Analysis of zz-www.sudokuwiki.org-0010-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=10
level: medium
position: ..1.7.......8..4..8.......31.3.2..8...45.37...5..1.3.22.......9..6..4.......9.1.. initial
Autosolve
position: ..1.7.......8..4..8...4...31.3.2..8..245837...58.1.3.22.......9..6..4.......9.1.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A2: 6,7 => CTR => A2: 3,5 * DIS # B4: 6,7 => CTR => B4: 9 * DIS # A6: 6,9 => CTR => A6: 7 * DIS # H5: 1 => CTR => H5: 6,9 * DIS # H5: 1,6 => CTR => H5: 9 * DIS # F7: 5,7 => CTR => F7: 1,6,8 * DIS # H7: 5,7 => CTR => H7: 3,4,6 * DIS # B8: 3,9 => CTR => B8: 1,8 * PRF # B7: 3,4 => SOL * DIS # B9: 3,4 => CTR => B9: 8 * DIS # H9: 3,4 => CTR => H9: 2,5,6,7 * CNT 11 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:
* DIS # A2: 6,7 => CTR => A2: 3,5 * DIS A2: 3,5 # H5: 1 => CTR => H5: 6,9 * DIS A2: 3,5 + H5: 6,9 # F7: 5,7 => CTR => F7: 1,6,8 * DIS A2: 3,5 + H5: 6,9 + F7: 1,6,8 # H7: 5,7 => CTR => H7: 3,4,6 * DIS A2: 3,5 + H5: 6,9 + F7: 1,6,8 + H7: 3,4,6 # B8: 3,9 => CTR => B8: 1,8 * PRF A2: 3,5 + H5: 6,9 + F7: 1,6,8 + H7: 3,4,6 + B8: 1,8 # B7: 3,4 => SOL * STA A2: 3,5 + H5: 6,9 + F7: 1,6,8 + H7: 3,4,6 + B8: 1,8 + B7: 3,4 * CNT 6 HDP CHAINS / 18 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..1.7.......8..4..8.......31.3.2..8...45.37...5..1.3.22.......9..6..4.......9.1.. | initial |
| ..1.7.......8..4..8...4...31.3.2..8..245837...58.1.3.22.......9..6..4.......9.1.. | autosolve |
| 431279856569831427872645913193427685624583791758916342247168539916354278385792164 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) C2: 2,9 B3: 6,7 C3: 2,9 A5: 6,9 I5: 1,6 C7: 5,7 A8: 3,9 A9: 3,4 C9: 5,7 E8: 3,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H5,I5: 1.. / H5 = 1 => 0 pairs (X) / I5 = 1 => 10 pairs (_) B7,B8: 1.. / B7 = 1 => 19 pairs (_) / B8 = 1 => 17 pairs (_) B8,D8: 1.. / B8 = 1 => 17 pairs (_) / D8 = 1 => 19 pairs (_) I2,I5: 1.. / I2 = 1 => 0 pairs (X) / I5 = 1 => 10 pairs (_) C2,C3: 2.. / C2 = 2 => 8 pairs (_) / C3 = 2 => 8 pairs (_) D1,E2: 3.. / D1 = 3 => 12 pairs (_) / E2 = 3 => 18 pairs (_) A1,B1: 4.. / A1 = 4 => 16 pairs (_) / B1 = 4 => 13 pairs (_) D4,D6: 4.. / D4 = 4 => 0 pairs (*) / D6 = 4 => 0 pairs (X) I4,H6: 4.. / I4 = 4 => 13 pairs (_) / H6 = 4 => 0 pairs (*) D4,I4: 4.. / D4 = 4 => 0 pairs (*) / I4 = 4 => 0 pairs (X) D6,H6: 4.. / D6 = 4 => 13 pairs (_) / H6 = 4 => 0 pairs (*) B7,H7: 4.. / B7 = 4 => 0 