Analysis of xx-top500-417-base.sdk
Contents
Original Sudoku
level: medium
position: 6.7....3..5..1.............2..3.5....8....1.4...7........6..8....3....5.4........ initial
Autosolve
position: 6.7....3185..13...13.......271345...385...174946781.2.5..6..8..7.3....5.4.8...... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D1: 2,9 => CTR => D1: 4,5,8 * DIS # F1: 2,9 => CTR => F1: 4,8 * DIS # G1: 2,9 => CTR => G1: 4,5 * PRF # B7: 2,9 => SOL * DIS # B7: 1 => CTR => B7: 2,9 * DIS # B8: 2,9 => CTR => B8: 1,6 * DIS # B9: 2,9 => CTR => B9: 1,6 * DIS # E5: 2,9 => CTR => E5: 6 * DIS # D1: 2,9 => CTR => D1: 4,5,8 * DIS # D3: 2,9 => CTR => D3: 4,5 * DIS # D8: 2,9 => CTR => D8: 1,4,8 * DIS # D9: 2,9 => CTR => D9: 1,5 * DIS # G8: 6,9 => CTR => G8: 2,4 * PRF # B7: 2,9 => SOL * DIS # B7: 1 => CTR => B7: 2,9 * DIS # B8: 2,9 => CTR => B8: 1,6 * DIS # B9: 2,9 => CTR => B9: 1,6 * DIS # E7: 2,9 => CTR => E7: 3,7 * DIS # F7: 2,9 => CTR => F7: 4,7 * DIS # I7: 2,9 => CTR => I7: 3,7 * DIS # E7: 2,9 => CTR => E7: 3,7 * DIS # F7: 2,9 => CTR => F7: 4,7 * DIS # D8: 2,9 => CTR => D8: 1,4,8 * PRF # F8: 2,9 => SOL * DIS # D9: 2,9 => CTR => D9: 1,5 * DIS # E9: 2,9 => CTR => E9: 3,5,7 * DIS # B8: 2,9 => CTR => B8: 1,6 * DIS # G8: 2,9 => CTR => G8: 4,6 * DIS # E5: 2,9 => CTR => E5: 6 * CNT 29 HDP CHAINS / 68 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D1: 2,9 => CTR => D1: 4,5,8 * DIS D1: 4,5,8 # F1: 2,9 => CTR => F1: 4,8 * DIS D1: 4,5,8 + F1: 4,8 # G1: 2,9 => CTR => G1: 4,5 * PRF D1: 4,5,8 + F1: 4,8 + G1: 4,5 # B7: 2,9 => SOL * STA D1: 4,5,8 + F1: 4,8 + G1: 4,5 + B7: 2,9 * CNT 4 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6.7....3..5..1.............2..3.5....8....1.4...7........6..8....3....5.4........ | initial |
| 6.7....3185..13...13.......271345...385...174946781.2.5..6..8..7.3....5.4.8...... | autosolve |
| 697428531854913762132576948271345689385269174946781325529634817713892456468157293 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) B1: 2,9 E3: 6,7 F3: 6,7 D5: 2,9 G4: 6,9 G6: 3,5 I6: 3,5 C7: 2,9 E8: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D8,D9: 1.. / D8 = 1 => 0 pairs (X) / D9 = 1 => 0 pairs (_) H7,H9: 1.. / H7 = 1 => 0 pairs (*) / H9 = 1 => 0 pairs (X) B7,H7: 1.. / B7 = 1 => 0 pairs (X) / H7 = 1 => 0 pairs (_) B8,D8: 1.. / B8 = 1 => 0 pairs (*) / D8 = 1 => 0 pairs (X) G6,I6: 3.. / G6 = 3 => 7 pairs (_) / I6 = 3 => 0 pairs (X) E7,E9: 3.. / E7 = 3 => 9 pairs (_) / E9 = 3 => 0 pairs (X) E7,I7: 3.. / E7 = 3 => 9 pairs (_) / I7 = 3 => 0 pairs (X) G6,G9: 3.. / G6 = 3 => 7 pairs (_) / G9 = 3 => 0 pairs (X) C2,C3: 4.. / C2 = 4 => 14 pairs (_) / C3 = 4 => 11 pairs (_) H7,G8: 4.. / H7 = 4 => 0 pairs (X) / G8 = 4 => 0 pairs (_) F7,H7: 4.. / F7 = 4 => 0 pairs (*) / H7 = 4 => 0 pairs (X) G6,I6: 5.. / G6 = 5 => 0 pairs (X) / I6 = 5 => 7 pairs (_) D9,E9: 5.. / D9 = 5 => 0 pairs (X) / E9 = 5 => 11 pairs (_) E1,E9: 5.. / E1 = 5 => 0 pairs (X) / E9 = 5 => 11 pairs (_) I3,I6: 5.. / I3 = 5 => 0 pairs (X) / I6 = 5 => 7 pairs (_) E3,F3: 6.. / E3 = 6 => 0 pairs (X) / F3 = 6 => 8 pairs (_) E5,F5: 6.. / E5 = 6 => 8 pairs (_) / F5 = 6 => 0 pairs (X) B8,B9: 6.. / B8 = 6 => 0 pairs (X) / B9 = 6 => 10 pairs (_) E3,E5: 6.. / E3 = 6 => 0 pairs (X) / E5 = 6 => 8 pairs (_) F3,F5: 6.. / F3 = 6 => 8 pairs (_) / F5 = 6 => 0 pairs (X) E3,F3: 7.. / E3 = 7 => 8 pairs (_) / F3 = 7 => 0 pairs (X) G2,I2: 7.. / G2 = 7 => 9 pairs (_) / I2 = 7 => 13 pairs (_) G2,G9: 7.. / G2 = 7 => 9 pairs (_) / G9 = 7 => 13 pairs (_) D1,F1: 8.. / D1 = 8 => 9 pairs (_) / F1 = 8 => 0 pairs (*) H3,I3: 8.. / H3 = 8 => 10 pairs (_) / I3 = 8 => 9 pairs (_) H4,I4: 8.. / H4 = 8 => 9 pairs (_) / I4 = 8 => 10 pairs (_) D8,F8: 8.. / D8 = 8 => 0 pairs (*) / F8 = 8 => 0 pairs (X) D1,D8: 8.. / D1 = 8 => 9 pairs (_) / D8 = 8 => 0 pairs (*) F1,F8: 8.. / F1 = 8 => 0 pairs (*) / F8 = 8 => 0 pairs (X) H3,H4: 8.. / H3 = 8 => 10 pairs (_) / H4 = 8 => 9 pairs (_) I3,I4: 8.. / I3 = 8 => 9 pairs (_) / I4 = 8 => 10 pairs (_) * DURATION: 0:00:48.424962 START: 17:04:24.127167 END: 17:05:12.552129 2017-05-04 * CP COUNT: (31) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,C7,D5,E3,E8,F3,G4,G6,I6) * 6.7....3185..13...13.......271345...385...174946781.2.5..6..8..7.3....5.4.8...... * PAIR B1: 2,9 BLK 1 C2: 2,9,4 # reduction candidate for 2,9 C2: 2,9 # 11 pairs C3: 2,9,4 # reduction candidate for 2,9 C3: 2,9 # 14 pairs * PAIR B1: 2,9 ROW 1 D1: 2,9,4,5,8 # reduction candidate for 2,9 D1: 2,9 => CTR * 6.7..843185..13...13.......271345...385...174946781.2.5..6..84.7.38.4.5.4.815.... D1: 4,5,8 # 9 pairs E1: 2,9,5 # reduction candidate for 2,9 E1: 2,9 # 11 pairs F1: 2,9,4,8 # reduction candidate for 2,9 F1: 2,9 => CTR * 6.78..43185..13...13.......271345...385...174946781.2.5..6..84.7.3....5.4.8...... F1: 4,8 # 10 pairs G1: 2,9,4,5 # reduction candidate for 2,9 G1: 2,9 => CTR * 6.7....3185..13...13.......271345...385...174946781.2.5..6..8..7.3....5.4.8...... G1: 4,5 # 10 pairs * PAIR B1: 2,9 COL B B7: 2,9,1 # reduction candidate for 