Analysis of xx-top95-047-base.sdk
Contents
Original Sudoku
level: medium
position: ..9.....3.....9...7.....5.6..65..4.....3......28......3..75.6..6...........12.3.8 initial
Autosolve
position: ..9.75..3....39...7432815969365124871..34896242896713538.7546.96..893.5.59.1263.8 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B2: 1,6 => SOL * DIS # B2: 5 => CTR => B2: 1,6 * DIS # G2: 2,8 => CTR => G2: 7 * PRF # G2: 7 => SOL * DIS # B2: 1,5 => CTR => B2: 6 * PRF # B2: 6 => SOL * DIS # G2: 2,8 => CTR => G2: 7 * PRF # G2: 7 => SOL * DIS # G2: 8 => CTR => G2: 2,7 * PRF # C8: 1,2 => SOL * DIS # C8: 4,7 => CTR => C8: 1,2 * PRF # C8: 1,7 => SOL * DIS # C8: 4,7 => CTR => C8: 1,2 * PRF # C8: 1,2 => SOL * DIS # C8: 2,7 => CTR => C8: 1,4 * PRF # C8: 1,4 => SOL * DIS # G2: 8 => CTR => G2: 2,7 * PRF # C8: 1,4 => SOL * DIS # C8: 2,7 => CTR => C8: 1,4 * CNT 19 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 # B2: 1,6 => SOL * STA B2: 1,6 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..9.....3.....9...7.....5.6..65..4.....3......28......3..75.6..6...........12.3.8 | initial |
| ..9.75..3....39...7432815969365124871..34896242896713538.7546.96..893.5.59.1263.8 | autosolve |
| 219675843865439721743281596936512487157348962428967135382754619671893254594126378 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) A1: 2,8 B1: 1,6 A2: 2,8 C2: 1,5 D1: 4,6 D2: 4,6 G1: 2,8 H1: 1,4 H2: 2,7 I2: 1,4 B5: 5,7 C5: 5,7 C7: 1,2 B8: 1,7 C9: 4,7 H7: 1,2 G8: 2,7 I8: 1,4 H9: 4,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H1,I2: 1.. / H1 = 1 => 0 pairs (X) / I2 = 1 => 0 pairs (_) H7,I8: 1.. / H7 = 1 => 0 pairs (*) / I8 = 1 => 0 pairs (X) B1,H1: 1.. / B1 = 1 => 0 pairs (*) / H1 = 1 => 0 pairs (X) C7,H7: 1.. / C7 = 1 => 0 pairs (X) / H7 = 1 => 0 pairs (_) H1,H7: 1.. / H1 = 1 => 0 pairs (X) / H7 = 1 => 0 pairs (_) I2,I8: 1.. / I2 = 1 => 0 pairs (*) / I8 = 1 => 0 pairs (X) A1,A2: 2.. / A1 = 2 => 17 pairs (_) / A2 = 2 => 0 pairs (X) C7,C8: 2.. / C7 = 2 => 0 pairs (*) / C8 = 2 => 0 pairs (X) H7,G8: 2.. / H7 = 2 => 0 pairs (X) / G8 = 2 => 0 pairs (_) A1,G1: 2.. / A1 = 2 => 17 pairs (_) / G1 = 2 => 0 pairs (X) C7,H7: 2.. / C7 = 2 => 0 pairs (*) / H7 = 2 => 0 pairs (X) C8,G8: 2.. / C8 = 2 => 0 pairs (X) / G8 = 2 => 0 pairs (_) H2,H7: 2.. / H2 = 2 => 0 pairs (*) / H7 = 2 => 0 pairs (X) D1,D2: 4.. / D1 = 4 => 0 pairs (X) / D2 = 4 => 0 pairs (_) H1,I2: 4.. / H1 = 4 => 0 pairs (*) / I2 = 4 => 0 pairs (X) C8,C9: 4.. / C8 = 4 => 0 pairs (X) / C9 = 4 => 0 pairs (_) I8,H9: 4.. / I8 = 4 => 0 pairs (*) / H9 = 4 => 0 pairs (X) D1,H1: 4.. / D1 = 4 => 0 pairs (X) / H1 = 4 => 0 pairs (_) D2,I2: 4.. / D2 = 4 => 0 pairs (*) / I2 = 4 => 0 pairs (X) C8,I8: 4.. / C8 = 4 => 0 pairs (X) / I8 = 4 => 0 pairs (_) C9,H9: 4.. / C9 = 4 => 0 pairs (*) / H9 = 4 => 0 pairs (X) H1,H9: 4.. / H1 = 4 => 0 pairs (*) / H9 = 4 => 0 pairs (X) I2,I8: 4.. / I2 = 4 => 0 pairs (X) / I8 = 4 => 0 pairs (_) B2,C2: 5.. / B2 = 5 => 0 pairs (X) / C2 = 5 => 0 pairs (_) B5,C5: 5.. / B5 = 5 => 0 pairs (*) / C5 = 5 => 0 pairs (X) B2,B5: 5.. / B2 = 5 => 0 pairs (X) / B5 = 5 => 0 pairs (_) C2,C5: 5.. / C2 = 5 => 0 pairs (*) / C5 = 5 => 0 pairs (X) B1,B2: 6.. / B1 = 6 => 0 pairs (X) / B2 = 6 => 0 pairs (_) D1,D2: 6.. / D1 = 6 => 0 pairs (*) / D2 = 6 => 0 pairs (X) B1,D1: 6.. / B1 = 6 => 0 pairs (X) / D1 = 6 => 0 pairs (_) B2,D2: 6.. / B2 = 6 => 0 pairs (*) / D2 = 6 => 0 pairs (X) G2,H2: 7.. / G2 = 7 => 0 pairs (*) / H2 = 7 => 0 pairs (X) B5,C5: 7.. / B5 = 7 => 0 pairs (X) / C5 = 7 => 0 pairs (_) G8,H9: 7.. / G8 = 7 => 0 pairs (X) / H9 = 7 => 0 pairs (_) C9,H9: 7.. / C9 = 7 => 0 pairs (X) / H9 = 7 => 0 pairs (_) B5,B8: 7.. / B5 = 7 => 0 pairs (X) / B8 = 7 => 0 pairs (_) G2,G8: 7.. / G2 = 7 => 0 pairs (*) / G8 = 7 => 0 pairs (X) H2,H9: 7.. / H2 = 7 => 0 pairs (X) / H9 = 7 => 0 pairs (_) A1,A2: 8.. / A1 = 8 => 0 pairs (X) / A2 = 8 => 17 pairs (_) G1,G2: 8.. / G1 = 8 => 17 pairs (_) / G2 = 8 => 0 pairs (X) A1,G1: 8.. / A1 = 8 => 0 pairs (X) / G1 = 8 => 17 pairs (_) A2,G2: 8.. / A2 = 8 => 17 pairs (_) / G2 = 8 => 0 pairs (X) * DURATION: 0:01:30.274061 START: 23:47:25.925235 END: 23:48:56.199296 2017-05-03 * CP COUNT: (42) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,B1,B5,B8,C2,C5,C7,C9,D1,D2,G1,G8,H1,H2,H7,H9,I2,I8) * ..9.75..3....39...7432815969365124871..34896242896713538.7546.96..893.5.59.1263.8 * PAIR B1: 1,6 BLK 1 B2: 1,6,5 # reduction candidate for 1,6 B2: 1,6 => SOLVED * 219675843865439721743281596936512487157348962428967135382754619671893254594126378 B2: 5 => CTR * .69475.13.51639..47432815969365124871753489624289671353827546.96..893.5.59.1263.8 * PAIR A2: 2,8 ROW 2 G2: 2,8,7 # reduction candidate for 2,8 G2: 2,8 => CTR * ..9.75..3....39.7.7432815969365124871..34896242896713538.7546296.289375.59.1263.8 G2: 7 => SOLVED * 219675843865439721743281596936512487157348962428967135382754619671893254594126378 * PAIR C2: 1,5 BLK 1 B2: 1,5,6 # reduction candidate for 1,5 B2: 1,5 => CTR * .69475.13...639..47432815969365124871..34896242896713538175462967.893.5.59.1263.8 B2: 6 => SOLVED * 219675843865439721743281596936512487157348962428967135382754619671893254594126378 * PAIR G1: 2,8 BLK 3 G2: 2,8,7 # reduction candidate for 2,8 G2: 2,8 => CTR * ..9.75..3....39.7.7432815969365124871..34896242896713538.7546296.289375.59.1263.8 G2: 7 => SOLVED * 219675843865439721743281596936512487157348962428967135382754619671893254594126378 * PAIR H2: 2,7 BLK 3 G2: 2,7,8 # reduction candidate for 2,7 G2: 8 => CTR * ..9.75..3....3987.7432815969365124871..34896242896713538.7546296.289375.59.1263.8 G2: 2,7 # 17 pairs * PAIR C7: 1,2 BLK 7 C8: 1,2,4,7 # reduction candidate for 1,2 C8: 1,2 => SOLVED * 219675843865439721743281596936512487157348962428967135382754619671893254594126378 C8: 4,7 => CTR * ..9.75..3....39...7432815969365124871..34896242896713538275461961.893254594126378 * PAIR B8: 1,7 BLK 7 C8: 1,7,2,4 # reduction candidate for 1,7 C8: 1,7 => SOLVED * 219675843865439721743281596936512487157348962428967135382754619671893254594126378 C8: 2,4 # 20 pairs * PAIR C9: 4,7 BLK 7 C8: 4,7,1,2 # reduction candidate for 4,7 C8: 4,7 => CTR * ..9.75..3....39...7432815969365124871..34896242896713538275461961.893254594126378 C8: 1,2 => SOLVED * 219675843865439721743281596936512487157348962428967135382754619671893254594126378 * PAIR G8: 2,7 ROW 8 C8: 2,7,1,4 # reduction candidate for 2,7 C8: 2,7 => CTR * ..9.75.43...4397217432815969365124871..34896242896713538.7546.96..893.54594126378 C8: 1,4 => SOLVED * 219675843865439721743281596936512487157348962428967135382754619671893254594126378 * PAIR G8: 2,7 COL G G2: 2,7,8 # reduction candidate for 2,7 G2: 8 => CTR * ..9.75..3....3987.7432815969365124871..34896242896713538.7546296.289375.59.1263.8 G2: 2,7 # 17 pairs * PAIR I8: 1,4 ROW 8 C8: 1,4,2,7 # reduction candidate for 1,4 C8: 1,4 => SOLVED * 219675843865439721743281596936512487157348962428967135382754619671893254594126378 C8: 2,7 => CTR * ..9.75.43...4397217432815969365124871..34896242896713538.7546.96..893.54594126378 * INCONCLUSIVE * SAVE PR GRAPH xx-top95-047-base-pr-000.dot * REASONING * PRF # B2: 1,6 => SOL * DIS # B2: 5 => CTR => B2: 1,6 * DIS # G2: 2,8 => CTR => G2: 7 * PRF # G2: 7 => SOL * DIS # B2: 1,5 => CTR => B2: 6 * PRF # B2: 6 => SOL * DIS # G2: 2,8 => CTR => G2: 7 * PRF # G2: 7 => SOL * DIS # G2: 8 => CTR => G2: 2,7 * PRF # C8: 1,2 => SOL * DIS # C8: 4,7 => CTR => C8: 1,2 * PRF # C8: 1,7 => SOL * DIS # C8: 4,7 => CTR => C8: 1,2 * PRF # C8: 1,2 => SOL * DIS # C8: 2,7 => CTR => C8: 1,4 * PRF # C8: 1,4 => SOL * DIS # G2: 8 => CTR => G2: 2,7 * PRF # C8: 1,4 => SOL * DIS # C8: 2,7 => CTR => C8: 1,4 * CNT 19 HDP CHAINS / 22 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,B1,B5,B8,C2,C5,C7,C9,D1,D2,G1,G8,H1,H2,H7,H9,I2,I8) * ..9.75..3....39...7432815969365124871..34896242896713538.7546.96..893.5.59.1263.8 * PAIR B1: 1,6 BLK 1 B2: 1,6,5 # reduction candidate for 1,6 B2: 1,6 => SOLVED * 219675843865439721743281596936512487157348962428967135382754619671893254594126378 * DURATION: 0:00:02.242593 START: 23:49:27.539355 END: 23:49:29.781948 2017-05-03 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-047-base-pr-001.dot * REASONING * PRF # B2: 1,6 => SOL * STA B2: 1,6 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 95 Sudokus 047 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 219675843865439721743281596936512487157348962428967135382754619671893254594126378 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 # B2: 1,6 => SOL * DIS # B2: 5 => CTR => B2: 1,6 * DIS # G2: 2,8 => CTR => G2: 7 * PRF # G2: 7 => SOL * DIS # B2: 1,5 => CTR => B2: 6 * PRF # B2: 6 => SOL * DIS # G2: 2,8 => CTR => G2: 7 * PRF # G2: 7 => SOL * INC # G2: 2,7 => UNS * DIS # G2: 8 => CTR => G2: 2,7 * PRF # C8: 1,2 => SOL * DIS # C8: 4,7 => CTR => C8: 1,2 * PRF # C8: 1,7 => SOL * INC # C8: 2,4 => UNS * DIS # C8: 4,7 => CTR => C8: 1,2 * PRF # C8: 1,2 => SOL * DIS # C8: 2,7 => CTR => C8: 1,4 * PRF # C8: 1,4 => SOL * INC # G2: 2,7 => UNS * DIS # G2: 8 => CTR => G2: 2,7 * PRF # C8: 1,4 => SOL * DIS # C8: 2,7 => CTR => C8: 1,4 * CNT 22 HDP CHAINS / 22 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # B2: 1,6 => SOL * STA B2: 1,6 * CNT 1 HDP CHAINS / 1 HYP OPENED