Analysis of xx-top500-055-base.sdk
Contents
Original Sudoku
level: medium
position: ...7...82.51...............6..8.9....3....1...............1.56....23....8.....4.. initial
Autosolve
position: 3..751.82.51.8..34...3...1561.8.9357.3....1..5..1.32......185631.523.8798.3...421 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C1: 4,9 => SOL * DIS # C1: 6 => CTR => C1: 4,9 * PRF # E3: 6,9 => SOL * DIS # E3: 4 => CTR => E3: 6,9 * PRF # D9: 6,9 => SOL * DIS # F3: 2,6 => CTR => F3: 4 * PRF # F3: 4 => SOL * DIS # C1: 6,9 => CTR => C1: 4 * PRF # C1: 4 => SOL * DIS # C5: 2,4 => CTR => C5: 7,8,9 * DIS # C7: 2,4 => CTR => C7: 7,9 * DIS # C6: 7,8 => CTR => C6: 4,9 * DIS # B3: 2 => CTR => B3: 7,8 * PRF # E5: 2,4 => SOL * DIS # E5: 6,7 => CTR => E5: 2,4 * PRF # A5: 4,9 => SOL * DIS # A5: 2,7 => CTR => A5: 4,9 * DIS # C5: 4,9 => CTR => C5: 2,7,8 * DIS # C6: 7,8 => CTR => C6: 4,9 * DIS # A7: 2,7 => CTR => A7: 4,9 * DIS # B3: 2,7 => CTR => B3: 8 * PRF # D9: 6,9 => SOL * DIS # C7: 4,9 => CTR => C7: 2,7 * DIS # F3: 2 => CTR => F3: 4,6 * CNT 24 HDP CHAINS / 45 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C1: 4,9 => SOL * STA C1: 4,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...7...82.51...............6..8.9....3....1...............1.56....23....8.....4.. | initial |
| 3..751.82.51.8..34...3...1561.8.9357.3....1..5..1.32......185631.523.8798.3...421 | autosolve |
| 394751682751682934286394715612849357438527196579163248927418563145236879863975421 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) B1: 4,9 D2: 6,9 F2: 2,6 G1: 6,9 C4: 2,4 B6: 7,8 E4: 2,4 F5: 5,7 H5: 4,9 I5: 6,8 H6: 4,9 I6: 6,8 B7: 2,7 B8: 4,6 B9: 6,9 D7: 4,9 F8: 4,6 F9: 5,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F2,F3: 2.. / F2 = 2 => 19 pairs (_) / F3 = 2 => 0 pairs (X) E4,E5: 2.. / E4 = 2 => 0 pairs (X) / E5 = 2 => 0 pairs (_) A2,F2: 2.. / A2 = 2 => 0 pairs (X) / F2 = 2 => 19 pairs (_) C4,E4: 2.. / C4 = 2 => 0 pairs (*) / E4 = 2 => 0 pairs (X) B3,B7: 2.. / B3 = 2 => 0 pairs (X) / B7 = 2 => 18 pairs (_) B1,C1: 4.. / B1 = 4 => 0 pairs (X) / C1 = 4 => 0 pairs (_) E3,F3: 4.. / E3 = 4 => 0 pairs (X) / F3 = 4 => 0 pairs (_) H5,H6: 4.. / H5 = 4 => 0 pairs (X) / H6 = 4 => 18 pairs (_) D7,F8: 4.. / D7 = 4 => 0 pairs (*) / F8 = 4 => 0 pairs (X) C4,E4: 4.. / C4 = 4 => 0 pairs (X) / E4 = 4 => 0 pairs (_) B8,F8: 4.. / B8 = 4 => 0 pairs (*) / F8 = 4 => 0 pairs (X) A5,A7: 4.. / A5 = 4 => 0 pairs (*) / A7 = 4 => 0 pairs (X) B1,B8: 4.. / B1 = 4 => 0 pairs (X) / B8 = 4 => 0 pairs (_) D5,D7: 4.. / D5 = 4 => 0 pairs (X) / D7 = 4 => 0 pairs (_) F3,F8: 4.. / F3 = 4 => 0 pairs (*) / F8 = 4 => 0 pairs (X) D5,F5: 5.. / D5 = 5 => 0 pairs (*) / F5 = 5 => 0 pairs (X) D9,F9: 5.. / D9 = 5 => 18 pairs (_) / F9 = 5 => 0 pairs (*) D5,D9: 5.. / D5 = 5 => 0 pairs (*) / D9 = 5 => 0 pairs (X) F5,F9: 5.. / F5 = 5 => 18 pairs (_) / F9 = 5 => 0 pairs (*) C1,C3: 6.. / C1 = 6 => 0 pairs (X) / C3 = 6 => 0 