pairs (*) / H7 = 4 => 0 pairs (X) A1,A9: 4.. / A1 = 4 => 16 pairs (_) / A9 = 4 => 13 pairs (_) I4,I9: 4.. / I4 = 4 => 13 pairs (_) / I9 = 4 => 0 pairs (*) A1,A2: 5.. / A1 = 5 => 21 pairs (_) / A2 = 5 => 13 pairs (_) G4,I4: 5.. / G4 = 5 => 13 pairs (_) / I4 = 5 => 0 pairs (*) C7,C9: 5.. / C7 = 5 => 10 pairs (_) / C9 = 5 => 8 pairs (_) E2,E7: 6.. / E2 = 6 => 13 pairs (_) / E7 = 6 => 12 pairs (_) B4,A6: 7.. / B4 = 7 => 0 pairs (X) / A6 = 7 => 12 pairs (_) C7,C9: 7.. / C7 = 7 => 8 pairs (_) / C9 = 7 => 10 pairs (_) B3,H3: 7.. / B3 = 7 => 13 pairs (_) / H3 = 7 => 12 pairs (_) A2,A6: 7.. / A2 = 7 => 0 pairs (X) / A6 = 7 => 12 pairs (_) G1,I1: 8.. / G1 = 8 => 13 pairs (_) / I1 = 8 => 11 pairs (_) F7,F9: 8.. / F7 = 8 => 11 pairs (_) / F9 = 8 => 0 pairs (X) C2,C3: 9.. / C2 = 9 => 8 pairs (_) / C3 = 9 => 8 pairs (_) A8,B8: 9.. / A8 = 9 => 13 pairs (_) / B8 = 9 => 0 pairs (X) A5,H5: 9.. / A5 = 9 => 0 pairs (X) / H5 = 9 => 13 pairs (_) B4,B8: 9.. / B4 = 9 => 13 pairs (_) / B8 = 9 => 0 pairs (X) * DURATION: 0:00:44.616984 START: 03:32:24.475795 END: 03:33:09.092779 2017-05-01 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A8,A9,B3,C2,C3,C7,C9,E8,I5) * ..1.7.......8..4..8...4...31.3.2..8..245837...58.1.3.22.......9..6..4.......9.1.. * PAIR C2: 2,9 ROW 2 F2: 2,9,1,5,6 # reduction candidate for 2,9 F2: 2,9 # 11 pairs H2: 2,9,1,5,6,7 # reduction candidate for 2,9 H2: 2,9 # 13 pairs * PAIR B3: 6,7 BLK 1 A2: 6,7,3,5 # reduction candidate for 6,7 A2: 6,7 => CTR * 54137.....3.86.4..86..4..73173.2.584.245837...584173.221..38.49396154...48..9.13. A2: 3,5 # 13 pairs B2: 6,7,3 # reduction candidate for 6,7 B2: 6,7 # 15 pairs * PAIR B3: 6,7 ROW 3 H3: 6,7,1,2,5,9 # reduction candidate for 6,7 H3: 1,2,5,9 # 13 pairs H3: 6,7 # 11 pairs * PAIR B3: 6,7 COL B B4: 6,7,9 # reduction candidate for 6,7 B4: 6,7 => CTR * .4137.....3.86.4..8...4...31.3.2.584.245837...5841.3.2215738649396154...487.9.135 B4: 9 # 13 pairs * PAIR C3: 2,9 ROW 3 D3: 2,9,1,6 # reduction candidate for 2,9 D3: 2,9 # 12 pairs F3: 2,9,1,5,6 # reduction candidate for 2,9 F3: 2,9 # 14 pairs G3: 2,9,5,6 # reduction candidate for 2,9 G3: 2,9 # 12 pairs H3: 2,9,1,5,6,7 # reduction candidate for 2,9 H3: 2,9 # 18 pairs * PAIR A5: 6,9 BLK 4 B4: 6,9,7 # reduction candidate for 6,9 B4: 6,9 # 12 pairs A6: 6,9,7 # reduction candidate for 6,9 A6: 6,9 => CTR * 54137....73.8..4..86..41573173.2..85.245837...58.1.34221......939615482748..9.136 A6: 7 # 12 