Analysis of zz-www.sudokuwiki.org-0093-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=93
level: medium
position: 8....25...9..6....2..9...7........69.3..4..1.42........6...5..8....7..4...86....1 initial
Autosolve
position: 8....259..9..6....2..9...7..8....46963..4..1.42...6....6...5..8....7..4...86....1 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D2: 1,3 => CTR => D2: 4,5,7,8 * DIS # E3: 1,3 => CTR => E3: 5,8 * DIS # E4: 1,3 => CTR => E4: 2,5 * DIS # C8: 1,5 => CTR => C8: 2,3 * DIS # G7: 2,3 => CTR => G7: 7,9 * DIS # G8: 2,3 => CTR => G8: 6,9 * CNT 6 HDP CHAINS / 35 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D2: 1,3 => CTR => D2: 4,5,7,8 * DIS D2: 4,5,7,8 # E3: 1,3 => CTR => E3: 5,8 * DIS D2: 4,5,7,8 + E3: 5,8 # E4: 1,3 => CTR => E4: 2,5 * DIS D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 # H6: 3,8 => CTR => H6: 5 * DIS D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 + H6: 5 # C7: 2,3 => CTR => C7: 4,7 * DIS D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 + H6: 5 + C7: 4,7 # E7: 2,3 => CTR => E7: 1,9 * DIS D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 + H6: 5 + C7: 4,7 + E7: 1,9 # D7: 1,4 => CTR => D7: 2,3 * DIS D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 + H6: 5 + C7: 4,7 + E7: 1,9 + D7: 2,3 # D1: 1 => CTR => D1: 4,7 * DIS D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 + H6: 5 + C7: 4,7 + E7: 1,9 + D7: 2,3 + D1: 4,7 # D4: 2,5 => CTR => D4: 3,7 * PRF D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 + H6: 5 + C7: 4,7 + E7: 1,9 + D7: 2,3 + D1: 4,7 + D4: 3,7 => SOL * STA D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 + H6: 5 + C7: 4,7 + E7: 1,9 + D7: 2,3 + D1: 4,7 + D4: 3,7 * CNT 10 HDP CHAINS / 29 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 8....25...9..6....2..9...7........69.3..4..1.42........6...5..8....7..4...86....1 | initial |
| 8....259..9..6....2..9...7..8....46963..4..1.42...6....6...5..8....7..4...86....1 | autosolve |
| 871432596593761284246958173185327469637549812429186357764215938912873645358694721 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) E1: 1,3 G5: 2,8 G6: 3,8 B8: 1,5 H7: 2,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G2,G3: 1.. / G2 = 1 => 5 pairs (_) / G3 = 1 => 8 pairs (_) D4,E4: 2.. / D4 = 2 => 5 pairs (_) / E4 = 2 => 19 pairs (_) G5,I5: 2.. / G5 = 2 => 7 pairs (_) / I5 = 2 => 14 pairs (_) C7,C8: 2.. / C7 = 2 => 17 pairs (_) / C8 = 2 => 5 pairs (_) C7,B9: 4.. / C7 = 4 => 6 pairs (_) / B9 = 4 => 12 pairs (_) D7,F9: 4.. / D7 = 4 => 12 pairs (_) / F9 = 4 => 6 pairs (_) C7,D7: 4.. / C7 = 4 => 6 pairs (_) / D7 = 4 => 12 pairs (_) B9,F9: 4.. / B9 = 4 => 12 pairs (_) / F9 = 4 => 6 pairs (_) D2,E3: 5.. / D2 = 5 => 6 pairs (_) / E3 = 5 => 0 pairs (*) I8,H9: 5.. / I8 = 5 => 14 pairs (_) / H9 = 5 => 10 pairs (_) H6,H9: 5.. / H6 = 5 => 14 pairs (_) / H9 = 5 => 10 pairs (_) C1,C3: 6.. / C1 = 6 => 6 pairs (_) / C3 = 