Analysis of xx-top500-155-base.sdk
Contents
Original Sudoku
level: medium
position: 57.....4.1....3......8.......8....3..9.2.........4....6...5.1........9.8......2.. initial
Autosolve
position: 573.9284.1824.3.9.9468.532.4.85.973239.28.41.2..34..8962495817373..249.88.973.2.4 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # I2: 6,7 => SOL * DIS # I2: 5 => CTR => I2: 6,7 * DIS # I2: 5,6 => CTR => I2: 7 * PRF # I2: 7 => SOL * PRF # B6: 1,6 => SOL * DIS # B6: 5 => CTR => B6: 1,6 * PRF # C6: 5,7 => SOL * DIS # C6: 1 => CTR => C6: 5,7 * DIS # F6: 1,6 => CTR => F6: 7 * PRF # F6: 7 => SOL * PRF # F6: 6,7 => SOL * DIS # F6: 1 => CTR => F6: 6,7 * DIS # I2: 5,6 => CTR => I2: 7 * PRF # I2: 7 => SOL * PRF # B6: 1 => SOL * PRF # C6: 1,5 => SOL * DIS # C6: 7 => CTR => C6: 1,5 * PRF # B6: 1,5 => SOL * DIS # B6: 6 => CTR => B6: 1,5 * DIS # F6: 1,6 => CTR => F6: 7 * PRF # F6: 7 => SOL * CNT 21 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # I2: 6,7 => SOL * STA I2: 6,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 57.....4.1....3......8.......8....3..9.2.........4....6...5.1........9.8......2.. | initial |
| 573.9284.1824.3.9.9468.532.4.85.973239.28.41.2..34..8962495817373..249.88.973.2.4 | autosolve |
| 573192846182463597946875321468519732397286415215347689624958173731624958859731264 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) D1: 1,6 E2: 6,7 E3: 1,7 I1: 1,6 G2: 5,6 I3: 1,7 B4: 1,6 C5: 5,7 E4: 1,6 F5: 6,7 I5: 5,6 G6: 5,6 C8: 1,5 B9: 1,5 D8: 1,6 F9: 1,6 H8: 5,6 H9: 5,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,E3: 1.. / D1 = 1 => 0 pairs (*) / E3 = 1 => 0 pairs (X) I1,I3: 1.. / I1 = 1 => 0 pairs (X) / I3 = 1 => 0 pairs (_) E4,F6: 1.. / E4 = 1 => 0 pairs (*) / F6 = 1 => 0 pairs (X) C8,B9: 1.. / C8 = 1 => 0 pairs (*) / B9 = 1 => 0 pairs (X) D8,F9: 1.. / D8 = 1 => 0 pairs (X) / F9 = 1 => 0 pairs (_) D1,I1: 1.. / D1 = 1 => 0 pairs (*) / I1 = 1 => 0 pairs (X) E3,I3: 1.. / E3 = 1 => 0 pairs (X) / I3 = 1 => 0 pairs (_) B4,E4: 1.. / B4 = 1 => 0 pairs (X) / E4 = 1 => 0 pairs (_) C8,D8: 1.. / C8 = 1 => 0 pairs (*) / D8 = 1 => 0 pairs (X) B9,F9: 1.. / B9 = 1 => 0 pairs (X) / F9 = 1 => 0 pairs (_) C6,C8: 1.. / C6 = 1 => 0 pairs (X) / C8 = 1 => 0 pairs (_) D1,D8: 1.. / D1 = 1 => 0 pairs (*) / D8 = 1 => 0 pairs (X) E3,E4: 1.. / E3 = 1 => 0 pairs (X) / E4 = 1 => 0 pairs (_) F6,F9: 1.. / F6 = 1 => 0 pairs (X) / F9 = 1 => 0 pairs (_) G2,I2: 5.. / G2 = 5 => 0 pairs (*) / I2 = 5 => 0 pairs (X) I5,G6: 5.. / I5 = 5 => 0 pairs (*) / G6 = 5 => 0 pairs (X) C8,B9: 5.. / C8 = 5 => 0 pairs (X) / B9 = 5 => 0 pairs (_) H8,H9: 5.. / H8 = 5 => 0 pairs (*) / H9 = 5 => 0 pairs (X) C5,I5: 5.. / C5 = 5 => 0 pairs (X) / I5 = 5 => 0 pairs (_) C8,H8: 5.. / C8 = 5 => 0 pairs (X) / H8 = 5 => 0 pairs (_) B9,H9: 5.. / B9 = 5 => 0 pairs (*) / H9 = 5 => 0 pairs (X) B6,B9: 5.. / B6 = 5 => 0 pairs (X) / B9 = 5 => 0 pairs (_) G2,G6: 5.. / G2 = 5 => 0 pairs (*) / G6 = 5 => 0 pairs (X) I2,I5: 5.. / I2 = 5 => 0 pairs (X) / I5 = 5 => 0 pairs (_) D1,E2: 6.. / D1 = 6 => 0 pairs (X) / E2 = 6 => 0 pairs (_) B4,B6: 6.. / B4 = 6 => 0 pairs (*) / B6 = 6 => 0 pairs (X) I5,G6: 6.. / I5 = 6 => 0 pairs (X) / G6 = 6 => 0 pairs (_) D8,F9: 6.. / D8 = 6 => 0 pairs (*) / F9 = 6 => 0 