Analysis of zz-www.sudokuwiki.org-0117-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=117
level: medium
position: ..36..9...2..19.8..4.....7....3....2..1.7.4..5....8..........6..9.15......8..37.. initial
Autosolve
position: ..36..9...2..19.8..4..3..7....3.1..2..1.7.4..5....8..7.......6..9.15......8..37.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F1: 2,5 => CTR => F1: 4,7 * DIS # A5: 3,6 => CTR => A5: 2,8,9 * CNT 2 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F1: 2,5 => CTR => F1: 4,7 * DIS F1: 4,7 # A5: 3,6 => CTR => A5: 2,8,9 * DIS F1: 4,7 + A5: 2,8,9 # D2: 5 => CTR => D2: 4,7 * DIS F1: 4,7 + A5: 2,8,9 + D2: 4,7 # F8: 4,7 => CTR => F8: 2,6 * PRF F1: 4,7 + A5: 2,8,9 + D2: 4,7 + F8: 2,6 # F5: 6 => SOL * STA F1: 4,7 + A5: 2,8,9 + D2: 4,7 + F8: 2,6 + F5: 6 * CNT 5 HDP CHAINS / 34 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..36..9...2..19.8..4.....7....3....2..1.7.4..5....8..........6..9.15......8..37.. | initial |
| ..36..9...2..19.8..4..3..7....3.1..2..1.7.4..5....8..7.......6..9.15......8..37.. | autosolve |
| 873624915625719384149835276987341652231576498564298137312487569796152843458963721 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) A2: 6,7 F3: 2,5 B6: 3,6 H4: 5,9 H5: 3,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G6,H6: 1.. / G6 = 1 => 8 pairs (_) / H6 = 1 => 6 pairs (_) H1,G3: 2.. / H1 = 2 => 8 pairs (_) / G3 = 2 => 10 pairs (_) A5,C6: 2.. / A5 = 2 => 7 pairs (_) / C6 = 2 => 13 pairs (_) G2,I2: 3.. / G2 = 3 => 7 pairs (_) / I2 = 3 => 16 pairs (_) D2,I2: 4.. / D2 = 4 => 13 pairs (_) / I2 = 4 => 11 pairs (_) D5,F5: 5.. / D5 = 5 => 8 pairs (_) / F5 = 5 => 17 pairs (_) G4,H4: 5.. / G4 = 5 => 0 pairs (X) / H4 = 5 => 5 pairs (_) F8,E9: 6.. / F8 = 6 => 8 pairs (_) / E9 = 6 => 14 pairs (_) F5,F8: 6.. / F5 = 6 => 14 pairs (_) / F8 = 6 => 8 pairs (_) F1,D2: 7.. / F1 = 7 => 10 pairs (_) / D2 = 7 => 9 pairs (_) D2,D7: 7.. / D2 = 7 => 9 pairs (_) / D7 = 7 => 10 pairs (_) E1,D3: 8.. / E1 = 8 => 17 pairs (_) / D3 = 8 => 6 pairs (_) G4,I5: 8.. / G4 = 8 => 6 pairs (_) / I5 = 8 => 12 pairs (_) D7,E7: 8.. / D7 = 8 => 17 pairs (_) / E7 = 8 => 6 pairs (_) G8,I8: 8.. / G8 = 8 => 12 pairs (_) / I8 = 8 => 6 pairs (_) A3,D3: 8.. / A3 = 8 => 17 pairs (_) / D3 = 8 => 6 pairs (_) D3,D7: 8.. / D3 = 8 => 6 pairs (_) / D7 = 8 => 17 pairs (_) E1,E7: 8.. / E1 = 8 => 17 pairs (_) / E7 = 8 => 6 pairs (_) G4,G8: 8.. / G4 = 8 => 6 pairs (_) / G8 = 8 => 12 pairs (_) I5,I8: 