6 => 8 pairs (_) G8,I8: 6.. / G8 = 6 => 7 pairs (_) / I8 = 6 => 11 pairs (_) C1,I1: 6.. / C1 = 6 => 6 pairs (_) / I1 = 6 => 8 pairs (_) G3,G8: 6.. / G3 = 6 => 11 pairs (_) / G8 = 6 => 7 pairs (_) I5,I6: 7.. / I5 = 7 => 0 pairs (X) / I6 = 7 => 6 pairs (_) G7,G9: 7.. / G7 = 7 => 5 pairs (_) / G9 = 7 => 6 pairs (_) B1,B9: 7.. / B1 = 7 => 6 pairs (_) / B9 = 7 => 6 pairs (_) D8,F8: 8.. / D8 = 8 => 8 pairs (_) / F8 = 8 => 8 pairs (_) E3,E6: 8.. / E3 = 8 => 6 pairs (_) / E6 = 8 => 0 pairs (*) H2,H6: 8.. / H2 = 8 => 6 pairs (_) / H6 = 8 => 14 pairs (_) C5,C6: 9.. / C5 = 9 => 0 pairs (X) / C6 = 9 => 8 pairs (_) F5,E6: 9.. / F5 = 9 => 8 pairs (_) / E6 = 9 => 0 pairs (X) C5,F5: 9.. / C5 = 9 => 0 pairs (X) / F5 = 9 => 8 pairs (_) C6,E6: 9.. / C6 = 9 => 8 pairs (_) / E6 = 9 => 0 pairs (X) * DURATION: 0:00:31.619321 START: 05:09:29.573488 END: 05:10:01.192809 2017-05-01 * CP COUNT: (25) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,E1,G5,G6,H7) * 8....259..9..6....2..9...7..8....46963..4..1.42...6....6...5..8....7..4...86....1 * PAIR E1: 1,3 BLK 2 D1: 1,3,4,7 # reduction candidate for 1,3 D1: 1,3 # 10 pairs D2: 1,3,4,5,7,8 # reduction candidate for 1,3 D2: 1,3 => CTR * 87.4.259..9..67.8.24.958.7..8....46963..49812429186357.64..5..8.12873.45.586.4..1 D2: 4,5,7,8 # 5 pairs F2: 1,3,4,7,8 # reduction candidate for 1,3 F2: 1,3 # 10 pairs E3: 1,3,5,8 # reduction candidate for 1,3 E3: 1,3 => CTR * 8....259..9.56..8.2..9.8.7..8..5.469635749812429186357.6...5..8.1.873.45..86....1 E3: 5,8 # 6 pairs F3: 1,3,4,8 # reduction candidate for 1,3 F3: 1,3 # 8 pairs * PAIR E1: 1,3 ROW 1 C1: 1,3,4,6,7 # reduction candidate for 1,3 C1: 1,3 # 11 pairs C1: 4,6,7 # 5 pairs * PAIR E1: 1,3 COL E E4: 1,3,2,5 # reduction candidate for 1,3 E4: 1,3 => CTR * 8...1259..9..6....21.9...7..8.237469637.49.1.4291.6..7.6...5..8.5.871.4...86...51 E4: 2,5 # 6 pairs E7: 1,3,2,9 # reduction candidate for 1,3 E7: 1,3 # 9 pairs * PAIR G5: 2,8 COL G G2: 2,8,1,3 # reduction candidate for 2,8 G2: 2,8 # 10 pairs G2: 1,3 # 6 pairs * PAIR G6: 3,8 BLK 6 H6: 3,8,5 # reduction candidate for 3,8 H6: 5 # 14 pairs H6: 3,8 # 10 pairs * PAIR G6: 3,8 COL G G2: 3,8,1,2 # reduction candidate for 3,8 G2: 3,8 # 12 pairs G3: 3,8,1,6 # reduction candidate for 3,8 G3: 3,8 # 14 pairs * PAIR B8: 1,5 BLK 7 A8: 1,5,3,9 # reduction candidate for 1,5 A8: 1,5 # 13 pairs C8: 1,5,2,3 # reduction candidate for 1,5 C8: 1,5 => CTR * 87.13259.19.56782.25.98417.58732146963..4.21.421.9638..62415.38.15.7..4..486...51 C8: 2,3 # 6 pairs * PAIR B8: 1,5 COL B B3: 1,5,4 # reduction candidate for 1,5 B3: 4 # 8 pairs B3: 1,5 # 8 pairs * PAIR H7: 2,3 BLK 9 G7: 2,3,7,9 # reduction candidate for 2,3 G7: 2,3 => CTR * 876..2594.9356.1822..98.673.8.2..46963..4.21.42...683..6.4.5328..2.7.946.4862.751 G7: 7,9 # 6 pairs G8: 2,3,6,9 # reduction candidate for 2,3 G8: 2,3 => CTR * 876312594394567182215984673587231469639.4.21.42...683..63495728952.7.346748623951 