pairs * PAIR A5: 6,9 ROW 5 H5: 6,9,1 # reduction candidate for 6,9 H5: 1 => CTR * .4137...8.3.86.4.18...41.531.3.2.584924583716.5841.392215738649396154827487.9.135 H5: 6,9 # 10 pairs * PAIR I5: 1,6 BLK 6 H5: 1,6,9 # reduction candidate for 1,6 H5: 1,6 => CTR * .4137.....3.86.4..8...4...31.3.2.5849245837...5841.392215738649396154...487.9.135 H5: 9 # 13 pairs * PAIR I5: 1,6 COL I I2: 1,6,5,7 # reduction candidate for 1,6 I2: 1,6 # 13 pairs I2: 5,7 # 11 pairs * PAIR C7: 5,7 ROW 7 F7: 5,7,1,6,8 # reduction candidate for 5,7 F7: 5,7 => CTR * ..1.7..285.98.24168.2.4...31937265846245837917584193622.5..7.499.6.54.37..7.981.. F7: 1,6,8 # 10 pairs H7: 5,7,3,4,6 # reduction candidate for 5,7 H7: 5,7 => CTR * 4.137....53.86.4.787..4..63193.2.586624583791758.1.34224.1386.991675423838..9.1.4 H7: 3,4,6 # 10 pairs * PAIR A8: 3,9 BLK 7 B8: 3,9,1,8 # reduction candidate for 3,9 B8: 3,9 => CTR * .4137.......86.4..8...4...31.3.2.584.245837...5841.3.2215738649..6154...487.9.135 B8: 1,8 # 14 pairs * PAIR A9: 3,4 BLK 7 B7: 3,4,1,8 # reduction candidate for 3,4 B7: 3,4 => SOLVED * 431279856569831427872645913193427685624583791758916342247168539916354278385792164 B7: 1,8 # 16 pairs B9: 3,4,8 # reduction candidate for 3,4 B9: 3,4 => CTR * ..1.7......98.241.8.2.45.73193.2.5846245837917584193622.5..1.49916254837..76981.. B9: 8 # 11 pairs * PAIR A9: 3,4 ROW 9 H9: 3,4,2,5,6,7 # reduction candidate for 3,4 H9: 3,4 => CTR * ..137.......86.4..8...4...31.3.2.584.245837...5841.3.22....86.9..6..4....8..9.1.. H9: 2,5,6,7 # 10 pairs * PAIR A9: 3,4 COL A A1: 3,4,5,6 # reduction candidate for 3,4 A1: 5,6 # 15 pairs A1: 3,4 # 15 pairs * PAIR C9: 5,7 ROW 9 F9: 5,7,2,6,8 # reduction candidate for 5,7 F9: 5,7 # 13 pairs H9: 5,7,2,3,4,6 # reduction candidate for 5,7 H9: 5,7 # 11 pairs I9: 5,7,4,6,8 # reduction candidate for 5,7 I9: 5,7 # 14 pairs * PAIR E8: 3,5 BLK 8 E7: 3,5,6 # reduction candidate for 3,5 E7: 3,5 # 13 pairs E7: 6 # 12 pairs * PAIR E8: 3,5 ROW 8 H8: 3,5,2,7 # reduction candidate for 3,5 H8: 3,5 # 17 pairs H8: 2,7 # 11 pairs * PAIR E8: 3,5 COL E E2: 3,5,6 # reduction candidate for 3,5 E2: 6 # 13 pairs E2: 3,5 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0010-base-pr-000.dot * REASONING * DIS # A2: 6,7 => CTR => A2: 3,5 * DIS # B4: 6,7 => CTR => B4: 9 * DIS # A6: 6,9 => CTR => A6: 7 * DIS # H5: 1 => CTR => H5: 6,9 * DIS # H5: 1,6 => CTR => H5: 9 * DIS # F7: 5,7 => CTR => F7: 1,6,8 * DIS # H7: 5,7 => CTR => H7: 3,4,6 * DIS # B8: 3,9 => CTR => B8: 1,8 * PRF # B7: 3,4 => SOL * DIS # B9: 3,4 => CTR => B9: 8 * DIS # H9: 3,4 => CTR => H9: 2,5,6,7 * CNT 11 HDP CHAINS / 45 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A8,A9,B3,C2,C3,C7,C9,E8,I5) * ..1.7.......8..4..8...4...31.3.2..8..245837...58.1.3.22.......9..6..4.......9.1.. * PAIR C2: 2,9 ROW 2 F2: 2,9,1,5,6 # reduction candidate for 2,9 F2: 2,9 # 11 pairs H2: 2,9,1,5,6,7 # reduction candidate for 2,9 H2: 2,9 # 13 pairs * PAIR B3: 6,7 BLK 1 A2: 6,7,3,5 # reduction candidate for 6,7 A2: 6,7 => CTR * 54137.....3.86.4..86..4..73173.2.584.245837...584173.221..38.49396154...48..9.13. B2: 6,7,3 # reduction candidate for 6,7 B2: 6,7 # 15 pairs * RESTART * PAIR B3: 6,7 BLK 1 B2: 6,7,3 # reduction candidate for 6,7 B2: 3 # 17 pairs B2: 6,7 # 15 pairs * PAIR B3: 6,7 ROW 3 H3: 6,7,1,2,5,9 # reduction candidate for 6,7 H3: 6,7 # 14 pairs H3: 1,2,5,9 # 14 pairs * PAIR C3: 2,9 ROW 3 D3: 2,9,1,6 # reduction candidate for 2,9 D3: 2,9 # 15 pairs F3: 2,9,1,5,6 # reduction candidate for 2,9 F3: 2,9 # 17 pairs G3: 2,9,5,6 # reduction candidate for 2,9 G3: 2,9 # 15 pairs H3: 2,9,1,5,6,7 # reduction candidate for 2,9 H3: 2,9 # 19 pairs * PAIR A5: 6,9 ROW 5 H5: 6,9,1 # reduction candidate for 6,9 H5: 1 => CTR * 6413759..53.86.4.187..41..3163.2..8492458371675841639221..38.49396154...48..9.13. * PAIR RESTART * PAIR C7: 5,7 ROW 7 F7: 5,7,1,6,8 # reduction candidate for 5,7 F7: 5,7 => CTR * ..1.7...8.798..4..86294...3193.2.5846245837917584193622.5..7.499.6.54.37..7.981.. H7: 5,7,3,4,6 # reduction candidate for 5,7 H7: 5,7 => CTR * 4.137....53.86.4.787..4..63193.2.586624583791758.1.34224.1386.991675423838..9.1.4 * RESTART * PAIR RESTART * PAIR A8: 3,9 BLK 7 B8: 3,9,1,8 # reduction candidate for 3,9 B8: 3,9 => CTR * .4137...6...86.4..86..4..73193.2.5846245837917584193.221...8649..61.4...48..9.1.. * PAIR A9: 3,4 BLK 7 B7: 3,4,1,8 # reduction candidate for 3,4 B7: 3,4 => SOLVED * 431279856569831427872645913193427685624583791758916342247168539916354278385792164 * DURATION: 0:00:18.926699 START: 03:33:45.691683 END: 03:34:04.618382 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0010-base-pr-001.dot * REASONING * DIS # A2: 6,7 => CTR => A2: 3,5 * DIS A2: 3,5 # H5: 1 => CTR => H5: 6,9 * DIS A2: 3,5 + H5: 6,9 # F7: 5,7 => CTR => F7: 1,6,8 * DIS A2: 3,5 + H5: 6,9 + F7: 1,6,8 # H7: 5,7 => CTR => H7: 3,4,6 * DIS A2: 3,5 + H5: 6,9 + F7: 1,6,8 + H7: 3,4,6 # B8: 3,9 => CTR => B8: 1,8 * PRF A2: 3,5 + H5: 6,9 + F7: 1,6,8 + H7: 3,4,6 + B8: 1,8 # B7: 3,4 => SOL * STA A2: 3,5 + H5: 6,9 + F7: 1,6,8 + H7: 3,4,6 + B8: 1,8 + B7: 3,4 * CNT 6 HDP CHAINS / 18 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=10
