Analysis of zz-www.sudokuwiki.org-0110-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=110
level: medium
position: 4..3.......8.4.7...3......1.5...1.968...9....96.5...1.7......4...1.8.5.......3..2 initial
Autosolve
position: 47.31....1.8.4.7...3....4.1.5...1.9681..9....96.5...1.7......4...1.8.5.......3..2 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 2,9 => CTR => C1: 5,6 * DIS # B7: 2,9 => CTR => B7: 8 * DIS # F1: 6,9 => CTR => F1: 2,5,8 * DIS # G9: 6,9 => CTR => G9: 1 * DIS # C4: 2,3 => CTR => C4: 4,7 * DIS # C6: 2,3 => CTR => C6: 4,7 * DIS # G4: 2,3 => CTR => G4: 8 * DIS # G4: 2,3 => CTR => G4: 8 * DIS # C5: 4,7 => CTR => C5: 2,3 * DIS # F6: 4,7 => CTR => F6: 2,8 * DIS # C7: 5,6 => CTR => C7: 2,3,9 * DIS # C9: 5,6 => CTR => C9: 9 * DIS # E9: 7 => CTR => E9: 5,6 * CNT 13 HDP CHAINS / 44 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 2,9 => CTR => C1: 5,6 * DIS C1: 5,6 # B7: 2,9 => CTR => B7: 8 * DIS C1: 5,6 + B7: 8 # B8: 4 => CTR => B8: 2,9 * PRF C1: 5,6 + B7: 8 + B8: 2,9 # C3: 5,6 => SOL * STA C1: 5,6 + B7: 8 + B8: 2,9 + C3: 5,6 * CNT 4 HDP CHAINS / 12 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 4..3.......8.4.7...3......1.5...1.968...9....96.5...1.7......4...1.8.5.......3..2 | initial |
| 47.31....1.8.4.7...3....4.1.5...1.9681..9....96.5...1.7......4...1.8.5.......3..2 | autosolve |
| 476315928198246735235879461357421896812697354964538217783152649621984573549763182 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) B2: 2,9 G1: 6,9 A4: 2,3 G5: 2,3 H5: 5,7 I6: 4,7 A9: 5,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D7,D9: 1.. / D7 = 1 => 8 pairs (_) / D9 = 1 => 0 pairs (X) G7,G9: 1.. / G7 = 1 => 0 pairs (X) / G9 = 1 => 8 pairs (_) D7,G7: 1.. / D7 = 1 => 8 pairs (_) / G7 = 1 => 0 pairs (X) D9,G9: 1.. / D9 = 1 => 0 pairs (X) / G9 = 1 => 8 pairs (_) H2,I2: 3.. / H2 = 3 => 9 pairs (_) / I2 = 3 => 13 pairs (_) E4,E6: 3.. / E4 = 3 => 0 pairs (X) / E6 = 3 => 9 pairs (_) C7,A8: 3.. / C7 = 3 => 11 pairs (_) / A8 = 3 => 0 pairs (X) C5,G5: 3.. / C5 = 3 => 0 pairs (X) / G5 = 3 => 8 pairs (_) C7,I7: 3.. / C7 = 3 => 11 pairs (_) / I7 = 3 => 0 pairs (X) A4,A8: 3.. / A4 = 3 => 11 pairs (_) / A8 = 3 => 0 pairs (X) H2,H8: 3.. / H2 = 3 => 9 pairs (_) / H8 = 3 => 13 pairs (_) I5,I6: 4.. / I5 = 4 => 9 pairs (_) / I6 = 4 => 7 pairs (_) B8,B9: 4.. / B8 = 4 => 12 pairs (_) / B9 = 4 => 9 pairs (_) C4,D4: 4.. / C4 = 4 => 8 pairs (_) / D4 = 4 => 10 pairs (_) B9,D9: 4.. / B9 = 4 => 9 pairs (_) / D9 = 4 => 12 pairs (_) H5,I5: 5.. / H5 = 5 => 8 pairs (_) / I5 = 5 => 9 pairs (_) A3,A9: 5.. / A3 = 5 => 11 pairs (_) / A9 = 5 => 9 pairs (_) D5,F5: 6.. / D5 = 6 => 10 pairs (_) / F5 = 6 => 7 pairs (_) D4,F6: 8.. / D4 = 8 => 0 pairs (X) / F6 = 8 => 8 pairs (_) G4,G6: 8.. / G4 = 8 => 8 pairs (_) / G6 = 8 => 0 pairs (X) B7,B9: 8.. / B7 = 8 => 9 pairs (_) / B9 = 8 => 0 pairs (X) I7,H9: 8.. / I7 = 8 => 0 pairs (X) / H9 = 8 => 9 pairs (_) D4,G4: 8.. / D4 = 8 => 0 pairs (X) / G4 = 8 => 8 pairs (_) F6,G6: 8.. / F6 = 8 => 8 pairs (_) / G6 = 8 => 0 pairs (X) B7,I7: 8.. / B7 = 8 => 9 pairs (_) / I7 = 8 => 0 pairs (X) B9,H9: 8.. / B9 = 8 => 0 pairs (X) / H9 = 8 => 9 pairs (_) D3,D4: 8.. / D3 = 8 => 8 pairs (_) / D4 = 8 => 0 pairs (X) I1,I7: 8.. / I1 = 8 => 9 pairs (_) / I7 = 8 => 0 pairs (X) * DURATION: 0:00:39.371081 START: 05:28:18.395074 END: 05:28:57.766155 2017-05-01 * CP COUNT: (28) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A9,B2,G1,G5,H5,I6) * 47.31....1.8.4.7...3....4.1.5...1.9681..9....96.5...1.7......4...1.8.5.......3..2 * PAIR B2: 2,9 BLK 1 C1: 2,9,5,6 # reduction candidate for 2,9 C1: 2,9 => CTR * 47231.658198.4.7...3....4.1.5...1.9681..9....96.5...1.7..1...433.1.8.56...9..3182 C1: 5,6 # 8 pairs C3: 2,9,5,6 # reduction candidate for 2,9 C3: 2,9 # 11 pairs * PAIR B2: 2,9 ROW 2 D2: 2,9,6 # reduction candidate for 2,9 D2: 2,9 # 10 pairs F2: 2,9,5,6 # reduction candidate for 2,9 F2: 2,9 # 11 pairs * PAIR B2: 2,9 COL B B7: 2,9,8 # reduction candidate for 2,9 B7: 2,9 => CTR * 47.31..8.198.4.72323.8.94.1354721896812.9.3..9675382147231...48641.8.5..5894.31.2 B7: 8 # 9 pairs B8: 2,9,4 # reduction candidate for 2,9 B8: 2,9 # 9 pairs * PAIR G1: 6,9 ROW 1 C1: 6,9,2,5 # reduction candidate for 6,9 C1: 6,9 # 9 pairs F1: 6,9,2,5,8 # reduction candidate for 6,9 F1: 6,9 => CTR * 47.3169..198245763236.7.45135..2189681.69.37596.5382147.315.64.6.1.875395.94631.2 F1: 2,5,8 # 7 pairs * PAIR G1: 6,9 COL G G7: 6,9,1 # reduction candidate for 6,9 G7: 6,9 # 8 pairs G9: 6,9,1 # reduction candidate for 6,9 G9: 6,9 => CTR * 47.3196.81286457...398.74.1.5...189681..9....96.5.8.1.78....14..91.8.5...4.173982 G9: 1 # 8 pairs * PAIR A4: 2,3 BLK 4 C4: 2,3,4,7 # reduction candidate for 2,3 C4: 2,3 => CTR * 47.31...81.8.4.7...398.74.1.5.47189681..9.3..96.53821.78.1...4..91.845...4.7.3182 C4: 4,7 # 8 pairs C5: 2,3,4,7 # reduction candidate for 2,3 C5: 2,3 # 12 pairs C6: 2,3,4,7 # reduction candidate for 2,3 C6: 2,3 => CTR * 47.318.2.198.4.763236.5.4813548712968176923..9625348177.31...486.1.8.5..589463172 C6: 4,7 # 10 pairs * PAIR A4: 2,3 ROW 4 E4: 2,3,7 # reduction candidate for 2,3 E4: 2,3 # 11 pairs G4: 2,3,8 # reduction candidate for 2,3 G4: 2,3 => CTR * 47.3189.5198.457.323....481.54871.9681..9..5.96.53.81.7231...48641.8.539589463172 G4: 8 # 8 pairs * PAIR A4: 2,3 COL A A8: 2,3,6 # reduction candidate for 2,3 A8: 6 # 17 pairs A8: 2,3 # 9 pairs * PAIR G5: 2,3 BLK 6 G4: 2,3,8 # reduction candidate for 2,3 G4: 2,3 => CTR * 