Analysis of xx-top500-034-base.sdk
Contents
Original Sudoku
level: medium
position: ...8...9.42.......6.........1..64.....7....3.....5....5.....6.42..3...........1.. initial
Autosolve
position: 1..8...9.42.......6........31..64...9.7....3.8...53...5.....6.42..3.....7.....1.3 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C2: 3,5 => CTR => C2: 8,9 * DIS # C3: 3,5 => CTR => C3: 8,9 * DIS # G1: 3,5 => CTR => G1: 2,4,7 * PRF # F1: 5,6 => SOL * DIS # F1: 2,7 => CTR => F1: 5,6 * DIS # F2: 5,6 => CTR => F2: 1,7,9 * DIS # I2: 5,6 => CTR => I2: 1,7,8 * PRF # D9: 5,6 => SOL * DIS # D9: 4 => CTR => D9: 5,6 * DIS # G3: 4,5 => CTR => G3: 2,3,7,8 * DIS # D9: 4,5 => CTR => D9: 6 * PRF # D9: 6 => SOL * DIS # I2: 1,6 => CTR => I2: 5,7,8 * DIS # F2: 1,6 => CTR => F2: 5,7,9 * DIS # H6: 1,6 => CTR => H6: 4 * PRF # H6: 4 => SOL * DIS # E3: 1,4 => CTR => E3: 2,3,7,9 * PRF # H6: 1,4 => SOL * DIS # H6: 6 => CTR => H6: 1,4 * DIS # C6: 4,6 => CTR => C6: 2 * DIS # H6: 1 => CTR => H6: 4,6 * DIS # B8: 4,6 => CTR => B8: 8 * DIS # B9: 4,6 => CTR => B9: 8,9 * DIS # I6: 7,9 => CTR => I6: 1,2,6 * PRF # B5: 4,5 => SOL * DIS # B5: 6 => CTR => B5: 4,5 * DIS # G3: 4,5 => CTR => G3: 2,3,7,8 * DIS # B5: 5,6 => CTR => B5: 4 * PRF # B5: 4 => SOL * DIS # I2: 5,6 => CTR => I2: 1,7,8 * DIS # E7: 1,2 => CTR => E7: 7,8,9 * DIS # F7: 1,2 => CTR => F7: 7,8,9 * CNT 32 HDP CHAINS / 62 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C2: 3,5 => CTR => C2: 8,9 * DIS C2: 8,9 # C3: 3,5 => CTR => C3: 8,9 * DIS C2: 8,9 + C3: 8,9 # G1: 3,5 => CTR => G1: 2,4,7 * PRF C2: 8,9 + C3: 8,9 + G1: 2,4,7 # F1: 5,6 => SOL * STA C2: 8,9 + C3: 8,9 + G1: 2,4,7 + F1: 5,6 * CNT 4 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...8...9.42.......6.........1..64.....7....3.....5....5.....6.42..3...........1.. | initial |
| 1..8...9.42.......6........31..64...9.7....3.8...53...5.....6.42..3.....7.....1.3 | autosolve |
| 153876492428519367679432815315964278947128536862753941531297684286341759794685123 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) C1: 3,5 D2: 5,6 D3: 4,5 H2: 1,6 H3: 1,4 C4: 2,5 B6: 4,6 D4: 7,9 D5: 1,2 D6: 7,9 G5: 4,5 I5: 5,6 D7: 1,2 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H6,I6: 1.. / H6 = 1 => 0 pairs (X) / I6 = 1 => 24 pairs (_) C7,C8: 1.. / C7 = 1 => 16 pairs (_) / C8 = 1 => 0 pairs (X) D5,D7: 1.. / D5 = 1 => 14 pairs (_) / D7 = 1 => 0 pairs (X) C4,C6: 2.. / C4 = 2 => 0 pairs (X) / C6 = 2 => 26 pairs (_) H7,H9: 2.. / H7 = 2 => 0 pairs (X) / H9 = 2 => 14 pairs (_) D5,D7: 2.. / D5 = 2 => 0 pairs (X) / D7 = 2 => 14 pairs (_) B7,C7: 3.. / B7 = 3 => 14 pairs (_) / C7 = 3 => 0 pairs (X) E1,G1: 4.. / E1 = 4 => 0 pairs (X) / G1 = 4 => 0 pairs (_) B5,G5: 4.. / B5 = 4 => 0 pairs (*) / G5 = 4 => 0 pairs (X) D3,D9: 4.. / D3 = 4 => 0 pairs (*) / D9 = 4 => 0 pairs (X) H3,H6: 4.. / H3 = 4 => 0 pairs (X) / H6 = 4 => 0 pairs (_) C4,B5: 5.. / C4 = 5 => 26 pairs (_) / B5 = 5 => 0 pairs (X) F1,I1: 6.. / F1 = 6 => 0 pairs (*) / I1 = 6 => 0 pairs (X) B5,I5: 6.. / B5 = 6 => 0 pairs (X) / I5 = 6 => 0 pairs (_) D2,D9: 6.. / D2 = 6 => 0 pairs (X) / D9 = 6 => 0 pairs (_) H2,H6: 6.. / H2 = 6 => 0 pairs (*) / H6 = 6 => 0 pairs (X) B1,B3: 7.. / B1 = 7 => 13 pairs (_) / B3 = 7 => 18 pairs (_) D4,D6: 7.. / D4 = 7 => 12 pairs (_) / D6 = 7 => 11 pairs (_) E5,F5: 8.. / E5 = 8 => 14 pairs (_) / F5 = 8 => 14 pairs (_) D4,D6: 9.. / D4 = 9 => 11 pairs (_) / D6 = 9 => 12 pairs (_) G8,I8: 9.. / G8 = 9 => 13 pairs (_) / I8 = 9 => 13 pairs (_) * DURATION: 0:00:39.121565 START: 03:49:58.052721 END: 03:50:37.174286 2017-05-04 * CP COUNT: (21) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,C1,C4,D2,D3,D4,D5,D6,D7,G5,H2,H3,I5) * 1..8...9.42.......6........31..64...9.7....3.8...53...5.....6.42..3.....7.....1.3 * PAIR C1: 3,5 BLK 1 B1: 3,5,7 # reduction candidate for 3,5 B1: 3,5 # 18 pairs C2: 3,5,8,9 # reduction candidate for 3,5 C2: 3,5 => CTR * 17.846.9.42.5.....6........312.64...957...4368...53.1.53....6.42..3.....7.....1.3 C2: 8,9 # 14 pairs B3: 3,5,7,8,9 # reduction candidate for 3,5 B3: 3,5 # 18 pairs C3: 3,5,8,9 # reduction candidate for 3,5 C3: 3,5 => CTR * 17.846.9.42.5.....6........312.64...957...4368...53.1.53....6.42..3.....7.....1.3 C3: 8,9 # 14 pairs * PAIR C1: 3,5 ROW 1 G1: 3,5,2,4,7 # reduction candidate for 3,5 G1: 3,5 => CTR * 15384..9642.6...1.6..5...4.31..64...967...435842.53.615.....6.42843.6...7964.51.3 G1: 2,4,7 # 13 pairs * PAIR D2: 5,6 BLK 2 F1: 5,6,2,7 # reduction candidate for 5,6 F1: 5,6 => SOLVED * 153876492428519367679432815315964278947128536862753941531297684286341759794685123 F1: 2,7 => CTR * 15384..9642.6..51.67.5..34.315.64872967128435842.53.615312..6.42843.6...796485123 F2: 5,6,1,7,9 # reduction candidate for 5,6 F2: 5,6 => CTR * 1..8...9642.....1.6..4.....31..64...9.7....3.8...53...5.....6.42..3.....7.....1.3 F2: 1,7,9 # 13 pairs * PAIR D2: 5,6 ROW 2 I2: 5,6,1,7,8 # reduction candidate for 5,6 I2: 5,6 => CTR * 