pairs (_) I5,I6: 6.. / I5 = 6 => 18 pairs (_) / I6 = 6 => 17 pairs (_) B8,B9: 6.. / B8 = 6 => 0 pairs (X) / B9 = 6 => 0 pairs (_) C1,G1: 6.. / C1 = 6 => 0 pairs (X) / G1 = 6 => 0 pairs (_) E6,I6: 6.. / E6 = 6 => 18 pairs (_) / I6 = 6 => 17 pairs (_) B8,F8: 6.. / B8 = 6 => 0 pairs (X) / F8 = 6 => 0 pairs (_) G2,G3: 7.. / G2 = 7 => 22 pairs (_) / G3 = 7 => 21 pairs (_) E9,F9: 7.. / E9 = 7 => 0 pairs (*) / F9 = 7 => 0 pairs (X) A2,G2: 7.. / A2 = 7 => 21 pairs (_) / G2 = 7 => 22 pairs (_) F5,F9: 7.. / F5 = 7 => 0 pairs (*) / F9 = 7 => 0 pairs (X) B3,C3: 8.. / B3 = 8 => 17 pairs (_) / C3 = 8 => 0 pairs (X) I5,I6: 8.. / I5 = 8 => 17 pairs (_) / I6 = 8 => 18 pairs (_) C5,I5: 8.. / C5 = 8 => 18 pairs (_) / I5 = 8 => 17 pairs (_) B3,B6: 8.. / B3 = 8 => 17 pairs (_) / B6 = 8 => 0 pairs (X) D2,E3: 9.. / D2 = 9 => 0 pairs (X) / E3 = 9 => 0 pairs (_) H5,H6: 9.. / H5 = 9 => 18 pairs (_) / H6 = 9 => 0 pairs (X) C6,H6: 9.. / C6 = 9 => 18 pairs (_) / H6 = 9 => 0 pairs (X) B1,B9: 9.. / B1 = 9 => 0 pairs (*) / B9 = 9 => 0 pairs (X) E3,E9: 9.. / E3 = 9 => 0 pairs (*) / E9 = 9 => 0 pairs (X) * DURATION: 0:01:06.085960 START: 04:33:19.889116 END: 04:34:25.975076 2017-05-04 * CP COUNT: (38) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B6,B7,B8,B9,C4,D2,D7,E4,F2,F5,F8,F9,G1,H5,H6,I5,I6) * 3..751.82.51.8..34...3...1561.8.9357.3....1..5..1.32......185631.523.8798.3...421 * PAIR B1: 4,9 BLK 1 C1: 4,9,6 # reduction candidate for 4,9 C1: 4,9 => SOLVED * 394751682751682934286394715612849357438527196579163248927418563145236879863975421 C1: 6 => CTR * 346751982.51.8..34...3...1561.8.9357.3....1..5..1.32......18563165234879893...421 * PAIR D2: 6,9 BLK 2 E3: 6,9,4 # reduction candidate for 6,9 E3: 6,9 => SOLVED * 394751682751682934286394715612849357438527196579163248927418563145236879863975421 E3: 4 => CTR * 3..751.82.5198..34...34..15614829357.3.4..1..5..1.32......185631.523.8798.3...421 * PAIR D2: 6,9 ROW 2 G2: 6,9,7 # reduction candidate for 6,9 G2: 7 # 22 pairs G2: 6,9 # 21 pairs * PAIR D2: 6,9 COL D D9: 6,9,5 # reduction candidate for 6,9 D9: 6,9 => SOLVED * 394751682751682934286394715612849357438527196579163248927418563145236879863975421 D9: 5 # 18 pairs * PAIR F2: 2,6 BLK 2 F3: 2,6,4 # reduction candidate for 2,6 F3: 2,6 => CTR * 3..751.82.51.8..34...34..15614829357.3.4.519.5.91.324.4..918563165234879893567421 F3: 4 => SOLVED * 394751682751682934286394715612849357438527196579163248927418563145236879863975421 * PAIR G1: 6,9 BLK 3 G2: 6,9,7 # reduction candidate for 6,9 G2: 6,9 # 21 pairs G3: 6,9,7 # reduction candidate for 6,9 G3: 6,9 # 22 pairs * PAIR G1: 6,9 ROW 1 C1: 6,9,4 # reduction candidate for 6,9 C1: 6,9 => CTR * 34.751.82.51.8..34...3...1561.8.9357.3....1..5..1.32......18563165234879893...421 C1: 4 => SOLVED * 394751682751682934286394715612849357438527196579163248927418563145236879863975421 * PAIR C4: 2,4 BLK 4 A5: 2,4,7,9 # reduction candidate for 2,4 