2,9 B7: 2,9 => SOLVED * 697428531854913762132576948271345689385269174946781325529634817713892456468157293 B7: 1 => CTR * 6.78.4.3185..13...13.......271345...385...174946781.2.51.6..89.7.31.845.4.8....1. B8: 2,9,1,6 # reduction candidate for 2,9 B8: 2,9 => CTR * 6.78.4.3185..13...13.......271345...385...174946781.2.51.6..89.793128456468....1. B8: 1,6 # 10 pairs B9: 2,9,1,6 # reduction candidate for 2,9 B9: 2,9 => CTR * 6.78.4.3185..13...13.......271345...385...174946781.2.51.6..89.763198452498....1. B9: 1,6 # 10 pairs * PAIR D5: 2,9 BLK 5 E5: 2,9,6 # reduction candidate for 2,9 E5: 2,9 => CTR * 6.785.43185..13...13..67...271345...385..6174946781.2.5..6.48..7.3....5.4.8...... E5: 6 # 8 pairs F5: 2,9,6 # reduction candidate for 2,9 F5: 2,9 # 8 pairs * PAIR D5: 2,9 COL D D1: 2,9,4,5,8 # reduction candidate for 2,9 D1: 2,9 => CTR * 6.7..843185..13...13.......271345...385...174946781.2.5..6..84.7.38.4.5.4.815.... D1: 4,5,8 # 9 pairs D2: 2,9,4 # reduction candidate for 2,9 D2: 2,9 # 12 pairs D3: 2,9,4,5 # reduction candidate for 2,9 D3: 2,9 => CTR * 6.7....3185.413...134......271345...385...174946781.2.5..6..84.7.3..4.5.4.8....1. D3: 4,5 # 10 pairs D8: 2,9,1,4,8 # reduction candidate for 2,9 D8: 2,9 => CTR * 6.78.453185..13...13.5.....271345...385...1749467813255..63.81.713..845646815..93 D8: 1,4,8 # 9 pairs D9: 2,9,1,5 # reduction candidate for 2,9 D9: 2,9 => CTR * 6.78.453185..13...13.5.....271345...385...1749467813255..63.8..7.31.845.4.8.5...3 D9: 1,5 # 10 pairs * PAIR G4: 6,9 BLK 6 H4: 6,9,8 # reduction candidate for 6,9 H4: 6,9 # 10 pairs I4: 6,9,8 # reduction candidate for 6,9 I4: 6,9 # 9 pairs * PAIR G4: 6,9 COL G G2: 6,9,2,4,7 # reduction candidate for 6,9 G2: 6,9 # 15 pairs G8: 6,9,2,4 # reduction candidate for 6,9 G8: 6,9 => CTR * 6.7....3185..13...13.......271345...385...174946781.2.51.6..84.7.31...5.4.8....1. G8: 2,4 # 10 pairs G9: 6,9,2,3,7 # reduction candidate for 6,9 G9: 6,9 # 16 pairs * PAIR C7: 2,9 BLK 7 B7: 2,9,1 # reduction candidate for 2,9 B7: 2,9 => SOLVED * 697428531854913762132576948271345689385269174946781325529634817713892456468157293 B7: 1 => CTR * 6.78.4.3185..13...13.......271345...385...174946781.2.51.6..89.7.31.845.4.8....1. B8: 2,9,1,6 # reduction candidate for 2,9 B8: 2,9 => CTR * 6.78.4.3185..13...13.......271345...385...174946781.2.51.6..89.793128456468....1. B8: 1,6 # 10 pairs B9: 2,9,1,6 # reduction candidate for 2,9 B9: 2,9 => CTR * 6.78.4.3185..13...13.......271345...385...174946781.2.51.6..89.763198452498....1. B9: 