Analysis of zz-www.sudokuwiki.org-0097-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=97
level: medium
position: .....46....35.....1......89..8..9.2..3..2..9..9.3..4..28......6.....85....47..... initial
Autosolve
position: .2...465..635.....145....89..8..9.2..3..2..9..923..46.28......6.....85....47..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A1: 8 => SOL * DIS # E1: 8,9 => CTR => E1: 1,3 * DIS # E1: 8,9 => CTR => E1: 1,3 * DIS # A5: 5,7 => CTR => A5: 4,6 * DIS # I6: 5,7 => CTR => I6: 1,8 * DIS # C8: 1,7 => CTR => C8: 6,9 * DIS # I8: 1,7 => CTR => I8: 2,4 * DIS # F9: 1,3 => CTR => F9: 2,6 * CNT 8 HDP CHAINS / 40 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A1: 8 => SOL * STA A1: 8 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .....46....35.....1......89..8..9.2..3..2..9..9.3..4..28......6.....85....47..... | initial |
| .2...465..635.....145....89..8..9.2..3..2..9..923..46.28......6.....85....47..... | autosolve |
| 827914653963587214145236789718649325436825197592371468281453976379168542654792831 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) C1: 7,9 A2: 8,9 E2: 8,9 D3: 2,6 I1: 1,3 A6: 5,7 B8: 1,7 B9: 1,5 H9: 1,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B4,C5: 1.. / B4 = 1 => 11 pairs (_) / C5 = 1 => 14 pairs (_) D8,F9: 2.. / D8 = 2 => 0 pairs (X) / F9 = 2 => 14 pairs (_) D8,I8: 2.. / D8 = 2 => 0 pairs (X) / I8 = 2 => 14 pairs (_) D3,D8: 2.. / D3 = 2 => 14 pairs (_) / D8 = 2 => 0 pairs (X) I1,G3: 3.. / I1 = 3 => 10 pairs (_) / G3 = 3 => 0 pairs (X) G4,I4: 3.. / G4 = 3 => 10 pairs (_) / I4 = 3 => 0 pairs (X) A8,A9: 3.. / A8 = 3 => 9 pairs (_) / A9 = 3 => 13 pairs (_) E1,I1: 3.. / E1 = 3 => 0 pairs (X) / I1 = 3 => 10 pairs (_) G3,G4: 3.. / G3 = 3 => 0 pairs (X) / G4 = 3 => 10 pairs (_) I1,I4: 3.. / I1 = 3 => 10 pairs (_) / I4 = 3 => 0 pairs (X) H2,I2: 4.. / H2 = 4 => 0 pairs (X) / I2 = 4 => 10 pairs (_) A4,A5: 4.. / A4 = 4 => 13 pairs (_) / A5 = 4 => 9 pairs (_) A5,D5: 4.. / A5 = 4 => 9 pairs (_) / D5 = 4 => 13 pairs (_) I2,I8: 4.. / I2 = 4 => 10 pairs (_) / I8 = 4 => 0 pairs (X) A9,B9: 5.. / A9 = 5 => 18 pairs (_) / B9 = 5 => 9 pairs (_) E7,F7: 5.. / E7 = 5 => 10 pairs (_) / F7 = 5 => 10 pairs (_) B4,B9: 5.. / B4 = 5 => 18 pairs (_) / B9 = 5 => 9 pairs (_) C5,C8: 6.. / C5 = 6 => 13 pairs (_) / C8 = 6 => 12 pairs (_) A1,C1: 7.. / A1 = 7 => 13 pairs (_) / C1 = 7 => 11 pairs (_) B4,B8: 7.. / B4 = 7 => 13 pairs (_) / B8 = 7 => 10 pairs (_) A1,A2: 8.. / A1 = 8 => 0 pairs (*) / A2 = 8 => 0 pairs (X) D5,E6: 8.. / D5 = 8 => 16 pairs (_) / E6 = 8 => 9 pairs (_) G9,I9: 8.. / G9 = 8 => 14 pairs (_) / I9 = 8 => 12 pairs (_) A2,E2: 8.. / A2 = 8 => 9 pairs (_) / E2 = 8 => 0 pairs (*) E6,I6: 8.. / E6 = 8 => 9 pairs (_) / I6 = 8 => 16 pairs (_) D1,D5: 8.. / D1 = 8 => 9 pairs (_) / D5 = 8 => 16 pairs (_) G5,G9: 8.. / G5 = 8 => 12 pairs (_) / G9 = 8 => 14 pairs (_) G7,G9: 9.. / G7 = 9 => 12 pairs (_) / G9 = 9 => 13 pairs (_) A2,E2: 9.. / A2 = 9 => 0 pairs (*) / E2 = 9 => 0 pairs (X) * DURATION: 0:00:44.302516 START: 05:14:07.990255 END: 05:14:52.292771 2017-05-01 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,B8,B9,C1,D3,E2,H9,I1) * .2...465..635.....145....89..8..9.2..3..2..9..923..46.28......6.....85....47..... * PAIR C1: 7,9 BLK 1 A1: 7,9,8 # reduction candidate for 7,9 A1: 8 => SOLVED * 827914653963587214145236789718649325436825197592371468281453976379168542654792831 A1: 7,9 # 9 pairs * PAIR C1: 7,9 COL C C7: 7,9,1 # reduction candidate for 7,9 C7: 7,9 # 12 pairs C8: 7,9,1,6 # reduction candidate for 7,9 C8: 7,9 # 14 pairs * PAIR A2: 8,9 BLK 1 A1: 8,9,7 # reduction candidate for 8,9 A1: 7 # 13 pairs A1: 8,9 # 11 pairs * PAIR E2: 8,9 BLK 2 D1: 8,9,1 # reduction candidate for 8,9 D1: 8,9 # 11 pairs E1: 8,9,1,3 # reduction candidate for 8,9 E1: 8,9 => CTR * .291846538635972141452..789..864932.43682.197.9237146828.453976...9.85.29547.28.1 E1: 1,3 # 11 pairs * PAIR D3: 2,6 BLK 2 F3: 2,6,3,7 # reduction candidate for 2,6 F3: 2,6 # 13 pairs F3: 3,7 # 10 pairs * PAIR D3: 2,6 COL D D8: 2,6,1,4,9 # reduction candidate for 2,6 D8: 1,4,9 # 15 pairs D8: 2,6 # 11 pairs * PAIR I1: 1,3 ROW 1 E1: 1,3,8,9 # reduction candidate for 1,3 E1: 8,9 => CTR * .291846538635972141452..789..864932.43682.197.9237146828.453976...9.85.29547.28.1 E1: 1,3 # 11 pairs * PAIR I1: 1,3 COL I I4: 1,3,5,7 # reduction candidate for 1,3 I4: 1,3 # 12 pairs I4: 5,7 # 11 pairs * PAIR A6: 5,7 BLK 4 A4: 5,7,4,6 # reduction candidate for 5,7 A4: 5,7 # 16 pairs B4: 5,7,1 # reduction candidate for 5,7 B4: 5,7 # 14 pairs A5: 5,7,4,6 # reduction candidate for 5,7 A5: 5,7 => CTR * 9278.465.86359.2.41452.6.894186.9.2..3642.89..9238.46.28..531.6.7...85.2.547.29.8 A5: 4,6 # 10 pairs * PAIR A6: 5,7 ROW 6 E6: 5,7,1,8 # reduction candidate for 5,7 E6: 5,7 # 19 pairs F6: 5,7,1 # reduction candidate for 5,7 F6: 5,7 # 12 pairs I6: 5,7,1,8 # reduction candidate for 5,7 I6: 5,7 => CTR * .2.81465386359....1452.6789..8.7932..3..25.9..9238146.287.53.46.1.9485729547..... I6: 1,8 # 10 pairs * PAIR B8: 1,7 BLK 7 C7: 1,7,9 # reduction candidate for 1,7 C7: 1,7 # 11 pairs C8: 1,7,6,9 # reduction candidate for 1,7 C8: 1,7 => CTR * .278.465.86359.2.41452.6.89.18..9.2..36.2.89..9238.46.289..3176.719.8542.54712938 C8: 6,9 # 10 pairs * PAIR B8: 1,7 ROW 8 H8: 1,7,3,4 # reduction candidate for 1,7 H8: 1,7 # 12 pairs I8: 1,7,2,4 # reduction candidate for 1,7 I8: 1,7 => CTR * 8279.465.96358...41456...89..8..9.2.43682..9..923..4682814..976.792.8541.5479.8.2 I8: 2,4 # 10 pairs * PAIR B8: 1,7 COL B B4: 1,7,5 # reduction candidate