8.. / I5 = 8 => 12 pairs (_) / I8 = 8 => 6 pairs (_) A3,C3: 9.. / A3 = 9 => 17 pairs (_) / C3 = 9 => 5 pairs (_) * DURATION: 0:00:23.041297 START: 05:37:18.223250 END: 05:37:41.264547 2017-05-01 * CP COUNT: (21) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B6,F3,H4,H5) * ..36..9...2..19.8..4..3..7....3.1..2..1.7.4..5....8..7.......6..9.15......8..37.. * PAIR A2: 6,7 BLK 1 C2: 6,7,5 # reduction candidate for 6,7 C2: 6,7 # 14 pairs C2: 5 # 8 pairs * PAIR A2: 6,7 COL A A4: 6,7,4,8,9 # reduction candidate for 6,7 A4: 6,7 # 11 pairs A8: 6,7,2,3,4 # reduction candidate for 6,7 A8: 6,7 # 7 pairs * PAIR F3: 2,5 BLK 2 F1: 2,5,4,7 # reduction candidate for 2,5 F1: 2,5 => CTR * ..364.9..62571938414983..7....3.1..22.15764..5.6428197....8..6..9.15....468..37.. F1: 4,7 # 6 pairs D3: 2,5,8 # reduction candidate for 2,5 D3: 2,5 # 17 pairs * PAIR F3: 2,5 ROW 3 G3: 2,5,1,6 # reduction candidate for 2,5 G3: 2,5 # 9 pairs G3: 1,6 # 9 pairs * PAIR F3: 2,5 COL F F5: 2,5,6 # reduction candidate for 2,5 F5: 6 # 14 pairs F5: 2,5 # 8 pairs * PAIR B6: 3,6 BLK 4 A5: 3,6,2,8,9 # reduction candidate for 3,6 A5: 3,6 => CTR * 8536.79..726.19.8.14983..76974361852681.7.4.3532..8617.15784.69.97156..8..8..37.5 A5: 2,8,9 # 5 pairs B5: 3,6,8 # reduction candidate for 3,6 B5: 3,6 # 8 pairs * PAIR B6: 3,6 ROW 6 G6: 3,6,1 # reduction candidate for 3,6 G6: 1 # 8 pairs G6: 3,6 # 6 pairs * PAIR H4: 5,9 COL H H9: 5,9,1,2,4 # reduction candidate for 5,9 H9: 5,9 # 10 pairs H9: 1,2,4 # 5 pairs * PAIR H5: 3,9 BLK 6 I5: 3,9,6,8 # reduction candidate for 3,9 I5: 3,9 # 10 pairs H6: 3,9,1 # reduction candidate for 3,9 H6: 3,9 # 8 pairs * PAIR H5: 3,9 ROW 5 A5: 3,9,2,6,8 # reduction candidate for 3,9 A5: 3,9 # 16 pairs A5: 2,6,8 # 5 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0117-base-pr-000.dot * REASONING * DIS # F1: 2,5 => CTR => F1: 4,7 * DIS # A5: 3,6 => CTR => A5: 2,8,9 * CNT 2 HDP CHAINS / 22 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B6,F3,H4,H5) * ..36..9...2..19.8..4..3..7....3.1..2..1.7.4..5....8..7.......6..9.15......8..37.. * PAIR A2: 6,7 BLK 1 C2: 6,7,5 # reduction candidate for 6,7 C2: 6,7 # 14 pairs C2: 5 # 8 pairs * PAIR A2: 6,7 COL A A4: 6,7,4,8,9 # reduction candidate for 6,7 A4: 6,7 # 11 pairs A8: 6,7,2,3,4 # reduction candidate for 6,7 A8: 6,7 # 7 pairs * PAIR F3: 2,5 BLK 2 F1: 2,5,4,7 # reduction candidate for 2,5 F1: 2,5 => CTR * ..364.9..62571938414983..7....3.1..22.15764..5.6428197....8..6..9.15....468..37.. D3: 