Analysis of zz-www.sudokuwiki.org-0075-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=75
level: medium
position: ..61...7.4.......6....7.31...9..2....5..8..4....5..7...12.4....6.......4.3...59.. initial
Autosolve
position: 3.61..47.471.....6....7.31...9..2....5..8..4....5..7...12.4....6.......4.34..59.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C8: 5,8 => CTR => C8: 7 * DIS # F6: 1,3,9 => CTR => F6: 4,6 * DIS # F6: 1,3,9 => CTR => F6: 4,6 * DIS # C8: 5 => CTR => C8: 7,8 * CNT 4 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C8: 5,8 => CTR => C8: 7 * DIS C8: 7 # F6: 1,3,9 => CTR => F6: 4,6 * DIS C8: 7 + F6: 4,6 # D4: 4,6 => CTR => D4: 3,7 * DIS C8: 7 + F6: 4,6 + D4: 3,7 # I1: 2,8 => CTR => I1: 5,9 * PRF C8: 7 + F6: 4,6 + D4: 3,7 + I1: 5,9 # D2: 8,9 => SOL * STA C8: 7 + F6: 4,6 + D4: 3,7 + I1: 5,9 + D2: 8,9 * CNT 5 HDP CHAINS / 14 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..61...7.4.......6....7.31...9..2....5..8..4....5..7...12.4....6.......4.3...59.. | initial |
| 3.61..47.471.....6....7.31...9..2....5..8..4....5..7...12.4....6.......4.34..59.. | autosolve |
| 386129475471853296925476318749362581253781649168594732512947863697238154834615927 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) A3: 5,9 C3: 5,8 F1: 8,9 D3: 4,6 F3: 4,6 B4: 4,6 C5: 3,7 B6: 4,6 C6: 3,8 A7: 5,9 B8: 8,9 A9: 7,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G8,I9: 1.. / G8 = 1 => 19 pairs (_) / I9 = 1 => 13 pairs (_) E9,I9: 1.. / E9 = 1 => 19 pairs (_) / I9 = 1 => 13 pairs (_) B1,B3: 2.. / B1 = 2 => 15 pairs (_) / B3 = 2 => 16 pairs (_) A5,A6: 2.. / A5 = 2 => 14 pairs (_) / A6 = 2 => 13 pairs (_) B3,I3: 2.. / B3 = 2 => 16 pairs (_) / I3 = 2 => 15 pairs (_) C5,C6: 3.. / C5 = 3 => 12 pairs (_) / C6 = 3 => 0 pairs (X) D3,F3: 4.. / D3 = 4 => 8 pairs (_) / F3 = 4 => 11 pairs (_) B4,B6: 4.. / B4 = 4 => 8 pairs (_) / B6 = 4 => 11 pairs (_) D4,F6: 4.. / D4 = 4 => 11 pairs (_) / F6 = 4 => 8 pairs (_) B4,D4: 4.. / B4 = 4 => 8 pairs (_) / D4 = 4 => 11 pairs (_) B6,F6: 4.. / B6 = 4 => 11 pairs (_) / F6 = 4 => 8 pairs (_) D3,D4: 4.. / D3 = 4 => 8 pairs (_) / D4 = 4 => 11 pairs (_) F3,F6: 4.. / F3 = 4 => 11 pairs (_) / F6 = 4 => 8 pairs (_) A3,C3: 5.. / A3 = 5 => 0 pairs (X) / C3 = 5 => 13 pairs (_) E1,E2: 5.. / E1 = 5 => 13 pairs (_) / E2 = 5 => 14 pairs (_) A7,C8: 5.. / A7 = 5 => 13 pairs (_) / C8 = 5 => 0 pairs (X) E1,I1: 5.. / E1 = 5 => 13 pairs (_) / I1 = 5 => 14 pairs (_) A3,A7: 5.. / A3 = 5 => 0 pairs (X) / A7 = 5 => 13 pairs (_) C3,C8: 5.. / C3 = 5 => 13 pairs (_) / C8 = 5 => 0 pairs (X) D3,F3: 6.. / D3 = 6 => 11 pairs (_) / F3 = 6 => 8 pairs (_) B4,B6: 6.. / B4 = 6 => 11 pairs (_) / B6 = 6 => 8 pairs (_) C8,A9: 7.. / C8 = 7 => 12 pairs (_) / A9 = 7 => 0 pairs (X) I7,I9: 7.. / I7 = 7 => 12 pairs (_) / I9 = 7 => 0 pairs (*) A4,D4: 7.. / A4 = 7 => 12 pairs (_) / D4 = 7 => 9 pairs (_) C5,C8: 7.. / C5 = 7 => 0 pairs (X) / C8 = 7 => 12 pairs (_) A7,B8: 9.. / A7 = 9 => 0 pairs (X) / B8 = 9 => 13 pairs (_) A3,A7: 9.. / A3 = 9 => 13 pairs (_) / A7 = 9 => 0 pairs (X) H2,H6: 9.. / H2 = 9 => 15 pairs (_) / H6 = 9 => 15 pairs (_) * DURATION: 0:00:40.483701 START: 04:46:12.972391 END: 04:46:53.456092 