1,6 # 10 pairs * PAIR C7: 2,9 ROW 7 E7: 2,9,3,7 # reduction candidate for 2,9 E7: 2,9 => CTR * 6.7.5..3185..13...13..765..271345...385.6.17494678132551.6.78437.31...5.4.853..1. E7: 3,7 # 10 pairs F7: 2,9,4,7 # reduction candidate for 2,9 F7: 2,9 => CTR * 6.7....3185..13...13.......271345...385...174946781.2.51.6..84.7.31...5.4.8....1. F7: 4,7 # 10 pairs I7: 2,9,3,7 # reduction candidate for 2,9 I7: 2,9 => CTR * 6.7....3185..13...13..76...271345...385.6.174946781.2.51.63784.7.31...5.4.8....1. I7: 3,7 # 10 pairs * PAIR C7: 2,9 COL C C2: 2,9,4 # reduction candidate for 2,9 C2: 2,9 # 11 pairs C3: 2,9,4 # reduction candidate for 2,9 C3: 2,9 # 14 pairs * PAIR E8: 2,9 BLK 8 E7: 2,9,3,7 # reduction candidate for 2,9 E7: 2,9 => CTR * 6.7.5..3185..13...13..765..271345...385.6.17494678132551.6.78437.31...5.4.853..1. E7: 3,7 # 10 pairs F7: 2,9,4,7 # reduction candidate for 2,9 F7: 2,9 => CTR * 6.7....3185..13...13.......271345...385...174946781.2.51.6..84.7.31...5.4.8....1. F7: 4,7 # 10 pairs D8: 2,9,1,4,8 # reduction candidate for 2,9 D8: 2,9 => CTR * 6.78.453185..13...13.5.....271345...385...1749467813255..63.81.713..845646815..93 D8: 1,4,8 # 9 pairs F8: 2,9,4,8 # reduction candidate for 2,9 F8: 2,9 => SOLVED * 697428531854913762132576948271345689385269174946781325529634817713892456468157293 F8: 4,8 # 10 pairs D9: 2,9,1,5 # reduction candidate for 2,9 D9: 2,9 => CTR * 6.78.453185..13...13.5.....271345...385...1749467813255..63.8..7.31.845.4.8.5...3 D9: 1,5 # 10 pairs E9: 2,9,3,5,7 # reduction candidate for 2,9 E9: 2,9 => CTR * 6.7854.3185..13...13..76...271345...385.6.174946781.2.5..63.8..7.31.845.4.85..... E9: 3,5,7 # 9 pairs F9: 2,9,7 # reduction candidate for 2,9 F9: 2,9 # 14 pairs * PAIR E8: 2,9 ROW 8 B8: 2,9,1,6 # reduction candidate for 2,9 B8: 2,9 => CTR * 6.78.4.3185..13...13.......271345...385...174946781.2.51.6..89.793128456468....1. B8: 1,6 # 10 pairs G8: 2,9,4,6 # reduction candidate for 2,9 G8: 2,9 => CTR * 6.7....3185..13...13.......271345...385...174946781.2.51.6..84.7.31...5.4.8....1. G8: 4,6 # 10 pairs I8: 2,9,6 # reduction candidate for 2,9 I8: 2,9 # 13 pairs * PAIR E8: 2,9 COL E E1: 2,9,5 # reduction candidate for 2,9 E1: 2,9 # 11 pairs E5: 2,9,6 # reduction candidate for 2,9 E5: 2,9 => CTR * 6.785.43185..13...13..67...271345...385..6174946781.2.5..6.48..7.3....5.4.8...... E5: 6 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-417-base-pr-000.dot * REASONING * DIS # D1: 2,9 => CTR => D1: 4,5,8 * DIS # F1: 