47.3189.5198.457.323....481.54871.9681..9..5.96.53.81.7231...48641.8.539589463172 G4: 8 # 8 pairs G6: 2,3,8 # reduction candidate for 2,3 G6: 2,3 # 8 pairs * PAIR G5: 2,3 ROW 5 C5: 2,3,4,7 # reduction candidate for 2,3 C5: 4,7 => CTR * 47.318.2.198.4.7..23....481354871296817.9.3549625348177231...48641.82539589463172 C5: 2,3 # 12 pairs * PAIR H5: 5,7 BLK 6 I5: 5,7,4 # reduction candidate for 5,7 I5: 4 # 9 pairs I5: 5,7 # 7 pairs * PAIR I6: 4,7 BLK 6 I5: 4,7,5 # reduction candidate for 4,7 I5: 5 # 9 pairs I5: 4,7 # 8 pairs * PAIR I6: 4,7 ROW 6 C6: 4,7,2,3 # reduction candidate for 4,7 C6: 4,7 # 10 pairs F6: 4,7,2,8 # reduction candidate for 4,7 F6: 4,7 => CTR * 47.31.9..198.4.7..23..5.4.1354871296817.9.3549625348177.3125649621489573549763182 F6: 2,8 # 8 pairs * PAIR A9: 5,6 BLK 7 C7: 5,6,2,3,9 # reduction candidate for 5,6 C7: 5,6 => CTR * 47.31.9.8198.4.735.3....4.125...1.9681..9..5.96.5...1.78.....43321.8.579.49..3.82 C7: 2,3,9 # 8 pairs C9: 5,6,9 # reduction candidate for 5,6 C9: 5,6 => CTR * 47.3129.8128.4.7...39867421.5...189681..9....96.5.8.1.78.1596433.128657.....73182 C9: 9 # 13 pairs * PAIR A9: 5,6 ROW 9 E9: 5,6,7 # reduction candidate for 5,6 E9: 7 => CTR * 47.3129.8128.4.7...39867421.5...189681..9....96.5.8.1.78.1596433.128657.....73182 E9: 5,6 # 16 pairs * PAIR A9: 5,6 COL A A3: 5,6,2 # reduction candidate for 5,6 A3: 2 # 17 pairs A3: 5,6 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0110-base-pr-000.dot * REASONING * DIS # C1: 2,9 => CTR => C1: 5,6 * DIS # B7: 2,9 => CTR => B7: 8 * DIS # F1: 6,9 => CTR => F1: 2,5,8 * DIS # G9: 6,9 => CTR => G9: 1 * DIS # C4: 2,3 => CTR => C4: 4,7 * DIS # C6: 2,3 => CTR => C6: 4,7 * DIS # G4: 2,3 => CTR => G4: 8 * DIS # G4: 2,3 => CTR => G4: 8 * DIS # C5: 4,7 => CTR => C5: 2,3 * DIS # F6: 4,7 => CTR => F6: 2,8 * DIS # C7: 5,6 => CTR => C7: 2,3,9 * DIS # C9: 5,6 => CTR => C9: 9 * DIS # E9: 7 => CTR => E9: 5,6 * CNT 13 HDP CHAINS / 44 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A9,B2,G1,G5,H5,I6) * 47.31....1.8.4.7...3....4.1.5...1.9681..9....96.5...1.7......4...1.8.5.......3..2 * PAIR B2: 2,9 BLK 1 C1: 2,9,5,6 # reduction candidate for 2,9 C1: 2,9 => CTR * 47231.658198.4.7...3....4.1.5...1.9681..9....96.5...1.7..1...433.1.8.56...9..3182 C3: 2,9,5,6 # reduction candidate for 2,9 C3: 2,9 # 11 pairs * RESTART * PAIR B2: 2,9 BLK 1 C3: 2,9,5,6 # reduction candidate for 2,9 C3: 5,6 # 17 pairs C3: 2,9 # 11 pairs * PAIR B2: 2,9 ROW 2 D2: 2,9,6 # reduction candidate for 2,9 D2: 2,9 # 11 pairs F2: 2,9,5,6 # reduction candidate for 2,9 F2: 2,9 # 12 pairs * PAIR B2: 2,9 COL B B7: 2,9,8 # reduction candidate for 2,9 B7: 2,9 => CTR * 47.31..8.198.4.72323.8.94.1354721896812.9.3..9675382147231...48641.8.5..5894.31.2 B8: 2,9,4 # reduction candidate