1..8.6.9.42.5...166..4.....31..64...9.7....3.8...53...5.....6.42..3.....7.....1.3 I2: 1,7,8 # 13 pairs * PAIR D2: 5,6 COL D D9: 5,6,4 # reduction candidate for 5,6 D9: 5,6 => SOLVED * 153876492428519367679432815315964278947128536862753941531297684286341759794685123 D9: 4 => CTR * 15384729642.63951.67.5..34.315.64872967...4358427539615312..684284316759796485123 * PAIR D3: 4,5 ROW 3 G3: 4,5,2,3,7,8 # reduction candidate for 4,5 G3: 4,5 => CTR * 1..84..9.42.......6..5..41.31..64...947...536862.53.415.....6.42843.6...7964.51.3 G3: 2,3,7,8 # 13 pairs * PAIR D3: 4,5 COL D D9: 4,5,6 # reduction candidate for 4,5 D9: 4,5 => CTR * 15384729642.63951.67.5..34.315.64872967...4358427539615312..684284316759796485123 D9: 6 => SOLVED * 153876492428519367679432815315964278947128536862753941531297684286341759794685123 * PAIR H2: 1,6 BLK 3 I2: 1,6,5,7,8 # reduction candidate for 1,6 I2: 1,6 => CTR * 1..8.6.9.42.5.....6..4.....31..64...9.7....3.8...53...5.....6.42..3.....7.....1.3 I2: 5,7,8 # 13 pairs * PAIR H2: 1,6 ROW 2 F2: 1,6,5,7,9 # reduction candidate for 1,6 F2: 1,6 => CTR * 1..8..49.42.5.1.6.6..4...1.31..64...947...536862.53.415.....6.42863.....7..6..1.3 F2: 5,7,9 # 13 pairs * PAIR H2: 1,6 COL H H6: 1,6,4 # reduction candidate for 1,6 H6: 1,6 => CTR * 15384729642.63951.67.5..34.315.64872967...4358427539615312..684284316759796485123 H6: 4 => SOLVED * 153876492428519367679432815315964278947128536862753941531297684286341759794685123 * PAIR H3: 1,4 ROW 3 E3: 1,4,2,3,7,9 # reduction candidate for 1,4 E3: 1,4 => CTR * 1..84..9642.63..1.6..51..4.31..64...967...435842.53.615.....6.428437....7..4..1.3 E3: 2,3,7,9 # 13 pairs * PAIR H3: 1,4 COL H H6: 1,4,6 # reduction candidate for 1,4 H6: 1,4 => SOLVED * 153876492428519367679432815315964278947128536862753941531297684286341759794685123 H6: 6 => CTR * 15384729642.63951.67.5..34.315.64872967...4358427539615312..684284316759796485123 * PAIR C4: 2,5 ROW 4 G4: 2,5,7,8,9 # reduction candidate for 2,5 G4: 2,5 # 15 pairs I4: 2,5,7,8,9 # reduction candidate for 2,5 I4: 2,5 # 15 pairs * PAIR B6: 4,6 BLK 4 B5: 4,6,5 # reduction candidate for 4,6 B5: 4,6 # 26 pairs C6: 4,6,2 # reduction candidate for 4,6 C6: 4,6 => CTR * 1..846.9.42.5.....6........312.64...957...4368...53.1.5.....6.42..3.....7.....1.3 C6: 2 # 26 pairs * PAIR B6: 4,6 ROW 6 H6: 4,6,1 # reduction candidate for 4,6 H6: 1 => CTR * 1..8...9.42.....6.6......4.31..64...9.7....3.8...53.1.5.....6.42..3.....7.....1.3 H6: 4,6 # 24 pairs * PAIR B6: 4,6 COL B B8: 4,6,8 # reduction