2,5,8 # reduction candidate for 2,5 D3: 2,5 # 17 pairs * RESTART * PAIR F3: 2,5 BLK 2 D3: 2,5,8 # reduction candidate for 2,5 D3: 2,5 # 17 pairs D3: 8 # 7 pairs * PAIR F3: 2,5 ROW 3 G3: 2,5,1,6 # reduction candidate for 2,5 G3: 2,5 # 10 pairs G3: 1,6 # 10 pairs * PAIR F3: 2,5 COL F F5: 2,5,6 # reduction candidate for 2,5 F5: 6 # 25 pairs F5: 2,5 # 8 pairs * PAIR B6: 3,6 BLK 4 A5: 3,6,2,8,9 # reduction candidate for 3,6 A5: 3,6 => CTR * 8536.79..726.19.8.14983..76974361852681.7.4.3532..8617.15784.69.97156..8..8..37.5 B5: 3,6,8 # reduction candidate for 3,6 B5: 3,6 # 9 pairs * RESTART * PAIR B6: 3,6 BLK 4 B5: 3,6,8 # reduction candidate for 3,6 B5: 8 # 9 pairs B5: 3,6 # 9 pairs * PAIR B6: 3,6 ROW 6 G6: 3,6,1 # reduction candidate for 3,6 G6: 1 # 9 pairs G6: 3,6 # 7 pairs * PAIR H4: 5,9 COL H H9: 5,9,1,2,4 # reduction candidate for 5,9 H9: 5,9 # 11 pairs H9: 1,2,4 # 6 pairs * PAIR H5: 3,9 BLK 6 I5: 3,9,6,8 # reduction candidate for 3,9 I5: 3,9 # 12 pairs H6: 3,9,1 # reduction candidate for 3,9 H6: 3,9 # 9 pairs * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A2,B6,F1,F3,H4,H5) * ..36..9...2..19.8..4..3..7....3.1..2..1.7.4..5....8..7.......6..9.15......8..37.. * PAIR A2: 6,7 BLK 1 C2: 6,7,5 # reduction candidate for 6,7 C2: 6,7 # 15 pairs C2: 5 # 11 pairs * PAIR A2: 6,7 COL A A4: 6,7,4,8,9 # reduction candidate for 6,7 A4: 6,7 # 12 pairs A8: 6,7,2,3,4 # reduction candidate for 6,7 A8: 6,7 # 8 pairs * PAIR F1: 4,7 BLK 2 D2: 4,7,5 # reduction candidate for 4,7 D2: 5 => CTR * .83647925726519384.45832176.7.3.1.52.61.754..53.4.8617312784569497156238658..3741 * PAIR F1: 4,7 COL F F7: 4,7,2 # reduction candidate for 4,7 F7: 4,7 # 13 pairs F8: 4,7,2,6 # reduction candidate for 4,7 F8: 4,7 => CTR * ..36249..72..19.8..4.83527....3.1..22.15764..5..2.8..7....82.6.692157.....8.6372. * RESTART * PAIR RESTART * PAIR F3: 2,5 BLK 2 D3: 2,5,8 # reduction candidate for 2,5 D3: 2,5 # 20 pairs D3: 8 # 13 pairs * PAIR F3: 2,5 COL F F5: 2,5,6 # reduction candidate for 2,5 F5: 6 => SOLVED * 873624915625719384149835276987341652231576498564298137312487569796152843458963721 * DURATION: 0:00:25.655502 START: 05:37:55.043973 END: 05:38:20.699475 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0117-base-pr-001.dot * REASONING * DIS # F1: 2,5 => CTR => F1: 4,7 * DIS F1: 4,7 # A5: 3,6 => CTR => A5: 2,8,9 * DIS F1: 4,7 + A5: 2,8,9 # D2: 5 => CTR => D2: 4,7 * DIS F1: 4,7 + A5: 2,8,9 + D2: 4,7 # F8: 4,7 => CTR => F8: 2,6 * PRF F1: 4,7 + A5: 2,8,9 + D2: 4,7 + F8: 2,6 # F5: 6 => SOL * STA F1: 4,7 + A5: 2,8,9 + D2: 4,7 + F8: 2,6 + F5: 6 * CNT 5 HDP CHAINS / 34 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=117