for 2,9 B8: 2,9 # 10 pairs * RESTART * PAIR B2: 2,9 COL B B8: 2,9,4 # reduction candidate for 2,9 B8: 4 => CTR * 47.3129.812894.7...398.74212547318968136942..9675283147821..64334128657..9.473182 * PAIR RESTART * PAIR B2: 2,9 BLK 1 C3: 2,9,5,6 # reduction candidate for 2,9 C3: 5,6 => SOLVED * 476315928198246735235879461357421896812697354964538217783152649621984573549763182 * DURATION: 0:00:11.445944 START: 05:29:32.469681 END: 05:29:43.915625 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0110-base-pr-001.dot * REASONING * DIS # C1: 2,9 => CTR => C1: 5,6 * DIS C1: 5,6 # B7: 2,9 => CTR => B7: 8 * DIS C1: 5,6 + B7: 8 # B8: 4 => CTR => B8: 2,9 * PRF C1: 5,6 + B7: 8 + B8: 2,9 # C3: 5,6 => SOL * STA C1: 5,6 + B7: 8 + B8: 2,9 + C3: 5,6 * CNT 4 HDP CHAINS / 12 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=110
Solution
position: 476315928198246735235879461357421896812697354964538217783152649621984573549763182 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 # C1: 2,9 => CTR => C1: 5,6 * INC # C1: 5,6 => UNS * INC # C3: 2,9 => UNS * INC # D2: 2,9 => UNS * INC # F2: 2,9 => UNS * DIS # B7: 2,9 => CTR => B7: 8 * INC # B7: 8 => UNS * INC # B8: 2,9 => UNS * INC # C1: 6,9 => UNS * DIS # F1: 6,9 => CTR => F1: 2,5,8 * INC # F1: 2,5,8 => UNS * INC # G7: 6,9 => UNS * DIS # G9: 6,9 => CTR => G9: 1 * INC # G9: 1 => UNS * DIS # C4: 2,3 => CTR => C4: 4,7 * INC # C4: 4,7 => UNS * INC # C5: 2,3 => UNS * DIS # C6: 2,3 => CTR => C6: 4,7 * INC # C6: 4,7 => UNS * INC # E4: 2,3 => UNS * DIS # G4: 2,3 => CTR => G4: 8 * INC # G4: 8 => UNS * INC # A8: 2,3 => UNS * INC # A8: 6 => UNS * DIS # G4: 2,3 => CTR => G4: 8 * INC # G4: 8 => UNS * INC # G6: 2,3 => UNS * INC # C5: 2,3 => UNS * DIS # C5: 4,7 => CTR => C5: 2,3 * INC # I5: 5,7 => UNS * INC # I5: 4 => UNS * INC # I5: 4,7 => UNS * INC # I5: 5 => UNS * INC # C6: 4,7 => UNS * DIS # F6: 4,7 => CTR => F6: 2,8 * INC # F6: 2,8 => UNS * DIS # C7: 5,6 => CTR => C7: 2,3,9 * INC # C7: 2,3,9 => UNS * DIS # C9: 5,6 => CTR => C9: 9 * INC # C9: 9 => UNS * INC # E9: 5,6 => UNS * DIS # E9: 7 => CTR => E9: 5,6 * INC # A3: 5,6 => UNS * INC # A3: 2 => UNS * CNT 44 HDP CHAINS / 44 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C1: 2,9 => CTR => C1: 5,6 * INC C1: 5,6 # C3: 2,9 => UNS * INC C1: 5,6 # C3: 2,9 => UNS * INC C1: 5,6 # C3: 5,6 => UNS * INC C1: 5,6 # D2: 2,9 => UNS * INC C1: 5,6 # F2: 2,9 => UNS * DIS C1: 5,6 # B7: 2,9 => CTR => B7: 8 * INC C1: 5,6 + B7: 8 # B8: 2,9 => UNS * INC C1: 5,6 + B7: 8 # B8: 2,9 => UNS * DIS C1: 5,6 + B7: 8 # B8: 4 => CTR => B8: 2,9 * INC C1: 5,6 + B7: 8 + B8: 2,9 # C3: 2,9 => UNS * PRF C1: 5,6 + B7: 8 + B8: 2,9 # C3: 5,6 => SOL * STA C1: 5,6 + B7: 8 + B8: 2,9 + C3: 5,6 * CNT 12 HDP CHAINS / 12 HYP OPENED