G8: 6,9 # 6 pairs I8: 2,3,5,6 # reduction candidate for 2,3 I8: 2,3 # 14 pairs G9: 2,3,7,9 # reduction candidate for 2,3 G9: 2,3 # 12 pairs H9: 2,3,5 # reduction candidate for 2,3 H9: 2,3 # 14 pairs * PAIR H7: 2,3 ROW 7 C7: 2,3,1,4,7 # reduction candidate for 2,3 C7: 2,3 # 16 pairs D7: 2,3,1,4 # reduction candidate for 2,3 D7: 2,3 # 9 pairs E7: 2,3,1,9 # reduction candidate for 2,3 E7: 2,3 # 8 pairs * PAIR H7: 2,3 COL H H2: 2,3,8 # reduction candidate for 2,3 H2: 2,3 # 14 pairs H2: 8 # 6 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0093-base-pr-000.dot * REASONING * DIS # D2: 1,3 => CTR => D2: 4,5,7,8 * DIS # E3: 1,3 => CTR => E3: 5,8 * DIS # E4: 1,3 => CTR => E4: 2,5 * DIS # C8: 1,5 => CTR => C8: 2,3 * DIS # G7: 2,3 => CTR => G7: 7,9 * DIS # G8: 2,3 => CTR => G8: 6,9 * CNT 6 HDP CHAINS / 35 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,E1,G5,G6,H7) * 8....259..9..6....2..9...7..8....46963..4..1.42...6....6...5..8....7..4...86....1 * PAIR E1: 1,3 BLK 2 D1: 1,3,4,7 # reduction candidate for 1,3 D1: 1,3 # 10 pairs D2: 1,3,4,5,7,8 # reduction candidate for 1,3 D2: 1,3 => CTR * 87.4.259..9..67.8.24.958.7..8....46963..49812429186357.64..5..8.12873.45.586.4..1 F2: 1,3,4,7,8 # reduction candidate for 1,3 F2: 1,3 # 10 pairs E3: 1,3,5,8 # reduction candidate for 1,3 E3: 1,3 => CTR * 8....259..9.56..8.2..9.8.7..8..5.469635749812429186357.6...5..8.1.873.45..86....1 F3: 1,3,4,8 # reduction candidate for 1,3 F3: 1,3 # 8 pairs * PAIR E1: 1,3 ROW 1 C1: 1,3,4,6,7 # reduction candidate for 1,3 C1: 1,3 # 12 pairs C1: 4,6,7 # 6 pairs * PAIR E1: 1,3 COL E E4: 1,3,2,5 # reduction candidate for 1,3 E4: 1,3 => CTR * 8...1259..9..6....21.9...7..8.237469637.49.1.4291.6..7.6...5..8.5.871.4...86...51 E7: 1,3,2,9 # reduction candidate for 1,3 E7: 1,3 # 9 pairs * RESTART * PAIR E1: 1,3 COL E E7: 1,3,2,9 # reduction candidate for 1,3 E7: 1,3 # 9 pairs E7: 2,9 # 8 pairs * PAIR RESTART * PAIR E1: 1,3 BLK 2 D1: 1,3,4,7 # reduction candidate for 1,3 D1: 1,3 # 11 pairs F2: 1,3,4,7,8 # reduction candidate for 1,3 F2: 1,3 # 11 pairs F3: 1,3,4,8 # reduction candidate for 1,3 F3: 1,3 # 9 pairs * PAIR E1: 1,3 ROW 1 C1: 1,3,4,6,7 # reduction candidate for 1,3 C1: 1,3 # 13 pairs C1: 4,6,7 # 7 pairs * PAIR E1: 1,3 COL E E7: 1,3,2,9 # reduction candidate for 1,3 E7: 1,3 # 9 pairs E7: 2,9 # 8 pairs * PAIR G5: 2,8 COL G G2: 2,8,1,3 # reduction candidate for 2,8 G2: 2,8 # 12 pairs G2: 1,3 # 8 pairs * PAIR G6: 3,8 BLK 6 H6: 3,8,5 # reduction candidate for 3,8 H6: 3,8 => CTR * 841732596793561...25698..7.18725346963..4.21.42...6....6...5..851..7964...8624.51 * PAIR H7: 2,3 ROW 7 C7: 2,3,4,7 # reduction candidate for 2,3 C7: 2,3 => CTR * 87..3259..9..6..8.25.98..7..8..5.469635.49.1.42...6.5..6.415..8.1..7.645.486....1 D7: 2,3,1,4 # reduction candidate for 2,3 D7: 2,3 # 23 pairs E7: 2,3,1,9 # reduction candidate for 2,3 E7: 2,3 => CTR * 