candidate for 4,6 B8: 4,6 => CTR * 1..846.9.42.5.....6........31..64...957...4368...53.1.5.....6.42..3.....7.....1.3 B8: 8 # 20 pairs B9: 4,6,8,9 # reduction candidate for 4,6 B9: 4,6 => CTR * 1..846.9.42.5.....6........31..64...957...4368...53.1.5.....6.428.3.....7.....1.3 B9: 8,9 # 14 pairs * PAIR D4: 7,9 ROW 4 G4: 7,9,2,5,8 # reduction candidate for 7,9 G4: 7,9 # 15 pairs I4: 7,9,2,5,8 # reduction candidate for 7,9 I4: 7,9 # 15 pairs * PAIR D5: 1,2 BLK 5 E5: 1,2,8 # reduction candidate for 1,2 E5: 1,2 # 14 pairs F5: 1,2,8 # reduction candidate for 1,2 F5: 1,2 # 14 pairs * PAIR D6: 7,9 ROW 6 G6: 7,9,2,4 # reduction candidate for 7,9 G6: 7,9 # 14 pairs I6: 7,9,1,2,6 # reduction candidate for 7,9 I6: 7,9 => CTR * 1..8...9.42.....6.6......4.31..64...9.7....368...53.1.5.....6.42..3.....7.....1.3 I6: 1,2,6 # 14 pairs * PAIR G5: 4,5 ROW 5 B5: 4,5,6 # reduction candidate for 4,5 B5: 4,5 => SOLVED * 153876492428519367679432815315964278947128536862753941531297684286341759794685123 B5: 6 => CTR * 15384..9642.6..51.67.5..34.315.64872967128435842.53...5312..6.42843.6...796485123 * PAIR G5: 4,5 COL G G1: 4,5,2,3,7 # reduction candidate for 4,5 G1: 4,5 # 14 pairs G3: 4,5,2,3,7,8 # reduction candidate for 4,5 G3: 4,5 => CTR * 1..84..9.42.......6..5..41.31..64...947...536862.53.415.....6.42843.6...7964.51.3 G3: 2,3,7,8 # 13 pairs * PAIR I5: 5,6 ROW 5 B5: 5,6,4 # reduction candidate for 5,6 B5: 5,6 => CTR * 15384729642.63951.67.5..34.315.64872967...4358427539615312..684284316759796485123 B5: 4 => SOLVED * 153876492428519367679432815315964278947128536862753941531297684286341759794685123 * PAIR I5: 5,6 COL I I1: 5,6,2,7 # reduction candidate for 5,6 I1: 5,6 # 14 pairs I2: 5,6,1,7,8 # reduction candidate for 5,6 I2: 5,6 => CTR * 1..8.6.9.42.5...166..4.....31..64...9.7....3.8...53...5.....6.42..3.....7.....1.3 I2: 1,7,8 # 13 pairs * PAIR D7: 1,2 BLK 8 E7: 1,2,7,8,9 # reduction candidate for 1,2 E7: 1,2 => CTR * 1..846.9.42.5.....6........312.64...957...4368...53.1.5.....6.42.13.....7.....123 E7: 7,8,9 # 13 pairs F7: 1,2,7,8,9 # reduction candidate for 1,2 F7: 1,2 => CTR * 1..846.9.42.5.....6........312.64...957...4368...53.1.5.....6.42.13.....7.....123 F7: 7,8,9 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-034-base-pr-000.dot * REASONING * DIS # C2: 3,5 => CTR => C2: 8,9 * DIS # C3: 3,5 => CTR => C3: 8,9 * DIS # G1: 3,5 => CTR => G1: 2,4,7 * PRF # F1: 5,6 => SOL * DIS # F1: 2,7 => CTR => F1: 5,6 * DIS # F2: 5,6 => CTR => F2: 