Solution
position: 431279856569831427872645913193427685624583791758916342247168539916354278385792164 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 # F2: 2,9 => UNS * INC # H2: 2,9 => UNS * DIS # A2: 6,7 => CTR => A2: 3,5 * INC # A2: 3,5 => UNS * INC # B2: 6,7 => UNS * INC # H3: 6,7 => UNS * INC # H3: 1,2,5,9 => UNS * DIS # B4: 6,7 => CTR => B4: 9 * INC # B4: 9 => UNS * INC # D3: 2,9 => UNS * INC # F3: 2,9 => UNS * INC # G3: 2,9 => UNS * INC # H3: 2,9 => UNS * INC # B4: 6,9 => UNS * DIS # A6: 6,9 => CTR => A6: 7 * INC # A6: 7 => UNS * INC # H5: 6,9 => UNS * DIS # H5: 1 => CTR => H5: 6,9 * DIS # H5: 1,6 => CTR => H5: 9 * INC # H5: 9 => UNS * INC # I2: 1,6 => UNS * INC # I2: 5,7 => UNS * DIS # F7: 5,7 => CTR => F7: 1,6,8 * INC # F7: 1,6,8 => UNS * DIS # H7: 5,7 => CTR => H7: 3,4,6 * INC # H7: 3,4,6 => UNS * DIS # B8: 3,9 => CTR => B8: 1,8 * INC # B8: 1,8 => UNS * PRF # B7: 3,4 => SOL * INC # B7: 1,8 => UNS * DIS # B9: 3,4 => CTR => B9: 8 * INC # B9: 8 => UNS * DIS # H9: 3,4 => CTR => H9: 2,5,6,7 * INC # H9: 2,5,6,7 => UNS * INC # A1: 3,4 => UNS * INC # A1: 5,6 => UNS * INC # F9: 5,7 => UNS * INC # H9: 5,7 => UNS * INC # I9: 5,7 => UNS * INC # E7: 3,5 => UNS * INC # E7: 6 => UNS * INC # H8: 3,5 => UNS * INC # H8: 2,7 => UNS * INC # E2: 3,5 => UNS * INC # E2: 6 => UNS * CNT 45 HDP CHAINS / 45 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F2: 2,9 => UNS * INC # H2: 2,9 => UNS * DIS # A2: 6,7 => CTR => A2: 3,5 * INC A2: 3,5 # B2: 6,7 => UNS * INC A2: 3,5 # B2: 6,7 => UNS * INC A2: 3,5 # B2: 3 => UNS * INC A2: 3,5 # H3: 6,7 => UNS * INC A2: 3,5 # H3: 1,2,5,9 => UNS * INC A2: 3,5 # D3: 2,9 => UNS * INC A2: 3,5 # F3: 2,9 => UNS * INC A2: 3,5 # G3: 2,9 => UNS * INC A2: 3,5 # H3: 2,9 => UNS * INC A2: 3,5 # H5: 6,9 => UNS * DIS A2: 3,5 # H5: 1 => CTR => H5: 6,9 * DIS A2: 3,5 + H5: 6,9 # F7: 5,7 => CTR => F7: 1,6,8 * DIS A2: 3,5 + H5: 6,9 + F7: 1,6,8 # H7: 5,7 => CTR => H7: 3,4,6 * DIS A2: 3,5 + H5: 6,9 + F7: 1,6,8 + H7: 3,4,6 # B8: 3,9 => CTR => B8: 1,8 * PRF A2: 3,5 + H5: 6,9 + F7: 1,6,8 + H7: 3,4,6 + B8: 1,8 # B7: 3,4 => SOL * STA A2: 3,5 + H5: 6,9 + F7: 1,6,8 + H7: 3,4,6 + B8: 1,8 + B7: 3,4 * CNT 18 HDP CHAINS / 18 HYP OPENED