Analysis of zz-www.sudokuwiki.org-0106-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=106
level: medium
position: .1..3..5.7..62.........47.2.6..7...4..3...6..5...8..1.3.98.........47..8.8..5..9. initial
Autosolve
position: .1.73..5.7..62.........47.2.6..7...4..3...6..5...86.1.3.986.......947..8.8..5..9. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 8,9 => CTR => A1: 2,4,6 * DIS # A1: 6,9 => CTR => A1: 2,4,8 * PRF # A5: 1,9 => SOL * DIS # B7: 2,5 => CTR => B7: 4,7 * DIS # G8: 2,5 => CTR => G8: 1,3 * CNT 5 HDP CHAINS / 24 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 8,9 => CTR => A1: 2,4,6 * PRF A1: 2,4,6 # A5: 1,9 => SOL * STA A1: 2,4,6 + A5: 1,9 * CNT 2 HDP CHAINS / 15 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .1..3..5.7..62.........47.2.6..7...4..3...6..5...8..1.3.98.........47..8.8..5..9. | initial |
| .1.73..5.7..62.........47.2.6..7...4..3...6..5...86.1.3.986.......947..8.8..5..9. | autosolve |
| 412739856735628149896514732968173524123495687574286913349861275251947368687352491 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) F1: 8,9 D3: 1,5 E3: 1,9 I1: 6,9 E5: 1,9 B8: 2,5 F7: 1,2 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D3,E3: 1.. / D3 = 1 => 9 pairs (_) / E3 = 1 => 8 pairs (_) G2,I2: 1.. / G2 = 1 => 9 pairs (_) / I2 = 1 => 12 pairs (_) E3,E5: 1.. / E3 = 1 => 8 pairs (_) / E5 = 1 => 9 pairs (_) A1,C1: 2.. / A1 = 2 => 8 pairs (_) / C1 = 2 => 9 pairs (_) B2,B3: 3.. / B2 = 3 => 20 pairs (_) / B3 = 3 => 8 pairs (_) D9,F9: 3.. / D9 = 3 => 12 pairs (_) / F9 = 3 => 8 pairs (_) G8,H8: 3.. / G8 = 3 => 9 pairs (_) / H8 = 3 => 0 pairs (X) B3,H3: 3.. / B3 = 3 => 8 pairs (_) / H3 = 3 => 20 pairs (_) F4,F9: 3.. / F4 = 3 => 12 pairs (_) / F9 = 3 => 8 pairs (_) I2,I6: 3.. / I2 = 3 => 17 pairs (_) / I6 = 3 => 11 pairs (_) D5,D6: 4.. / D5 = 4 => 8 pairs (_) / D6 = 4 => 9 pairs (_) H2,H7: 4.. / H2 = 4 => 17 pairs (_) / H7 = 4 => 15 pairs (_) F2,D3: 5.. / F2 = 5 => 9 pairs (_) / D3 = 5 => 8 pairs (_) G4,I5: 5.. / G4 = 5 => 11 pairs (_) / I5 = 5 => 8 pairs (_) I5,I7: 5.. / I5 = 5 => 8 pairs (_) / I7 = 5 => 11 pairs (_) I1,H3: 6.. / I1 = 6 => 12 pairs (_) / H3 = 6 => 0 pairs (X) H8,I9: 6.. / H8 = 6 => 12 pairs (_) / I9 = 6 => 0 pairs (X) H3,H8: 6.. / H3 = 6 => 0 pairs (X) / H8 = 6 => 12 pairs (_) I1,I9: 6.. / I1 = 6 => 12 pairs (_) / I9 = 6 => 0 pairs (X) B7,C9: 7.. / B7 = 7 => 18 pairs (_) / C9 = 7 => 9 pairs (_) C9,I9: 7.. / C9 = 7 => 9 pairs (_) / I9 = 7 => 18 pairs (_) C6,C9: 7.. / C6 = 7 => 18 pairs (_) / C9 = 7 => 9 pairs (_) H5,H7: 7.. / H5 = 7 => 12 pairs (_) / H7 = 7 => 0 pairs (*) F1,F2: 8.. / F1 = 8 => 8 pairs (_) / F2 = 8 => 18 pairs (_) A5,H5: 8.. / A5 = 8 => 10 pairs (_) / H5 = 8 => 0 pairs (*) E3,E5: 9.. / E3 = 9 => 9 pairs (_) / E5 = 9 => 8 pairs (_) * DURATION: 0:00:31.504502 START: 05:22:03.415931 END: 05:22:34.920433 2017-05-01 * CP COUNT: (26) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,D3,E3,E5,F1,F7,I1) * .1.73..5.7..62.........47.2.6..7...4..3...6..5...86.1.3.986.......947..8.8..5..9. * PAIR F1: 8,9 BLK 2 F2: 8,9,5 # reduction candidate for 8,9 F2: 5 # 9 pairs F2: 8,9 # 8 pairs * PAIR F1: 8,9 ROW 1 A1: 8,9,2,4,6 # reduction candidate for 8,9 A1: 8,9 => CTR * 9127384567..62...96...947.216..7..248.3...67.5...869133.986..4....947368486.5..97 A1: 2,4,6 # 7 pairs G1: 8,9,4 # reduction candidate for 8,9 G1: 8,9 # 16 pairs * PAIR D3: 1,5 COL D D4: 1,5,2,3 # reduction candidate for 1,5 D4: 1,5 # 10 pairs D5: 1,5,2,4 # reduction candidate for 1,5 D5: 1,5 # 12 pairs * PAIR I1: 6,9 ROW 1 A1: 6,9,2,4,8 # reduction candidate for 6,9 A1: 6,9 => CTR * 6127384597..62...19...14762261.7.9848.3192675597.8621.3.986..4.1..947.2848..5.196 A1: 2,4,8 # 7 pairs * PAIR E5: 1,9 BLK 5 F4: 1,9,2,3,5 # reduction candidate for 1,9 F4: 1,9 # 10 pairs F5: 1,9,2,5 # reduction candidate for 1,9 F5: 1,9 # 9 pairs * PAIR E5: 1,9 ROW 5 A5: 1,9,2,4,8 # reduction candidate for 1,9 A5: 1,9 => SOLVED * 412739856735628149896514732968173524123495687574286913349861275251947368687352491 A5: 2,4,8 # 7 pairs * PAIR B8: 2,5 BLK 7 B7: 2,5,4,7 # reduction candidate for 2,5 B7: 2,5 => CTR * .1.7384597..62...1938514762.6..7...48.3...67557..869133.986..47...947..8487.5..96 B7: 4,7 # 8 pairs C8: 2,5,1,6 # reduction candidate for 2,5 C8: 2,5 # 12 pairs * PAIR B8: 2,5 ROW 8 G8: 2,5,1,3 # reduction candidate for 2,5 G8: 2,5 => CTR * .1.7384597..62.38193851476216..7.8248.3...67557..869133.986..47...947.38487.5..96 G8: 1,3 # 8 pairs * PAIR F7: 1,2 BLK 8 D9: 1,2,3 # reduction candidate for 1,2 D9: 1,2 # 8 pairs F9: 1,2,3 # reduction candidate for 1,2 F9: 1,2 # 12 pairs * PAIR F7: 1,2 ROW 7 G7: 1,2,4,5 # reduction candidate for 1,2 G7: 1,2 # 10 pairs G7: 4,5 # 8 pairs * PAIR F7: 1,2 COL F F4: 1,2,3,5,9 # reduction candidate for 1,2 F4: 1,2 # 11 pairs F5: 1,2,5,9 # reduction candidate for 1,2 F5: 1,2 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0106-base-pr-000.dot * REASONING * DIS # A1: 8,9 => CTR => A1: 2,4,6 * DIS # A1: 6,9 => CTR => A1: 2,4,8 * PRF # A5: 1,9 => SOL * DIS # B7: 2,5 => CTR => B7: 4,7 * DIS # G8: 2,5 => CTR => G8: 1,3 * CNT 5 HDP CHAINS / 24 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,D3,E3,E5,F1,F7,I1) * .1.73..5.7..62.........47.2.6..7...4..3...6..5...86.1.3.986.......947..8.8..5..9. * PAIR F1: 8,9 BLK 2 F2: 8,9,5 # reduction candidate for 8,9 F2: 5 # 9 pairs F2: 8,9 # 8 pairs * PAIR F1: 