for 1,7 B4: 5 # 18 pairs B4: 1,7 # 9 pairs * PAIR B9: 1,5 COL B B4: 1,5,7 # reduction candidate for 1,5 B4: 7 # 13 pairs B4: 1,5 # 10 pairs * PAIR H9: 1,3 BLK 9 H7: 1,3,4,7 # reduction candidate for 1,3 H7: 1,3 # 14 pairs H8: 1,3,4,7 # reduction candidate for 1,3 H8: 1,3 # 16 pairs * PAIR H9: 1,3 ROW 9 E9: 1,3,6,9 # reduction candidate for 1,3 E9: 1,3 # 13 pairs F9: 1,3,2,6 # reduction candidate for 1,3 F9: 1,3 => CTR * .2...465..635.....1456...896.8..9.2.43..26.95.923..46.28....9.63.62985..95476.... F9: 2,6 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0097-base-pr-000.dot * REASONING * PRF # A1: 8 => SOL * DIS # E1: 8,9 => CTR => E1: 1,3 * DIS # E1: 8,9 => CTR => E1: 1,3 * DIS # A5: 5,7 => CTR => A5: 4,6 * DIS # I6: 5,7 => CTR => I6: 1,8 * DIS # C8: 1,7 => CTR => C8: 6,9 * DIS # I8: 1,7 => CTR => I8: 2,4 * DIS # F9: 1,3 => CTR => F9: 2,6 * CNT 8 HDP CHAINS / 40 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,B8,B9,C1,D3,E2,H9,I1) * .2...465..635.....145....89..8..9.2..3..2..9..923..46.28......6.....85....47..... * PAIR C1: 7,9 BLK 1 A1: 7,9,8 # reduction candidate for 7,9 A1: 8 => SOLVED * 827914653963587214145236789718649325436825197592371468281453976379168542654792831 * DURATION: 0:00:03.091412 START: 05:15:24.116285 END: 05:15:27.207697 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0097-base-pr-001.dot * REASONING * PRF # A1: 8 => SOL * STA A1: 8 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=97
Solution
position: 827914653963587214145236789718649325436825197592371468281453976379168542654792831 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 # A1: 7,9 => UNS * PRF # A1: 8 => SOL * INC # C7: 7,9 => UNS * INC # C8: 7,9 => UNS * INC # A1: 8,9 => UNS * INC # A1: 7 => UNS * INC # D1: 8,9 => UNS * DIS # E1: 8,9 => CTR => E1: 1,3 * INC # E1: 1,3 => UNS * INC # F3: 2,6 => UNS * INC # F3: 3,7 => UNS * INC # D8: 2,6 => UNS * INC # D8: 1,4,9 => UNS * INC # E1: 1,3 => UNS * DIS # E1: 8,9 => CTR => E1: 1,3 * INC # I4: 1,3 => UNS * INC # I4: 5,7 => UNS * INC # A4: 5,7 => UNS * INC # B4: 5,7 => UNS * DIS # A5: 5,7 => CTR => A5: 4,6 * INC # A5: 4,6 => UNS * INC # E6: 5,7 => UNS * INC # F6: 5,7 => UNS * DIS # I6: 5,7 => CTR => I6: 1,8 * INC # I6: 1,8 => UNS * INC # C7: 1,7 => UNS * DIS # C8: 1,7 => CTR => C8: 6,9 * INC # C8: 6,9 => UNS * INC # H8: 1,7 => UNS * DIS # I8: 1,7 => CTR => I8: 2,4 * INC # I8: 2,4 => UNS * INC # B4: 1,7 => UNS * INC # B4: 5 => UNS * INC # B4: 1,5 => UNS * INC # B4: 7 => UNS * INC # H7: 1,3 => UNS * INC # H8: 1,3 => UNS * INC # E9: 1,3 => UNS * DIS # F9: 1,3 => CTR => F9: 2,6 * INC # F9: 2,6 => UNS * CNT 40 HDP CHAINS / 40 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 7,9 => UNS * PRF # A1: 8 => SOL * STA A1: 8 * CNT 2 HDP CHAINS / 2 HYP OPENED