2,9 => CTR => F1: 4,8 * DIS # G1: 2,9 => CTR => G1: 4,5 * PRF # B7: 2,9 => SOL * DIS # B7: 1 => CTR => B7: 2,9 * DIS # B8: 2,9 => CTR => B8: 1,6 * DIS # B9: 2,9 => CTR => B9: 1,6 * DIS # E5: 2,9 => CTR => E5: 6 * DIS # D1: 2,9 => CTR => D1: 4,5,8 * DIS # D3: 2,9 => CTR => D3: 4,5 * DIS # D8: 2,9 => CTR => D8: 1,4,8 * DIS # D9: 2,9 => CTR => D9: 1,5 * DIS # G8: 6,9 => CTR => G8: 2,4 * PRF # B7: 2,9 => SOL * DIS # B7: 1 => CTR => B7: 2,9 * DIS # B8: 2,9 => CTR => B8: 1,6 * DIS # B9: 2,9 => CTR => B9: 1,6 * DIS # E7: 2,9 => CTR => E7: 3,7 * DIS # F7: 2,9 => CTR => F7: 4,7 * DIS # I7: 2,9 => CTR => I7: 3,7 * DIS # E7: 2,9 => CTR => E7: 3,7 * DIS # F7: 2,9 => CTR => F7: 4,7 * DIS # D8: 2,9 => CTR => D8: 1,4,8 * PRF # F8: 2,9 => SOL * DIS # D9: 2,9 => CTR => D9: 1,5 * DIS # E9: 2,9 => CTR => E9: 3,5,7 * DIS # B8: 2,9 => CTR => B8: 1,6 * DIS # G8: 2,9 => CTR => G8: 4,6 * DIS # E5: 2,9 => CTR => E5: 6 * CNT 29 HDP CHAINS / 68 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,C7,D5,E3,E8,F3,G4,G6,I6) * 6.7....3185..13...13.......271345...385...174946781.2.5..6..8..7.3....5.4.8...... * PAIR B1: 2,9 BLK 1 C2: 2,9,4 # reduction candidate for 2,9 C2: 2,9 # 11 pairs C3: 2,9,4 # reduction candidate for 2,9 C3: 2,9 # 14 pairs * PAIR B1: 2,9 ROW 1 D1: 2,9,4,5,8 # reduction candidate for 2,9 D1: 2,9 => CTR * 6.7..843185..13...13.......271345...385...174946781.2.5..6..84.7.38.4.5.4.815.... E1: 2,9,5 # reduction candidate for 2,9 E1: 2,9 # 11 pairs F1: 2,9,4,8 # reduction candidate for 2,9 F1: 2,9 => CTR * 6.78..43185..13...13.......271345...385...174946781.2.5..6..84.7.3....5.4.8...... G1: 2,9,4,5 # reduction candidate for 2,9 G1: 2,9 => CTR * 6.7....3185..13...13.......271345...385...174946781.2.5..6..8..7.3....5.4.8...... * RESTART * PAIR B1: 2,9 COL B B7: 2,9,1 # reduction candidate for 2,9 B7: 2,9 => SOLVED * 697428531854913762132576948271345689385269174946781325529634817713892456468157293 * DURATION: 0:00:07.449036 START: 17:06:07.200646 END: 17:06:14.649682 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-417-base-pr-001.dot * REASONING * DIS # D1: 2,9 => CTR => D1: 4,5,8 * DIS D1: 4,5,8 # F1: 2,9 => CTR => F1: 4,8 * DIS D1: 4,5,8 + F1: 4,8 # G1: 2,9 => CTR => G1: 4,5 * PRF D1: 4,5,8 + F1: 4,8 + G1: 4,5 # B7: 2,9 => SOL * STA D1: 4,5,8 + F1: 4,8 + G1: 4,5 + B7: 2,9 * CNT 4 HDP CHAINS / 7 HYP OPENED
Header Info