A5: 2,4 # 20 pairs C5: 2,4,7,8,9 # reduction candidate for 2,4 C5: 2,4 => CTR * 34.751.82.51.8..34...3...1561.8.9357.3....1.85..1.32.6427918563165234879893...421 C5: 7,8,9 # 18 pairs * PAIR C4: 2,4 COL C C7: 2,4,7,9 # reduction candidate for 2,4 C7: 2,4 => CTR * 34.751.82.51.8..34...3...1561.8.9357.3....1..5..1.32......18563165234879893...421 C7: 7,9 # 19 pairs * PAIR B6: 7,8 BLK 4 C5: 7,8,2,4,9 # reduction candidate for 7,8 C5: 7,8 # 21 pairs C6: 7,8,4,9 # reduction candidate for 7,8 C6: 7,8 => CTR * 3..751.82.51.8..34...3...1561.8.9357.3....14.5..1432964..918563165234879893...421 C6: 4,9 # 20 pairs * PAIR B6: 7,8 COL B B3: 7,8,2 # reduction candidate for 7,8 B3: 2 => CTR * 346751982.51.82.34.2839461561.8.9357.3....1.858.1.32.6.7..185631.523.879893...421 B3: 7,8 # 18 pairs * PAIR E4: 2,4 BLK 5 E5: 2,4,6,7 # reduction candidate for 2,4 E5: 2,4 => SOLVED * 394751682751682934286394715612849357438527196579163248927418563145236879863975421 E5: 6,7 => CTR * 3..751.82.51.8..34...3...15614829357.3....1..5..1.32..4..918563165234879893...421 * PAIR H5: 4,9 ROW 5 A5: 4,9,2,7 # reduction candidate for 4,9 A5: 4,9 => SOLVED * 394751682751682934286394715612849357438527196579163248927418563145236879863975421 A5: 2,7 => CTR * 3..751.82.51.8..34...3...1561.8.9357.3....1..5..1.32..4..918563165234879893...421 C5: 4,9,2,7,8 # reduction candidate for 4,9 C5: 4,9 => CTR * 3..751.82.51.8..34...3...1561.8.9357.3....1.85..1.32.64..918563165234879893...421 C5: 2,7,8 # 18 pairs * PAIR H6: 4,9 ROW 6 C6: 4,9,7,8 # reduction candidate for 4,9 C6: 7,8 => CTR * 3..751.82.51.8..34...3...1561.8.9357.3....14.5..1432964..918563165234879893...421 C6: 4,9 # 20 pairs * PAIR B7: 2,7 BLK 7 A7: 2,7,4,9 # reduction candidate for 2,7 A7: 2,7 => CTR * 3..751.82.51.8..34...3...1561.8.935743....19.5.91.324.....185631.523.8798.3...421 A7: 4,9 # 20 pairs C7: 2,7,4,9 # reduction candidate for 2,7 C7: 2,7 # 20 pairs * PAIR B7: 2,7 COL B B3: 2,7,8 # reduction candidate for 2,7 B3: 2,7 => CTR * 346751982.51.8..34..839461561.8.9357.3....1.858.1.32.6....185631.523.879893...421 B3: 8 # 17 pairs * PAIR B9: 6,9 ROW 9 D9: 6,9,5 # reduction candidate for 6,9 D9: 6,9 => SOLVED * 394751682751682934286394715612849357438527196579163248927418563145236879863975421 D9: 5 # 18 pairs E9: 6,9,7 # reduction candidate for 6,9 E9: 6,9 # 18 pairs * PAIR D7: 4,9 ROW 7 A7: 4,9,2,7 # reduction candidate for 4,9 A7: 4,9 # 20 pairs C7: 4,9,2,7 # reduction candidate for 4,9 C7: 4,9 => CTR * 3..751.82.51.8..34...3...1561.8.935743....19.5.91.324...4.185631.523.8798.3...421 C7: 2,7 # 20 pairs * PAIR F8: 4,6 COL F F3: 4,6,2 # reduction candidate for 4,6 F3: 2 => CTR * 3..751.82.51.8..34...342.15614829357.3.4.519.5.91.324.427918563165234879893567421 F3: 4,6 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-055-base-pr-000.dot * REASONING * PRF # C1: 4,9 => SOL * DIS # C1: 6 => CTR => C1: 4,9 * PRF # E3: 6,9 => SOL * DIS # E3: 4 => CTR => E3: 6,9 * PRF # D9: 6,9 => SOL * DIS # F3: 2,6 => CTR => F3: 4 * PRF # F3: 4 => SOL * DIS # C1: 6,9 => CTR => C1: 4 * PRF # C1: 4 => SOL * DIS # C5: 2,4 => CTR => C5: 7,8,9 * DIS # C7: 2,4 => CTR => C7: 7,9 * DIS # C6: 7,8 => CTR => C6: 4,9 * DIS # B3: 2 => CTR => B3: 7,8 * PRF # E5: 2,4 => SOL * DIS # E5: 6,7 => CTR => E5: 2,4 * PRF # A5: 4,9 => SOL * DIS # A5: 2,7 => CTR => A5: 4,9 * DIS # C5: 4,9 => CTR => C5: 2,7,8 * DIS # C6: 7,8 => CTR => C6: 4,9 * DIS # A7: 2,7 => CTR => A7: 4,9 * DIS # B3: 2,7 => CTR => B3: 8 * PRF # D9: 6,9 => SOL * DIS # C7: 4,9 => CTR => C7: 2,7 * DIS # F3: 2 => CTR => F3: 4,6 * CNT 24 HDP CHAINS / 45 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B6,B7,B8,B9,C4,D2,D7,E4,F2,F5,F8,F9,G1,H5,H6,I5,I6) * 3..751.82.51.8..34...3...1561.8.9357.3....1..5..1.32......185631.523.8798.3...421 * PAIR B1: 4,9 BLK 1 C1: 4,9,6 # reduction candidate for 4,9 C1: 4,9 => SOLVED * 394751682751682934286394715612849357438527196579163248927418563145236879863975421 * DURATION: 0:00:02.449057 START: 04:35:10.460188 END: 04:35:12.909245 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-055-base-pr-001.dot * REASONING * PRF # C1: 4,9 => SOL * STA C1: 4,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 055 solution: 394751682751682934286394715612849357438527196579163248927418563145236879863975421 info: 1411 FNBTHWXY S8.f 11379 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 394751682751682934286394715612849357438527196579163248927418563145236879863975421 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 # C1: 4,9 => SOL * DIS # C1: 6 => CTR => C1: 4,9 * PRF # E3: 6,9 => SOL * DIS # E3: 4 => CTR => E3: 6,9 * INC # G2: 6,9 => UNS * INC # G2: 7 => UNS * PRF # D9: 6,9 => SOL * INC # D9: 5 => UNS * DIS # F3: 2,6 => CTR => F3: 4 * PRF # F3: 4 => SOL * INC # G2: 6,9 => UNS * INC # G3: 6,9 => UNS * DIS # C1: 6,9 => CTR => C1: 4 * PRF # C1: 4 => SOL * INC # A5: 2,4 => UNS * DIS # C5: 2,4 => CTR => C5: 7,8,9 * INC # C5: 7,8,9 => UNS * DIS # C7: 2,4 => CTR => C7: 7,9 * INC # C7: 7,9 => UNS * INC # C5: 7,8 => UNS * DIS # C6: 7,8 => CTR => C6: 4,9 * INC # C6: 4,9 => UNS * INC # B3: 7,8 => UNS * DIS # B3: 2 => CTR => B3: 7,8 * PRF # E5: 2,4 => SOL * DIS # E5: 6,7 => CTR => E5: 2,4 * PRF # A5: 4,9 => SOL * DIS # A5: 2,7 => CTR => A5: 4,9 * DIS # C5: 4,9 => CTR => C5: 2,7,8 * INC # C5: 2,7,8 => UNS * INC # C6: 4,9 => UNS * DIS # C6: 7,8 => CTR => C6: 4,9 * DIS # A7: 2,7 => CTR => A7: 4,9 * INC # A7: 4,9 => UNS * INC # C7: 2,7 => UNS * DIS # B3: 2,7 => CTR => B3: 8 * INC # B3: 8 => UNS * PRF # D9: 6,9 => SOL * INC # D9: 5 => UNS * INC # E9: 6,9 => UNS * INC # A7: 4,9 => UNS * DIS # C7: 4,9 => CTR => C7: 2,7 * INC # C7: 2,7 => UNS * INC # F3: 4,6 => UNS * DIS # F3: 2 => CTR => F3: 4,6 * CNT 45 HDP CHAINS / 45 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C1: 4,9 => SOL * STA C1: 4,9 * CNT 1 HDP CHAINS / 1 HYP OPENED