871..259..9..6..8.2..9...7..8.253469635.49.1.429.16.5..641.5..8912378645..8694721 * RESTART * PAIR H7: 2,3 ROW 7 D7: 2,3,1,4 # reduction candidate for 2,3 D7: 1,4 => CTR * 8...3259..9.567.8.25.98137..8.253469635.49.1.429.16853364195728912378645578624931 * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A7,A8,B1,B3,B9,D7,D8,E3,E4,E6,E9,F2,F3,G3,G5,G6,G7,G9,H7,H9,I1,I5,I6) * 8...3259..9..6..8.2..9...7..8....46963..4..1.42...6.5..64.15..8.12.7.645..86.4..1 * PAIR B1: 4,7 ROW 1 D1: 4,7,1 # reduction candidate for 4,7 D1: 1 => CTR * 8..13259..9.467.8.2..958.7..8..2146963..49.1.42...6.5..64.15..8.12.7.645..86.4..1 * PAIR RESTART * PAIR E4: 2,5 BLK 5 D4: 2,5,3,7 # reduction candidate for 2,5 D4: 2,5 => CTR * 8.1.32596.93.6..8.2.69...7.187..3469635.49.1.429186357.64.15..8912.7.645..86.4..1 D4: 3,7 => SOLVED * 871432596593761284246958173185327469637549812429186357764215938912873645358694721 * DURATION: 0:00:25.905179 START: 05:10:25.525080 END: 05:10:51.430259 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0093-base-pr-001.dot * REASONING * DIS # D2: 1,3 => CTR => D2: 4,5,7,8 * DIS D2: 4,5,7,8 # E3: 1,3 => CTR => E3: 5,8 * DIS D2: 4,5,7,8 + E3: 5,8 # E4: 1,3 => CTR => E4: 2,5 * DIS D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 # H6: 3,8 => CTR => H6: 5 * DIS D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 + H6: 5 # C7: 2,3 => CTR => C7: 4,7 * DIS D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 + H6: 5 + C7: 4,7 # E7: 2,3 => CTR => E7: 1,9 * DIS D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 + H6: 5 + C7: 4,7 + E7: 1,9 # D7: 1,4 => CTR => D7: 2,3 * DIS D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 + H6: 5 + C7: 4,7 + E7: 1,9 + D7: 2,3 # D1: 1 => CTR => D1: 4,7 * DIS D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 + H6: 5 + C7: 4,7 + E7: 1,9 + D7: 2,3 + D1: 4,7 # D4: 2,5 => CTR => D4: 3,7 * PRF D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 + H6: 5 + C7: 4,7 + E7: 1,9 + D7: 2,3 + D1: 4,7 + D4: 3,7 => SOL * STA D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 + H6: 5 + C7: 4,7 + E7: 1,9 + D7: 2,3 + D1: 4,7 + D4: 3,7 * CNT 10 HDP CHAINS / 29 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=93
Solution
position: 871432596593761284246958173185327469637549812429186357764215938912873645358694721 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 # D1: 1,3 => UNS * DIS # D2: 1,3 => CTR => D2: 4,5,7,8 * INC # D2: 4,5,7,8 => UNS * INC # F2: 1,3 => UNS * DIS # E3: 1,3 => CTR => E3: 5,8 * INC # E3: 5,8 => UNS * INC # F3: 1,3 => UNS * INC # C1: 1,3 => UNS * INC # C1: 4,6,7 => UNS * DIS # E4: 1,3 => CTR => E4: 2,5 * INC # E4: 2,5 => UNS * INC # E7: 1,3 => UNS * INC # G2: 2,8 => UNS * INC # G2: 1,3 => UNS * INC # H6: 3,8 => UNS * INC # H6: 5 => UNS * INC # G2: 3,8 => UNS * INC # G3: 3,8 => UNS * INC # A8: 1,5 => UNS * DIS # C8: 1,5 => CTR => C8: 2,3 * INC # C8: 2,3 => UNS * INC # B3: 1,5 => UNS * INC # B3: 4 => UNS * DIS # G7: 2,3 => CTR => G7: 7,9 * INC # G7: 7,9 => UNS * DIS # G8: 2,3 => CTR => G8: 6,9 * INC # G8: 6,9 => UNS * INC # I8: 2,3 => UNS * INC # G9: 2,3 => UNS * INC # H9: 2,3 => UNS * INC # C7: 2,3 => UNS * INC # D7: 2,3 => UNS * INC # E7: 2,3 => UNS * INC # H2: 2,3 => UNS * INC # H2: 8 => UNS * CNT 35 HDP CHAINS / 35 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D1: 1,3 => UNS * DIS # D2: 1,3 => CTR => D2: 4,5,7,8 * INC D2: 4,5,7,8 # F2: 1,3 => UNS * DIS D2: 4,5,7,8 # E3: 1,3 => CTR => E3: 5,8 * INC D2: 4,5,7,8 + E3: 5,8 # F3: 1,3 => UNS * INC D2: 4,5,7,8 + E3: 5,8 # C1: 1,3 => UNS * INC D2: 4,5,7,8 + E3: 5,8 # C1: 4,6,7 => UNS * DIS D2: 4,5,7,8 + E3: 5,8 # E4: 1,3 => CTR => E4: 2,5 * INC D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 # E7: 1,3 => UNS * INC D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 # E7: 1,3 => UNS * INC D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 # E7: 2,9 => UNS * INC D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 # D1: 1,3 => UNS * INC D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 # F2: 1,3 => UNS * INC D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 # F3: 1,3 => UNS * INC D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 # C1: 1,3 => UNS * INC D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 # C1: 4,6,7 => UNS * INC D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 # E7: 1,3 => UNS * INC D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 # E7: 2,9 => UNS * INC D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 # G2: 2,8 => UNS * INC D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 # G2: 1,3 => UNS * DIS D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 # H6: 3,8 => CTR => H6: 5 * DIS D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 + H6: 5 # C7: 2,3 => CTR => C7: 4,7 * INC D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 + H6: 5 + C7: 4,7 # D7: 2,3 => UNS * DIS D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 + H6: 5 + C7: 4,7 # E7: 2,3 => CTR => E7: 1,9 * INC D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 + H6: 5 + C7: 4,7 + E7: 1,9 # D7: 2,3 => UNS * DIS D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 + H6: 5 + C7: 4,7 + E7: 1,9 # D7: 1,4 => CTR => D7: 2,3 * INC D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 + H6: 5 + C7: 4,7 + E7: 1,9 + D7: 2,3 # D1: 4,7 => UNS * DIS D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 + H6: 5 + C7: 4,7 + E7: 1,9 + D7: 2,3 # D1: 1 => CTR => D1: 4,7 * DIS D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 + H6: 5 + C7: 4,7 + E7: 1,9 + D7: 2,3 + D1: 4,7 # D4: 2,5 => CTR => D4: 3,7 * PRF D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 + H6: 5 + C7: 4,7 + E7: 1,9 + D7: 2,3 + D1: 4,7 + D4: 3,7 => SOL * STA D2: 4,5,7,8 + E3: 5,8 + E4: 2,5 + H6: 5 + C7: 4,7 + E7: 1,9 + D7: 2,3 + D1: 4,7 + D4: 3,7 * CNT 30 HDP CHAINS / 29 HYP OPENED