2017-05-01 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A7,A9,B4,B6,B8,C3,C5,C6,D3,F1,F3) * 3.61..47.471.....6....7.31...9..2....5..8..4....5..7...12.4....6.......4.34..59.. * PAIR C3: 5,8 COL C C8: 5,8,7 # reduction candidate for 5,8 C8: 5,8 => CTR * 3.61.9475471.53.96...47631..49762..3257381649.635947...12.485376.5.371.4734.15968 C8: 7 # 12 pairs * PAIR F1: 8,9 BLK 2 D2: 8,9,2,3 # reduction candidate for 8,9 D2: 8,9 # 16 pairs F2: 8,9,3 # reduction candidate for 8,9 F2: 8,9 # 15 pairs * PAIR F1: 8,9 ROW 1 B1: 8,9,2 # reduction candidate for 8,9 B1: 8,9 # 16 pairs I1: 8,9,2,5 # reduction candidate for 8,9 I1: 8,9 # 15 pairs * PAIR F1: 8,9 COL F F7: 8,9,3,6,7 # reduction candidate for 8,9 F7: 8,9 # 14 pairs F8: 8,9,1,3,7 # reduction candidate for 8,9 F8: 8,9 # 16 pairs * PAIR D3: 4,6 COL D D4: 4,6,3,7 # reduction candidate for 4,6 D4: 4,6 # 16 pairs D4: 3,7 # 9 pairs * PAIR F3: 4,6 COL F F6: 4,6,1,3,9 # reduction candidate for 4,6 F6: 1,3,9 => CTR * 3.61..47.471.....69.567431.7694.2....53786.49.485..76.5129476..697.....48342.59.. F6: 4,6 # 13 pairs * PAIR B4: 4,6 ROW 4 D4: 4,6,3,7 # reduction candidate for 4,6 D4: 4,6 # 16 pairs D4: 3,7 # 9 pairs * PAIR C5: 3,7 ROW 5 D5: 3,7,6,9 # reduction candidate for 3,7 D5: 3,7 # 14 pairs F5: 3,7,1,6,9 # reduction candidate for 3,7 F5: 3,7 # 15 pairs * PAIR B6: 4,6 ROW 6 F6: 4,6,1,3,9 # reduction candidate for 4,6 F6: 1,3,9 => CTR * 3.61..47.471.....69.567431.7694.2....53786.49.485..76.5129476..697.....48342.59.. F6: 4,6 # 13 pairs * PAIR C6: 3,8 ROW 6 H6: 3,8,2,6,9 # reduction candidate for 3,8 H6: 3,8 # 17 pairs I6: 3,8,1,2,9 # reduction candidate for 3,8 I6: 3,8 # 14 pairs * PAIR B8: 8,9 ROW 8 D8: 8,9,2,3,7 # reduction candidate for 8,9 D8: 8,9 # 14 pairs F8: 8,9,1,3,7 # reduction candidate for 8,9 F8: 8,9 # 16 pairs * PAIR B8: 8,9 COL B B1: 8,9,2 # reduction candidate for 8,9 B1: 8,9 # 16 pairs B3: 8,9,2 # reduction candidate for 8,9 B3: 8,9 # 15 pairs * PAIR A9: 7,8 BLK 7 C8: 7,8,5 # reduction candidate for 7,8 C8: 5 => CTR * 326159478471....96598476312.497.2...257.81649.6359472.912.4...76859.7234734..59.1 C8: 7,8 # 13 pairs * PAIR A9: 7,8 ROW 9 D9: 7,8,2,6 # reduction candidate for 7,8 D9: 7,8 # 15 pairs I9: 7,8,1,2 # reduction candidate for 7,8 I9: 7,8 # 22 pairs * PAIR A9: 7,8 COL A A4: 7,8,1 # reduction candidate for 7,8 A4: 7,8 # 15 pairs A4: 1 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0075-base-pr-000.dot * REASONING * DIS # C8: 5,8 => CTR => C8: 7 * DIS # F6: 1,3,9 => CTR => F6: 4,6 * DIS # F6: 1,3,9 => CTR => F6: 4,6 * DIS # C8: 5 => CTR => C8: 7,8 * CNT 4 HDP CHAINS / 30 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A7,A9,B4,B6,B8,C3,C5,C6,D3,F1,F3) * 3.61..47.471.....6....7.31...9..2....5..8..4....5..7...12.4....6.......4.34..59.. * PAIR C3: 5,8 COL C C8: 5,8,7 # reduction candidate for 5,8 C8: 5,8 => CTR * 3.61.9475471.53.96...47631..49762..3257381649.635947...12.485376.5.371.4734.15968 * PAIR RESTART * PAIR F1: 8,9 BLK 2 D2: 8,9,2,3 # reduction candidate for 8,9 D2: 8,9 # 21 pairs F2: 8,9,3 # reduction candidate for 8,9 F2: 8,9 # 17 pairs * PAIR F1: 8,9 ROW 1 I1: 8,9,2,5 # reduction candidate for 8,9 I1: 2,5 # 14 pairs