1,7,9 * DIS # I2: 5,6 => CTR => I2: 1,7,8 * PRF # D9: 5,6 => SOL * DIS # D9: 4 => CTR => D9: 5,6 * DIS # G3: 4,5 => CTR => G3: 2,3,7,8 * DIS # D9: 4,5 => CTR => D9: 6 * PRF # D9: 6 => SOL * DIS # I2: 1,6 => CTR => I2: 5,7,8 * DIS # F2: 1,6 => CTR => F2: 5,7,9 * DIS # H6: 1,6 => CTR => H6: 4 * PRF # H6: 4 => SOL * DIS # E3: 1,4 => CTR => E3: 2,3,7,9 * PRF # H6: 1,4 => SOL * DIS # H6: 6 => CTR => H6: 1,4 * DIS # C6: 4,6 => CTR => C6: 2 * DIS # H6: 1 => CTR => H6: 4,6 * DIS # B8: 4,6 => CTR => B8: 8 * DIS # B9: 4,6 => CTR => B9: 8,9 * DIS # I6: 7,9 => CTR => I6: 1,2,6 * PRF # B5: 4,5 => SOL * DIS # B5: 6 => CTR => B5: 4,5 * DIS # G3: 4,5 => CTR => G3: 2,3,7,8 * DIS # B5: 5,6 => CTR => B5: 4 * PRF # B5: 4 => SOL * DIS # I2: 5,6 => CTR => I2: 1,7,8 * DIS # E7: 1,2 => CTR => E7: 7,8,9 * DIS # F7: 1,2 => CTR => F7: 7,8,9 * CNT 32 HDP CHAINS / 62 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,C1,C4,D2,D3,D4,D5,D6,D7,G5,H2,H3,I5) * 1..8...9.42.......6........31..64...9.7....3.8...53...5.....6.42..3.....7.....1.3 * PAIR C1: 3,5 BLK 1 B1: 3,5,7 # reduction candidate for 3,5 B1: 3,5 # 18 pairs C2: 3,5,8,9 # reduction candidate for 3,5 C2: 3,5 => CTR * 17.846.9.42.5.....6........312.64...957...4368...53.1.53....6.42..3.....7.....1.3 B3: 3,5,7,8,9 # reduction candidate for 3,5 B3: 3,5 # 18 pairs C3: 3,5,8,9 # reduction candidate for 3,5 C3: 3,5 => CTR * 17.846.9.42.5.....6........312.64...957...4368...53.1.53....6.42..3.....7.....1.3 * PAIR C1: 3,5 ROW 1 G1: 3,5,2,4,7 # reduction candidate for 3,5 G1: 3,5 => CTR * 15384..9642.6...1.6..5...4.31..64...967...435842.53.615.....6.42843.6...7964.51.3 * PAIR RESTART * PAIR C1: 3,5 BLK 1 B1: 3,5,7 # reduction candidate for 3,5 B1: 3,5 # 18 pairs B3: 3,5,7 # reduction candidate for 3,5 B3: 3,5 # 19 pairs * PAIR D2: 5,6 BLK 2 F1: 5,6,2,7 # reduction candidate for 5,6 F1: 5,6 => SOLVED * 153876492428519367679432815315964278947128536862753941531297684286341759794685123 * DURATION: 0:00:10.587295 START: 03:51:40.765852 END: 03:51:51.353147 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-034-base-pr-001.dot * REASONING * DIS # C2: 3,5 => CTR => C2: 8,9 * DIS C2: 8,9 # C3: 3,5 => CTR => C3: 8,9 * DIS C2: 8,9 + C3: 8,9 # G1: 3,5 => CTR => G1: 2,4,7 * PRF C2: 8,9 + C3: 8,9 + G1: 2,4,7 # F1: 5,6 => SOL * STA C2: 8,9 + C3: 8,9 + G1: 2,4,7 + F1: 5,6 * CNT 4 HDP CHAINS / 8 HYP OPENED
Header Info