pairs (X) H8,H9: 6.. / H8 = 6 => 0 pairs (X) / H9 = 6 => 0 pairs (_) D1,I1: 6.. / D1 = 6 => 0 pairs (X) / I1 = 6 => 0 pairs (_) B4,E4: 6.. / B4 = 6 => 0 pairs (*) / E4 = 6 => 0 pairs (X) F5,I5: 6.. / F5 = 6 => 0 pairs (*) / I5 = 6 => 0 pairs (X) D8,H8: 6.. / D8 = 6 => 0 pairs (*) / H8 = 6 => 0 pairs (X) F9,H9: 6.. / F9 = 6 => 0 pairs (X) / H9 = 6 => 0 pairs (_) D1,D8: 6.. / D1 = 6 => 0 pairs (X) / D8 = 6 => 0 pairs (_) E2,E4: 6.. / E2 = 6 => 0 pairs (*) / E4 = 6 => 0 pairs (X) G2,G6: 6.. / G2 = 6 => 0 pairs (X) / G6 = 6 => 0 pairs (_) E2,E3: 7.. / E2 = 7 => 0 pairs (X) / E3 = 7 => 0 pairs (_) I2,I3: 7.. / I2 = 7 => 0 pairs (*) / I3 = 7 => 0 pairs (X) C5,C6: 7.. / C5 = 7 => 0 pairs (*) / C6 = 7 => 0 pairs (X) F5,F6: 7.. / F5 = 7 => 0 pairs (X) / F6 = 7 => 0 pairs (_) E2,I2: 7.. / E2 = 7 => 0 pairs (X) / I2 = 7 => 0 pairs (_) E3,I3: 7.. / E3 = 7 => 0 pairs (*) / I3 = 7 => 0 pairs (X) C5,F5: 7.. / C5 = 7 => 0 pairs (*) / F5 = 7 => 0 pairs (X) C6,F6: 7.. / C6 = 7 => 0 pairs (X) / F6 = 7 => 0 pairs (_) * DURATION: 0:01:16.078644 START: 08:02:53.525109 END: 08:04:09.603753 2017-05-04 * CP COUNT: (45) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B9,C5,C8,D1,D8,E2,E3,E4,F5,F9,G2,G6,H8,H9,I1,I3,I5) * 573.9284.1824.3.9.9468.532.4.85.973239.28.41.2..34..8962495817373..249.88.973.2.4 * PAIR E2: 6,7 ROW 2 I2: 6,7,5 # reduction candidate for 6,7 I2: 6,7 => SOLVED * 573192846182463597946875321468519732397286415215347689624958173731624958859731264 I2: 5 => CTR * 573.9284.18247369594681532741856973239528741.2..34..8962495817373..249.88.973.2.4 * PAIR G2: 5,6 BLK 3 I2: 5,6,7 # reduction candidate for 5,6 I2: 5,6 => CTR * 573.9284.182473.9.94681532741856973239.28741.2..34..8962495817373..249.88.973.2.4 I2: 7 => SOLVED * 573192846182463597946875321468519732397286415215347689624958173731624958859731264 * PAIR B4: 1,6 BLK 4 B6: 1,6,5 # reduction candidate for 1,6 B6: 1,6 => SOLVED * 573192846182463597946875321468519732397286415215347689624958173731624958859731264 B6: 5 => CTR * 573.9284.1824.3.9.9468.532.46851973239.28.41.2513476896249581737351249688197362.4 * PAIR C5: 5,7 BLK 4 C6: 5,7,1 # reduction candidate for 5,7 C6: 5,7 => SOLVED * 573192846182463597946875321468519732397286415215347689624958173731624958859731264 C6: 1 => CTR * 573.9284.1824.3.9.9468.532.4.85.9732397286415251347689624958173735.249.88.973.2.4 * PAIR E4: 1,6 BLK 5 F6: 1,6,7 # reduction candidate for 1,6 F6: 1,6 => CTR * 573.9284.1824.3.9.9468.532.4.85.973239.2874162.734.5896249581737316249.88.973.2.4 F6: 7 => SOLVED * 573192846182463597946875321468519732397286415215347689624958173731624958859731264 * PAIR F5: 6,7 BLK 5 F6: 6,7,1 # reduction candidate for 6,7 F6: 6,7 => SOLVED * 573192846182463597946875321468519732397286415215347689624958173731624958859731264 F6: 1 => CTR * 573.9284.1824.3.9.9468.532.4.85.973239.287416267341589624958173731.249.88.973.2.4 * PAIR I5: 5,6 COL I I2: 5,6,7 # reduction candidate for 5,6 I2: 5,6 => CTR * 573.9284.182473.9.94681532741856973239.28741.2..34..8962495817373..249.88.973.2.4 I2: 7 => SOLVED * 573192846182463597946875321468519732397286415215347689624958173731624958859731264 * PAIR G6: 5,6 ROW 6 B6: 5,6,1 # reduction candidate for 5,6 B6: 1 => SOLVED * 573192846182463597946875321468519732397286415215347689624958173731624958859731264 B6: 5,6 # 21 pairs * PAIR C8: 1,5 COL C C6: 1,5,7 # reduction candidate for 1,5 C6: 1,5 => SOLVED * 573192846182463597946875321468519732397286415215347689624958173731624958859731264 C6: 7 => CTR * 57319284618246359.9468.532.4.85.973239.28.41.2.734..89624958173731624958859731264 * PAIR B9: 1,5 COL B B6: 1,5,6 # reduction candidate for 1,5 B6: 1,5 => SOLVED * 573192846182463597946875321468519732397286415215347689624958173731624958859731264 B6: 6 => CTR * 573.9284.1824.3.9.9468.532.4.85.973239.28.41.26.34.58962495817373..249.8859731264 * PAIR F9: 1,6 COL F F6: 1,6,7 # reduction candidate for 1,6 F6: 1,6 => CTR * 573.9284.1824.3.9.9468.532.4.85.973239.2874162.734.5896249581737316249.88.973.2.4 F6: 7 => SOLVED * 573192846182463597946875321468519732397286415215347689624958173731624958859731264 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-155-base-pr-000.dot * REASONING * PRF # I2: 6,7 => SOL * DIS # I2: 5 => CTR => I2: 6,7 * DIS # I2: 5,6 => CTR => I2: 7 * PRF # I2: 7 => SOL * PRF # B6: 1,6 => SOL * DIS # B6: 5 => CTR => B6: 1,6 * PRF # C6: 5,7 => SOL * DIS # C6: 1 => CTR => C6: 5,7 * DIS # F6: 1,6 => CTR => F6: 7 * PRF # F6: 7 => SOL * PRF # F6: 6,7 => SOL * DIS # F6: 1 => CTR => F6: 6,7 * DIS # I2: 5,6 => CTR => I2: 7 * PRF # I2: 7 => SOL * PRF # B6: 1 => SOL * PRF # C6: 1,5 => SOL * DIS # C6: 7 => CTR => C6: 1,5 * PRF # B6: 1,5 => SOL * DIS # B6: 6 => CTR => B6: 1,5 * DIS # F6: 1,6 => CTR => F6: 7 * PRF # F6: 7 => SOL * CNT 21 HDP CHAINS / 22 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B9,C5,C8,D1,D8,E2,E3,E4,F5,F9,G2,G6,H8,H9,I1,I3,I5) * 573.9284.1824.3.9.9468.532.4.85.973239.28.41.2..34..8962495817373..249.88.973.2.4 * PAIR E2: 6,7 ROW 2 I2: 6,7,5 # reduction candidate for 6,7 I2: 6,7 => SOLVED * 573192846182463597946875321468519732397286415215347689624958173731624958859731264 * DURATION: 0:00:01.947860 START: 08:04:34.885082 END: 08:04:36.832942 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-155-base-pr-001.dot * REASONING * PRF # I2: 6,7 => SOL * STA I2: 6,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 155 solution: 573192846182463597946875321468519732397286415215347689624958173731624958859731264 info: 1817 FNBWX S8.f 33859 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 573192846182463597946875321468519732397286415215347689624958173731624958859731264 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:
* PRF # I2: 6,7 => SOL * DIS # I2: 5 => CTR => I2: 6,7 * DIS # I2: 5,6 => CTR => I2: 7 * PRF # I2: 7 => SOL * PRF # B6: 1,6 => SOL * DIS # B6: 5 => CTR => B6: 1,6 * PRF # C6: 5,7 => SOL * DIS # C6: 1 => CTR => C6: 5,7 * DIS # F6: 1,6 => CTR => F6: 7 * PRF # F6: 7 => SOL * PRF # F6: 6,7 => SOL * DIS # F6: 1 => CTR => F6: 6,7 * DIS # I2: 5,6 => CTR => I2: 7 * PRF # I2: 7 => SOL * INC # B6: 5,6 => UNS * PRF # B6: 1 => SOL * PRF # C6: 1,5 => SOL * DIS # C6: 7 => CTR => C6: 1,5 * PRF # B6: 1,5 => SOL * DIS # B6: 6 => CTR => B6: 1,5 * DIS # F6: 1,6 => CTR => F6: 7 * PRF # F6: 7 => SOL * CNT 22 HDP CHAINS / 22 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # I2: 6,7 => SOL * STA I2: 6,7 * CNT 1 HDP CHAINS / 1 HYP OPENED