Top 500 Minimum 17 417 solution: 697428531854913762132576948271345689385269174946781325529634817713892456468157293 info: 95089 FNBHK S8.f 39972 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 697428531854913762132576948271345689385269174946781325529634817713892456468157293 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 # C2: 2,9 => UNS * INC # C3: 2,9 => UNS * DIS # D1: 2,9 => CTR => D1: 4,5,8 * INC # D1: 4,5,8 => UNS * INC # E1: 2,9 => UNS * DIS # F1: 2,9 => CTR => F1: 4,8 * INC # F1: 4,8 => UNS * DIS # G1: 2,9 => CTR => G1: 4,5 * INC # G1: 4,5 => UNS * PRF # B7: 2,9 => SOL * DIS # B7: 1 => CTR => B7: 2,9 * DIS # B8: 2,9 => CTR => B8: 1,6 * INC # B8: 1,6 => UNS * DIS # B9: 2,9 => CTR => B9: 1,6 * INC # B9: 1,6 => UNS * DIS # E5: 2,9 => CTR => E5: 6 * INC # E5: 6 => UNS * INC # F5: 2,9 => UNS * DIS # D1: 2,9 => CTR => D1: 4,5,8 * INC # D1: 4,5,8 => UNS * INC # D2: 2,9 => UNS * DIS # D3: 2,9 => CTR => D3: 4,5 * INC # D3: 4,5 => UNS * DIS # D8: 2,9 => CTR => D8: 1,4,8 * INC # D8: 1,4,8 => UNS * DIS # D9: 2,9 => CTR => D9: 1,5 * INC # D9: 1,5 => UNS * INC # H4: 6,9 => UNS * INC # I4: 6,9 => UNS * INC # G2: 6,9 => UNS * DIS # G8: 6,9 => CTR => G8: 2,4 * INC # G8: 2,4 => UNS * INC # G9: 6,9 => UNS * PRF # B7: 2,9 => SOL * DIS # B7: 1 => CTR => B7: 2,9 * DIS # B8: 2,9 => CTR => B8: 1,6 * INC # B8: 1,6 => UNS * DIS # B9: 2,9 => CTR => B9: 1,6 * INC # B9: 1,6 => UNS * DIS # E7: 2,9 => CTR => E7: 3,7 * INC # E7: 3,7 => UNS * DIS # F7: 2,9 => CTR => F7: 4,7 * INC # F7: 4,7 => UNS * DIS # I7: 2,9 => CTR => I7: 3,7 * INC # I7: 3,7 => UNS * INC # C2: 2,9 => UNS * INC # C3: 2,9 => UNS * DIS # E7: 2,9 => CTR => E7: 3,7 * INC # E7: 3,7 => UNS * DIS # F7: 2,9 => CTR => F7: 4,7 * INC # F7: 4,7 => UNS * DIS # D8: 2,9 => CTR => D8: 1,4,8 * INC # D8: 1,4,8 => UNS * PRF # F8: 2,9 => SOL * INC # F8: 4,8 => UNS * DIS # D9: 2,9 => CTR => D9: 1,5 * INC # D9: 1,5 => UNS * DIS # E9: 2,9 => CTR => E9: 3,5,7 * INC # E9: 3,5,7 => UNS * INC # F9: 2,9 => UNS * DIS # B8: 2,9 => CTR => B8: 1,6 * INC # B8: 1,6 => UNS * DIS # G8: 2,9 => CTR => G8: 4,6 * INC # G8: 4,6 => UNS * INC # I8: 2,9 => UNS * INC # E1: 2,9 => UNS * DIS # E5: 2,9 => CTR => E5: 6 * INC # E5: 6 => UNS * CNT 68 HDP CHAINS / 68 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C2: 2,9 => UNS * INC # C3: 2,9 => UNS * DIS # D1: 2,9 => CTR => D1: 4,5,8 * INC D1: 4,5,8 # E1: 2,9 => UNS * DIS D1: 4,5,8 # F1: 2,9 => CTR => F1: 4,8 * DIS D1: 4,5,8 + F1: 4,8 # G1: 2,9 => CTR => G1: 4,5 * PRF D1: 4,5,8 + F1: 4,8 + G1: 4,5 # B7: 2,9 => SOL * STA D1: 4,5,8 + F1: 4,8 + G1: 4,5 + B7: 2,9 * CNT 7 HDP CHAINS / 7 HYP OPENED