Solution
position: 873624915625719384149835276987341652231576498564298137312487569796152843458963721 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: 6,7 => UNS * INC # C2: 5 => UNS * INC # A4: 6,7 => UNS * INC # A8: 6,7 => UNS * DIS # F1: 2,5 => CTR => F1: 4,7 * INC # F1: 4,7 => UNS * INC # D3: 2,5 => UNS * INC # G3: 2,5 => UNS * INC # G3: 1,6 => UNS * INC # F5: 2,5 => UNS * INC # F5: 6 => UNS * DIS # A5: 3,6 => CTR => A5: 2,8,9 * INC # A5: 2,8,9 => UNS * INC # B5: 3,6 => UNS * INC # G6: 3,6 => UNS * INC # G6: 1 => UNS * INC # H9: 5,9 => UNS * INC # H9: 1,2,4 => UNS * INC # I5: 3,9 => UNS * INC # H6: 3,9 => UNS * INC # A5: 3,9 => UNS * INC # A5: 2,6,8 => UNS * CNT 22 HDP CHAINS / 22 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C2: 6,7 => UNS * INC # C2: 5 => UNS * INC # A4: 6,7 => UNS * INC # A8: 6,7 => UNS * DIS # F1: 2,5 => CTR => F1: 4,7 * INC F1: 4,7 # D3: 2,5 => UNS * INC F1: 4,7 # D3: 2,5 => UNS * INC F1: 4,7 # D3: 8 => UNS * INC F1: 4,7 # G3: 2,5 => UNS * INC F1: 4,7 # G3: 1,6 => UNS * INC F1: 4,7 # F5: 2,5 => UNS * INC F1: 4,7 # F5: 6 => UNS * DIS F1: 4,7 # A5: 3,6 => CTR => A5: 2,8,9 * INC F1: 4,7 + A5: 2,8,9 # B5: 3,6 => UNS * INC F1: 4,7 + A5: 2,8,9 # B5: 3,6 => UNS * INC F1: 4,7 + A5: 2,8,9 # B5: 8 => UNS * INC F1: 4,7 + A5: 2,8,9 # G6: 3,6 => UNS * INC F1: 4,7 + A5: 2,8,9 # G6: 1 => UNS * INC F1: 4,7 + A5: 2,8,9 # H9: 5,9 => UNS * INC F1: 4,7 + A5: 2,8,9 # H9: 1,2,4 => UNS * INC F1: 4,7 + A5: 2,8,9 # I5: 3,9 => UNS * INC F1: 4,7 + A5: 2,8,9 # H6: 3,9 => UNS * INC F1: 4,7 + A5: 2,8,9 # C2: 6,7 => UNS * INC F1: 4,7 + A5: 2,8,9 # C2: 5 => UNS * INC F1: 4,7 + A5: 2,8,9 # A4: 6,7 => UNS * INC F1: 4,7 + A5: 2,8,9 # A8: 6,7 => UNS * INC F1: 4,7 + A5: 2,8,9 # D2: 4,7 => UNS * DIS F1: 4,7 + A5: 2,8,9 # D2: 5 => CTR => D2: 4,7 * INC F1: 4,7 + A5: 2,8,9 + D2: 4,7 # F7: 4,7 => UNS * DIS F1: 4,7 + A5: 2,8,9 + D2: 4,7 # F8: 4,7 => CTR => F8: 2,6 * INC F1: 4,7 + A5: 2,8,9 + D2: 4,7 + F8: 2,6 # D3: 2,5 => UNS * INC F1: 4,7 + A5: 2,8,9 + D2: 4,7 + F8: 2,6 # D3: 8 => UNS * INC F1: 4,7 + A5: 2,8,9 + D2: 4,7 + F8: 2,6 # F5: 2,5 => UNS * PRF F1: 4,7 + A5: 2,8,9 + D2: 4,7 + F8: 2,6 # F5: 6 => SOL * STA F1: 4,7 + A5: 2,8,9 + D2: 4,7 + F8: 2,6 + F5: 6 * CNT 34 HDP CHAINS / 34 HYP OPENED