8,9 ROW 1 A1: 8,9,2,4,6 # reduction candidate for 8,9 A1: 8,9 => CTR * 9127384567..62...96...947.216..7..248.3...67.5...869133.986..4....947368486.5..97 G1: 8,9,4 # reduction candidate for 8,9 G1: 8,9 # 16 pairs * RESTART * PAIR F1: 8,9 ROW 1 G1: 8,9,4 # reduction candidate for 8,9 G1: 8,9 # 16 pairs G1: 4 # 16 pairs * PAIR RESTART * PAIR F1: 8,9 BLK 2 F2: 8,9,5 # reduction candidate for 8,9 F2: 5 # 13 pairs F2: 8,9 # 8 pairs * PAIR F1: 8,9 ROW 1 G1: 8,9,4 # reduction candidate for 8,9 G1: 8,9 # 16 pairs G1: 4 # 16 pairs * PAIR D3: 1,5 COL D D4: 1,5,2,3 # reduction candidate for 1,5 D4: 1,5 # 10 pairs D5: 1,5,2,4 # reduction candidate for 1,5 D5: 1,5 # 12 pairs * PAIR E5: 1,9 BLK 5 F4: 1,9,2,3,5 # reduction candidate for 1,9 F4: 1,9 # 10 pairs F5: 1,9,2,5 # reduction candidate for 1,9 F5: 1,9 # 9 pairs * PAIR E5: 1,9 ROW 5 A5: 1,9,2,4,8 # reduction candidate for 1,9 A5: 1,9 => SOLVED * 412739856735628149896514732968173524123495687574286913349861275251947368687352491 * DURATION: 0:00:12.187849 START: 05:22:51.377259 END: 05:23:03.565108 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0106-base-pr-001.dot * REASONING * DIS # A1: 8,9 => CTR => A1: 2,4,6 * PRF A1: 2,4,6 # A5: 1,9 => SOL * STA A1: 2,4,6 + A5: 1,9 * CNT 2 HDP CHAINS / 15 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=106
Solution
position: 412739856735628149896514732968173524123495687574286913349861275251947368687352491 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: 8,9 => UNS * INC # F2: 5 => UNS * DIS # A1: 8,9 => CTR => A1: 2,4,6 * INC # A1: 2,4,6 => UNS * INC # G1: 8,9 => UNS * INC # D4: 1,5 => UNS * INC # D5: 1,5 => UNS * DIS # A1: 6,9 => CTR => A1: 2,4,8 * INC # A1: 2,4,8 => UNS * INC # F4: 1,9 => UNS * INC # F5: 1,9 => UNS * PRF # A5: 1,9 => SOL * INC # A5: 2,4,8 => UNS * DIS # B7: 2,5 => CTR => B7: 4,7 * INC # B7: 4,7 => UNS * INC # C8: 2,5 => UNS * DIS # G8: 2,5 => CTR => G8: 1,3 * INC # G8: 1,3 => UNS * INC # D9: 1,2 => UNS * INC # F9: 1,2 => UNS * INC # G7: 1,2 => UNS * INC # G7: 4,5 => UNS * INC # F4: 1,2 => UNS * INC # F5: 1,2 => UNS * CNT 24 HDP CHAINS / 24 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F2: 8,9 => UNS * INC # F2: 5 => UNS * DIS # A1: 8,9 => CTR => A1: 2,4,6 * INC A1: 2,4,6 # G1: 8,9 => UNS * INC A1: 2,4,6 # G1: 8,9 => UNS * INC A1: 2,4,6 # G1: 4 => UNS * INC A1: 2,4,6 # F2: 8,9 => UNS * INC A1: 2,4,6 # F2: 5 => UNS * INC A1: 2,4,6 # G1: 8,9 => UNS * INC A1: 2,4,6 # G1: 4 => UNS * INC A1: 2,4,6 # D4: 1,5 => UNS * INC A1: 2,4,6 # D5: 1,5 => UNS * INC A1: 2,4,6 # F4: 1,9 => UNS * INC A1: 2,4,6 # F5: 1,9 => UNS * PRF A1: 2,4,6 # A5: 1,9 => SOL * STA A1: 2,4,6 + A5: 1,9 * CNT 15 HDP CHAINS / 15 HYP OPENED