Top 500 Minimum 17 034 solution: 153876492428519367679432815315964278947128536862753941531297684286341759794685123 info: 1358 FNBTHXY S8.f 40868 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 153876492428519367679432815315964278947128536862753941531297684286341759794685123 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 # B1: 3,5 => UNS * DIS # C2: 3,5 => CTR => C2: 8,9 * INC # C2: 8,9 => UNS * INC # B3: 3,5 => UNS * DIS # C3: 3,5 => CTR => C3: 8,9 * INC # C3: 8,9 => UNS * DIS # G1: 3,5 => CTR => G1: 2,4,7 * INC # G1: 2,4,7 => UNS * PRF # F1: 5,6 => SOL * DIS # F1: 2,7 => CTR => F1: 5,6 * DIS # F2: 5,6 => CTR => F2: 1,7,9 * INC # F2: 1,7,9 => UNS * DIS # I2: 5,6 => CTR => I2: 1,7,8 * INC # I2: 1,7,8 => UNS * PRF # D9: 5,6 => SOL * DIS # D9: 4 => CTR => D9: 5,6 * DIS # G3: 4,5 => CTR => G3: 2,3,7,8 * INC # G3: 2,3,7,8 => UNS * DIS # D9: 4,5 => CTR => D9: 6 * PRF # D9: 6 => SOL * DIS # I2: 1,6 => CTR => I2: 5,7,8 * INC # I2: 5,7,8 => UNS * DIS # F2: 1,6 => CTR => F2: 5,7,9 * INC # F2: 5,7,9 => UNS * DIS # H6: 1,6 => CTR => H6: 4 * PRF # H6: 4 => SOL * DIS # E3: 1,4 => CTR => E3: 2,3,7,9 * INC # E3: 2,3,7,9 => UNS * PRF # H6: 1,4 => SOL * DIS # H6: 6 => CTR => H6: 1,4 * INC # G4: 2,5 => UNS * INC # I4: 2,5 => UNS * INC # B5: 4,6 => UNS * DIS # C6: 4,6 => CTR => C6: 2 * INC # C6: 2 => UNS * INC # H6: 4,6 => UNS * DIS # H6: 1 => CTR => H6: 4,6 * DIS # B8: 4,6 => CTR => B8: 8 * INC # B8: 8 => UNS * DIS # B9: 4,6 => CTR => B9: 8,9 * INC # B9: 8,9 => UNS * INC # G4: 7,9 => UNS * INC # I4: 7,9 => UNS * INC # E5: 1,2 => UNS * INC # F5: 1,2 => UNS * INC # G6: 7,9 => UNS * DIS # I6: 7,9 => CTR => I6: 1,2,6 * INC # I6: 1,2,6 => UNS * PRF # B5: 4,5 => SOL * DIS # B5: 6 => CTR => B5: 4,5 * INC # G1: 4,5 => UNS * DIS # G3: 4,5 => CTR => G3: 2,3,7,8 * INC # G3: 2,3,7,8 => UNS * DIS # B5: 5,6 => CTR => B5: 4 * PRF # B5: 4 => SOL * INC # I1: 5,6 => UNS * DIS # I2: 5,6 => CTR => I2: 1,7,8 * INC # I2: 1,7,8 => UNS * DIS # E7: 1,2 => CTR => E7: 7,8,9 * INC # E7: 7,8,9 => UNS * DIS # F7: 1,2 => CTR => F7: 7,8,9 * INC # F7: 7,8,9 => UNS * CNT 62 HDP CHAINS / 62 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 3,5 => UNS * DIS # C2: 3,5 => CTR => C2: 8,9 * INC C2: 8,9 # B3: 3,5 => UNS * DIS C2: 8,9 # C3: 3,5 => CTR => C3: 8,9 * DIS C2: 8,9 + C3: 8,9 # G1: 3,5 => CTR => G1: 2,4,7 * INC C2: 8,9 + C3: 8,9 + G1: 2,4,7 # B1: 3,5 => UNS * INC C2: 8,9 + C3: 8,9 + G1: 2,4,7 # B3: 3,5 => UNS * PRF C2: 8,9 + C3: 8,9 + G1: 2,4,7 # F1: 5,6 => SOL * STA C2: 8,9 + C3: 8,9 + G1: 2,4,7 + F1: 5,6 * CNT 8 HDP CHAINS / 8 HYP OPENED