I1: 8,9 # 13 pairs * PAIR F1: 8,9 COL F F7: 8,9,3,6,7 # reduction candidate for 8,9 F7: 8,9 # 22 pairs F7: 3,6,7 # 13 pairs * PAIR D3: 4,6 COL D D4: 4,6,3,7 # reduction candidate for 4,6 D4: 4,6 # 16 pairs D4: 3,7 # 9 pairs * PAIR F3: 4,6 COL F F6: 4,6,1,3,9 # reduction candidate for 4,6 F6: 1,3,9 => CTR * 3.61..47.471.....69.567431.7694.2....53786.49.485..76.5129476..697.....48342.59.. * PAIR RESTART * PAIR B4: 4,6 ROW 4 D4: 4,6,3,7 # reduction candidate for 4,6 D4: 4,6 => CTR * 3.61..47.471...2.6925.7.3187.9..2185.53.8.64...85..7..512.4.86769721...4834.65921 * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A4,A6,B1,B3,D4,F1,G7,H9,I3) * 3.61..47.471.....69.547631..49..2....53.8..4..685.47..512.4....697.....4834..59.. * PAIR B1: 2,8 ROW 1 I1: 2,8,5,9 # reduction candidate for 2,8 I1: 2,8 => CTR * 3.615947.471...5969.547631.1497.2..5.53.8.24926859473151294...3697...154834.15927 * PAIR RESTART * PAIR F1: 8,9 BLK 2 D2: 8,9,2,3 # reduction candidate for 8,9 D2: 8,9 => SOLVED * 386129475471853296925476318749362581253781649168594732512947863697238154834615927 * DURATION: 0:00:17.943748 START: 04:47:16.479489 END: 04:47:34.423237 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0075-base-pr-001.dot * REASONING * DIS # C8: 5,8 => CTR => C8: 7 * DIS C8: 7 # F6: 1,3,9 => CTR => F6: 4,6 * DIS C8: 7 + F6: 4,6 # D4: 4,6 => CTR => D4: 3,7 * DIS C8: 7 + F6: 4,6 + D4: 3,7 # I1: 2,8 => CTR => I1: 5,9 * PRF C8: 7 + F6: 4,6 + D4: 3,7 + I1: 5,9 # D2: 8,9 => SOL * STA C8: 7 + F6: 4,6 + D4: 3,7 + I1: 5,9 + D2: 8,9 * CNT 5 HDP CHAINS / 14 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=75
Solution
position: 386129475471853296925476318749362581253781649168594732512947863697238154834615927 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:
* DIS # C8: 5,8 => CTR => C8: 7 * INC # C8: 7 => UNS * INC # D2: 8,9 => UNS * INC # F2: 8,9 => UNS * INC # B1: 8,9 => UNS * INC # I1: 8,9 => UNS * INC # F7: 8,9 => UNS * INC # F8: 8,9 => UNS * INC # D4: 4,6 => UNS * INC # D4: 3,7 => UNS * INC # F6: 4,6 => UNS * DIS # F6: 1,3,9 => CTR => F6: 4,6 * INC # D4: 4,6 => UNS * INC # D4: 3,7 => UNS * INC # D5: 3,7 => UNS * INC # F5: 3,7 => UNS * INC # F6: 4,6 => UNS * DIS # F6: 1,3,9 => CTR => F6: 4,6 * INC # H6: 3,8 => UNS * INC # I6: 3,8 => UNS * INC # D8: 8,9 => UNS * INC # F8: 8,9 => UNS * INC # B1: 8,9 => UNS * INC # B3: 8,9 => UNS * INC # C8: 7,8 => UNS * DIS # C8: 5 => CTR => C8: 7,8 * INC # D9: 7,8 => UNS * INC # I9: 7,8 => UNS * INC # A4: 7,8 => UNS * INC # A4: 1 => UNS * CNT 30 HDP CHAINS / 30 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C8: 5,8 => CTR => C8: 7 * INC C8: 7 # D2: 8,9 => UNS * INC C8: 7 # F2: 8,9 => UNS * INC C8: 7 # I1: 8,9 => UNS * INC C8: 7 # I1: 2,5 => UNS * INC C8: 7 # F7: 8,9 => UNS * INC C8: 7 # F7: 3,6,7 => UNS * INC C8: 7 # D4: 4,6 => UNS * INC C8: 7 # D4: 3,7 => UNS * INC C8: 7 # F6: 4,6 => UNS * DIS C8: 7 # F6: 1,3,9 => CTR => F6: 4,6 * DIS C8: 7 + F6: 4,6 # D4: 4,6 => CTR => D4: 3,7 * DIS C8: 7 + F6: 4,6 + D4: 3,7 # I1: 2,8 => CTR => I1: 5,9 * PRF C8: 7 + F6: 4,6 + D4: 3,7 + I1: 5,9 # D2: 8,9 => SOL * STA C8: 7 + F6: 4,6 + D4: 3,7 + I1: 5,9 + D2: 8,9 * CNT 14 HDP CHAINS / 14 HYP OPENED