 + D4: 5,7 # F4: 3,6 => CTR => F4: 4,5 * DIS B6: 3,6 + D4: 5,7 + F4: 4,5 # I5: 7 => CTR => I5: 3,6 * PRF B6: 3,6 + D4: 5,7 + F4: 4,5 + I5: 3,6 # G4: 6,8 => SOL * STA B6: 3,6 + D4: 5,7 + F4: 4,5 + I5: 3,6 + G4: 6,8 * CNT 5 HDP CHAINS / 26 HYP OPENED
Header Info
Top 95 Sudokus 022 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 132479658847563291956281347413725869528196473769348125271854936394617582685932714 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 # A4: 4,7 => UNS * INC # B4: 4,7 => UNS * INC # C4: 4,7 => UNS * DIS # B6: 4,7 => CTR => B6: 3,6 * INC # B6: 3,6 => UNS * INC # A2: 4,7 => UNS * INC # A2: 8,9 => UNS * DIS # D4: 3,6 => CTR => D4: 5,7 * INC # D4: 5,7 => UNS * DIS # F4: 3,6 => CTR => F4: 4,5 * INC # F4: 4,5 => UNS * INC # D6: 3,6 => UNS * INC # E6: 3,6 => UNS * INC # F6: 3,6 => UNS * INC # I5: 3,6 => UNS * DIS # I5: 7 => CTR => I5: 3,6 * INC # F1: 3,6 => UNS * INC # F2: 3,6 => UNS * PRF # G4: 6,8 => SOL * DIS # G4: 3 => CTR => G4: 6,8 * INC # H8: 6,8 => UNS * INC # H8: 1,9 => UNS * DIS # I5: 6,7 => CTR => I5: 3 * PRF # I5: 3 => SOL * INC # H2: 6,7 => UNS * INC # H2: 1,9 => UNS * INC # B7: 1,4 => UNS * INC # C7: 1,4 => UNS * INC # B8: 1,4 => UNS * INC # E8: 1,4 => UNS * INC # E8: 6,8 => UNS * INC # C4: 1,4 => UNS * INC # C4: 3,6,7 => UNS * INC # D2: 3,9 => UNS * INC # D3: 3,9 => UNS * INC # H9: 7,9 => UNS * INC # H9: 1 => UNS * INC # G2: 7,9 => UNS * INC # G3: 7,9 => UNS * CNT 39 HDP CHAINS / 39 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A4: 4,7 => UNS * INC # B4: 4,7 => UNS * INC # C4: 4,7 => UNS * DIS # B6: 4,7 => CTR => B6: 3,6 * INC B6: 3,6 # A2: 4,7 => UNS * INC B6: 3,6 # A2: 8,9 => UNS * INC B6: 3,6 # A4: 4,7 => UNS * INC B6: 3,6 # B4: 4,7 => UNS * INC B6: 3,6 # C4: 4,7 => UNS * INC B6: 3,6 # A2: 4,7 => UNS * INC B6: 3,6 # A2: 8,9 => UNS * DIS B6: 3,6 # D4: 3,6 => CTR => D4: 5,7 * DIS B6: 3,6 + D4: 5,7 # F4: 3,6 => CTR => F4: 4,5 * INC B6: 3,6 + D4: 5,7 + F4: 4,5 # D6: 3,6 => UNS * INC B6: 3,6 + D4: 5,7 + F4: 4,5 # E6: 3,6 => UNS * INC B6: 3,6 + D4: 5,7 + F4: 4,5 # F6: 3,6 => UNS * INC B6: 3,6 + D4: 5,7 + F4: 4,5 # I5: 3,6 => UNS * DIS B6: 3,6 + D4: 5,7 + F4: 4,5 # I5: 7 => CTR => I5: 3,6 * INC B6: 3,6 + D4: 5,7 + F4: 4,5 + I5: 3,6 # F1: 3,6 => UNS * INC B6: 3,6 + D4: 5,7 + F4: 4,5 + I5: 3,6 # F2: 3,6 => UNS * INC B6: 3,6 + D4: 5,7 + F4: 4,5 + I5: 3,6 # D6: 3,6 => UNS * INC B6: 3,6 + D4: 5,7 + F4: 4,5 + I5: 3,6 # E6: 3,6 => UNS * INC B6: 3,6 + D4: 5,7 + F4: 4,5 + I5: 3,6 # F6: 3,6 => UNS * INC B6: 3,6 + D4: 5,7 + F4: 4,5 + I5: 3,6 # F1: 3,6 => UNS * INC B6: 3,6 + D4: 5,7 + F4: 4,5 + I5: 3,6 # F2: 3,6 => UNS * PRF B6: 3,6 + D4: 5,7 + F4: 4,5 + I5: 3,6 # G4: 6,8 => SOL * STA B6: 3,6 + D4: 5,7 + F4: 4,5 + I5: 3,6 + G4: 6,8 * CNT 26 HDP CHAINS / 26 HYP OPENED