Analysis of xx-top500-349-base.sdk
Contents
Original Sudoku
level: medium
position: .7....2.3...1...........4.....5..61...32......4.......6...37...1......8.....4.... initial
Autosolve
position: .714..2.343.1.....26.3..4.17..5.3614.13264....4671..326...3714.1946..3873.7.41.26 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C3: 5 => SOL * DIS # F1: 8,9 => CTR => F1: 5,6 * PRF # C3: 5,9 => SOL * DIS # C3: 8 => CTR => C3: 5,9 * DIS # G2: 5,9 => CTR => G2: 7,8 * PRF # C4: 2,8 => SOL * DIS # C4: 9 => CTR => C4: 2,8 * DIS # C4: 2 => CTR => C4: 8,9 * PRF # E3: 8,9 => SOL * DIS # F1: 8,9 => CTR => F1: 5,6 * PRF # C4: 2,8 => SOL * DIS # C4: 9 => CTR => C4: 2,8 * DIS # B7: 2 => CTR => B7: 5,8 * DIS # G2: 5,9 => CTR => G2: 7,8 * DIS # G5: 5,9 => CTR => G5: 7,8 * CNT 15 HDP CHAINS / 46 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C3: 5 => SOL * STA C3: 5 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .7....2.3...1...........4.....5..61...32......4.......6...37...1......8.....4.... | initial |
| .714..2.343.1.....26.3..4.17..5.3614.13264....4671..326...3714.1946..3873.7.41.26 | autosolve |
| 871456293439172865265389471728593614913264758546718932652837149194625387387941526 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) A1: 8,9 C2: 5,9 B4: 2,8 E4: 8,9 F6: 8,9 C7: 2,8 B9: 5,8 D7: 8,9 E8: 2,5 F8: 2,5 D9: 8,9 I7: 5,9 G9: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,F2: 2.. / E2 = 2 => 15 pairs (_) / F2 = 2 => 13 pairs (_) B4,C4: 2.. / B4 = 2 => 13 pairs (_) / C4 = 2 => 0 pairs (X) B7,C7: 2.. / B7 = 2 => 0 pairs (X) / C7 = 2 => 13 pairs (_) E8,F8: 2.. / E8 = 2 => 13 pairs (_) / F8 = 2 => 15 pairs (_) B4,B7: 2.. / B4 = 2 => 13 pairs (_) / B7 = 2 => 0 pairs (X) C4,C7: 2.. / C4 = 2 => 0 pairs (X) / C7 = 2 => 13 pairs (_) E2,E8: 2.. / E2 = 2 => 15 pairs (_) / E8 = 2 => 13 pairs (_) F2,F8: 2.. / F2 = 2 => 13 pairs (_) / F8 = 2 => 15 pairs (_) C2,C3: 5.. / C2 = 5 => 15 pairs (_) / C3 = 5 => 0 pairs (*) A5,A6: 5.. / A5 = 5 => 15 pairs (_) / A6 = 5 => 15 pairs (_) B7,B9: 5.. / B7 = 5 => 11 pairs (_) / B9 = 5 => 13 pairs (_) E8,F8: 5.. / E8 = 5 => 15 pairs (_) / F8 = 5 => 13 pairs (_) I7,G9: 5.. / I7 = 5 => 13 pairs (_) / G9 = 5 => 11 pairs (_) A6,G6: 5.. / A6 = 5 => 15 pairs (_) / G6 = 5 => 15 pairs (_) B7,I7: 5.. / B7 = 5 => 11 pairs (_) / I7 = 5 => 13 pairs (_) B9,G9: 5.. / B9 = 5 => 13 pairs (_) / G9 = 5 => 11 pairs (_) F1,F2: 6.. / F1 = 6 => 14 pairs (_) / F2 = 6 => 14 pairs (_) H1,H2: 6.. / H1 = 6 => 14 pairs (_) / H2 = 6 => 14 pairs (_) F1,H1: 6.. / F1 = 6 => 14 pairs (_) / H1 = 6 => 14 pairs (_) F2,H2: 6.. / F2 = 6 => 14 pairs (_) / H2 = 6 => 14 pairs (_) E2,E3: 7.. / E2 = 7 => 14 pairs (_) / E3 = 7 => 14 pairs (_) G5,H5: 7.. / G5 = 7 => 17 pairs (_) / H5 = 7 => 15 pairs (_) E3,H3: 7.. / E3 = 7 => 14 pairs (_) / H3 = 7 => 14 pairs (_) G2,G5: 7.. / G2 = 7 => 15 pairs (_) / G5 = 7 => 17 pairs (_) A1,C3: 8.. / A1 = 8 => 0 pairs (*) / C3 = 8 => 0 pairs (X) G2,I2: 8.. / G2 = 8 => 20 pairs (_) / I2 = 8 => 14 pairs (_) E4,F6: 8.. / E4 = 8 => 0 pairs (X) / F6 = 8 => 0 pairs (_) D7,D9: 8.. / D7 = 8 => 11 pairs (_) / D9 = 8 => 13 pairs (_) B9,D9: 8.. / B9 = 8 => 11 pairs (_) / D9 = 8 => 13 pairs (_) I2,I5: 8.. / I2 = 8 => 14 pairs (_) / I5 = 8 => 20 pairs (_) E4,F6: 9.. / E4 = 9 => 0 pairs (*) / F6 = 9 => 0 pairs (X) D7,D9: 9.. / D7 = 9 => 13 pairs (_) / D9 = 9 => 11 pairs (_) I7,G9: 9.. / I7 = 9 => 11 pairs (_) / G9 = 9 => 13 pairs (_) C4,E4: 9.. / C4 = 9 => 0 pairs (X) / E4 = 9 => 0 pairs (_) D7,I7: 9.. / D7 = 9 => 13 pairs (_) / I7 = 9 => 11 pairs (_) D9,G9: 9.. / D9 = 9 => 11 pairs (_) / G9 = 9 => 13 pairs (_) * DURATION: 0:01:06.221584 START: 14:39:49.700608 END: 14:40:55.922192 2017-05-04 * CP COUNT: (36) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B4,B9,C2,C7,D7,D9,E4,E8,F6,F8,G9,I7) * .714..2.343.1.....26.3..4.17..5.3614.13264....4671..326...3714.1946..3873.7.41.26 * PAIR A1: 8,9 BLK 1 C3: 8,9,5 # reduction candidate for 8,9 C3: 5 => SOLVED * 871456293439172865265389471728593614913264758546718932652837149194625387387941526 C3: 8,9 # 15 pairs * PAIR A1: 8,9 ROW 1 E1: 8,9,5 # reduction candidate for 8,9 E1: 8,9 # 17 pairs F1: 8,9,5,6 # reduction candidate for 8,9 F1: 8,9 => CTR * .7145.26343.1.6...26.3..4.17..5.3614.13264....4671..326...3714.1946.23873.7.41.26 F1: 5,6 # 14 pairs * PAIR A1: 8,9 COL A A5: 8,9,5 # reduction candidate for 8,9 A5: 8,9 # 15 pairs A6: 8,9,5 # reduction candidate for 8,9 A6: 8,9 # 15 pairs * PAIR C2: 5,9 BLK 1 C3: 5,9,8 # reduction candidate for 5,9 C3: 5,9 => SOLVED * 871456293439172865265389471728593614913264758546718932652837149194625387387941526 C3: 8 => CTR * 97145.2.34351.....2683..4.17.9583614.13264....46719.326.2.3714.1946..3873.7.41.26 * PAIR C2: 5,9 ROW 2 E2: 5,9,2,7 # reduction candidate for 5,9 E2: 5,9 # 16 pairs F2: 5,9,2,6 # reduction candidate for 5,9 F2: 5,9 # 16 pairs G2: 5,9,7,8 # reduction candidate for 5,9 G2: 5,9 => CTR * 9714582.343.1....826.3..4.17..5836148132647..5467198326...3714.1946..3873.7.41.26 G2: 7,8 # 14 pairs H2: 5,9,6,7 # reduction candidate for 5,9 H2: 5,9 # 16 pairs I2: 5,9,8 # reduction candidate for 5,9 I2: 5,9 # 20 pairs * PAIR B4: 2,8 BLK 4 C4: 2,8,9 # reduction candidate for 2,8 C4: 2,8 => SOLVED * 871456293439172865265389471728593614913264758546718932652837149194625387387941526 C4: 9 => CTR * 9714582.343.1.....26.3..4.1729583614.13264....46719.326.2.3714.1946..3873.7.41.26 * PAIR B4: 2,8 COL B B7: 2,8,5 # reduction candidate for 2,8 B7: 2,8 # 13 pairs B7: 5 # 11 pairs * PAIR E4: 8,9 ROW 4 C4: 8,9,2 # reduction candidate for 8,9 C4: 2 => CTR * 87145629343.1.....26.389471782593614.132647.8946718532628937145194625387357841926 C4: 8,9 # 13 pairs * PAIR E4: 8,9 COL E E1: 8,9,5 # reduction candidate for 8,9 E1: 8,9 # 17 pairs E3: 8,9,5,7 # reduction candidate for 8,9 E3: 8,9 => SOLVED * 871456293439172865265389471728593614913264758546718932652837149194625387387941526 E3: 5,7 # 14 pairs * PAIR F6: 8,9 ROW 6 A6: 8,9,5 # reduction candidate for 8,9 A6: 8,9 # 15 pairs G6: 8,9,5 # reduction candidate for 8,9 G6: 8,9 # 15 pairs * PAIR F6: 8,9 COL F F1: 8,9,5,6 # reduction candidate for 8,9 F1: 8,9 => CTR * .7145.26343.1.6...26.3..4.17..5.3614.13264....4671..326...3714.1946.23873.7.41.26 F1: 5,6 # 14 pairs F3: 8,9,5 # reduction candidate for 8,9 F3: 8,9 # 15 pairs * PAIR C7: 2,8 BLK 7 B7: 2,8,5 # reduction candidate for 2,8 B7: 2,8 # 13 pairs B7: 5 # 11 pairs * PAIR C7: 2,8 COL C C4: 2,8,9 # reduction candidate for 2,8 C4: 2,8 => SOLVED * 871456293439172865265389471728593614913264758546718932652837149194625387387941526 C4: 9 => CTR * 9714582.343.1.....26.3..4.1729583614.13264....46719.326.2.3714.1946..3873.7.41.26 * PAIR B9: 5,8 BLK 7 B7: 5,8,2 # reduction candidate for 5,8 B7: 2 => CTR * 87145.2.343.1.....26.389471782593614513264798946718532628937145194625387357841926 B7: 5,8 # 13 pairs * PAIR E8: 2,5 COL E E2: 2,5,7,9 # reduction candidate for 2,5 E2: 2,5 # 18 pairs E2: 7,9 # 14 pairs * PAIR F8: 2,5 COL F F2: 2,5,6,9 # reduction candidate for 2,5 F2: 6,9 # 16 pairs F2: 2,5 # 16 pairs * PAIR I7: 5,9 COL I I2: 5,9,8 # reduction candidate for 5,9 I2: 5,9 # 20 pairs I5: 5,9,8 # reduction candidate for 5,9 I5: 5,9 # 14 pairs * PAIR G9: 5,9 COL G G2: 5,9,7,8 # reduction candidate for 5,9 G2: 5,9 => CTR * 9714582.343.1....826.3..4.17..5836148132647..5467198326...3714.1946..3873.7.41.26 G2: 7,8 # 14 pairs G5: 5,9,7,8 # reduction candidate for 5,9 G5: 5,9 => CTR * 9714..2.34351..7.826837.4.1729583614813264.7.5467198326.2.3714.1946..3873.7.41.26 G5: 7,8 # 14 pairs G6: 5,9,8 # reduction candidate for 5,9 G6: 5,9 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-349-base-pr-000.dot * REASONING * PRF # C3: 5 => SOL * DIS # F1: 8,9 => CTR => F1: 5,6 * PRF # C3: 5,9 => SOL * DIS # C3: 8 => CTR => C3: 5,9 * DIS # G2: 5,9 => CTR => G2: 7,8 * PRF # C4: 2,8 => SOL * DIS # C4: 9 => CTR => C4: 2,8 * DIS # C4: 2 => CTR => C4: 8,9 * PRF # E3: 8,9 => SOL * DIS # F1: 8,9 => CTR => F1: 5,6 * PRF # C4: 2,8 => SOL * DIS # C4: 9 => CTR => C4: 2,8 * DIS # B7: 2 => CTR => B7: 5,8 * DIS # G2: 5,9 => CTR => G2: 7,8 * DIS # G5: 5,9 => CTR => G5: 7,8 * CNT 15 HDP CHAINS / 46 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B4,B9,C2,C7,D7,D9,E4,E8,F6,F8,G9,I7) * .714..2.343.1.....26.3..4.17..5.3614.13264....4671..326...3714.1946..3873.7.41.26 * PAIR A1: 8,9 BLK 1 C3: 8,9,5 # reduction candidate for 8,9 C3: 5 => SOLVED * 871456293439172865265389471728593614913264758546718932652837149194625387387941526 * DURATION: 0:00:03.067461 START: 14:41:41.660710 END: 14:41:44.728171 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-349-base-pr-001.dot * REASONING * PRF # C3: 5 => SOL * STA C3: 5 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 349 solution: 871456293439172865265389471728593614913264758546718932652837149194625387387941526 info: 4882 FNBWX S8.f 22179 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 871456293439172865265389471728593614913264758546718932652837149194625387387941526 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 # C3: 8,9 => UNS * PRF # C3: 5 => SOL * INC # E1: 8,9 => UNS * DIS # F1: 8,9 => CTR => F1: 5,6 * INC # F1: 5,6 => UNS * INC # A5: 8,9 => UNS * INC # A6: 8,9 => UNS * PRF # C3: 5,9 => SOL * DIS # C3: 8 => CTR => C3: 5,9 * INC # E2: 5,9 => UNS * INC # F2: 5,9 => UNS * DIS # G2: 5,9 => CTR => G2: 7,8 * INC # G2: 7,8 => UNS * INC # H2: 5,9 => UNS * INC # I2: 5,9 => UNS * PRF # C4: 2,8 => SOL * DIS # C4: 9 => CTR => C4: 2,8 * INC # B7: 2,8 => UNS * INC # B7: 5 => UNS * INC # C4: 8,9 => UNS * DIS # C4: 2 => CTR => C4: 8,9 * INC # E1: 8,9 => UNS * PRF # E3: 8,9 => SOL * INC # E3: 5,7 => UNS * INC # A6: 8,9 => UNS * INC # G6: 8,9 => UNS * DIS # F1: 8,9 => CTR => F1: 5,6 * INC # F1: 5,6 => UNS * INC # F3: 8,9 => UNS * INC # B7: 2,8 => UNS * INC # B7: 5 => UNS * PRF # C4: 2,8 => SOL * DIS # C4: 9 => CTR => C4: 2,8 * INC # B7: 5,8 => UNS * DIS # B7: 2 => CTR => B7: 5,8 * INC # E2: 2,5 => UNS * INC # E2: 7,9 => UNS * INC # F2: 2,5 => UNS * INC # F2: 6,9 => UNS * INC # I2: 5,9 => UNS * INC # I5: 5,9 => UNS * DIS # G2: 5,9 => CTR => G2: 7,8 * INC # G2: 7,8 => UNS * DIS # G5: 5,9 => CTR => G5: 7,8 * INC # G5: 7,8 => UNS * INC # G6: 5,9 => UNS * CNT 46 HDP CHAINS / 46 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C3: 8,9 => UNS * PRF # C3: 5 => SOL * STA C3: 5 * CNT 2 HDP CHAINS / 2 HYP OPENED