Analysis of zz-www.sudokuwiki.org-0061-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=61
level: medium
position: .7.....8.4..8....25..4..9......23.5...39.41...2.78......7..9..11....8..9.6.....3. initial
Autosolve
position: .7.....8.4..8....25..4..9......23.5...39.412.62.78..9...7..9..11....8..9.6.....3. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A4: 9 => SOL * PRF # I5: 6 => SOL * CNT 2 HDP CHAINS / 19 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A4: 9 => SOL * STA A4: 9 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .7.....8.4..8....25..4..9......23.5...39.41...2.78......7..9..11....8..9.6.....3. | initial |
| .7.....8.4..8....25..4..9......23.5...39.412.62.78..9...7..9..11....8..9.6.....3. | autosolve |
| 271396584496875312538412967914623758783954126625781493357269841142538679869147235 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) A5: 7,8 B5: 5,8 C6: 1,5 D4: 1,6 E5: 5,6 F6: 1,5 G6: 3,4 I6: 3,4 H7: 4,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H2,H3: 1.. / H2 = 1 => 12 pairs (_) / H3 = 1 => 0 pairs (X) D4,F6: 1.. / D4 = 1 => 10 pairs (_) / F6 = 1 => 0 pairs (*) C6,F6: 1.. / C6 = 1 => 10 pairs (_) / F6 = 1 => 0 pairs (*) C3,F3: 2.. / C3 = 2 => 0 pairs (X) / F3 = 2 => 9 pairs (_) G6,I6: 3.. / G6 = 3 => 7 pairs (_) / I6 = 3 => 12 pairs (_) A1,A7: 3.. / A1 = 3 => 13 pairs (_) / A7 = 3 => 20 pairs (_) G1,I1: 4.. / G1 = 4 => 7 pairs (_) / I1 = 4 => 12 pairs (_) B4,C4: 4.. / B4 = 4 => 0 pairs (X) / C4 = 4 => 10 pairs (_) G6,I6: 4.. / G6 = 4 => 12 pairs (_) / I6 = 4 => 7 pairs (_) H7,H8: 4.. / H7 = 4 => 9 pairs (_) / H8 = 4 => 13 pairs (_) C9,E9: 4.. / C9 = 4 => 0 pairs (X) / E9 = 4 => 9 pairs (_) G1,G6: 4.. / G1 = 4 => 7 pairs (_) / G6 = 4 => 12 pairs (_) I1,I6: 4.. / I1 = 4 => 12 pairs (_) / I6 = 4 => 7 pairs (_) B5,C6: 5.. / B5 = 5 => 10 pairs (_) / C6 = 5 => 0 pairs (*) E5,F6: 5.. / E5 = 5 => 0 pairs (*) / F6 = 5 => 0 pairs (X) B5,E5: 5.. / B5 = 5 => 10 pairs (_) / E5 = 5 => 0 pairs (*) C6,F6: 5.. / C6 = 5 => 0 pairs (*) / F6 = 5 => 0 pairs (X) I1,I9: 5.. / I1 = 5 => 12 pairs (_) / I9 = 5 => 12 pairs (_) D4,E5: 6.. / D4 = 6 => 0 pairs (*) / E5 = 6 => 0 pairs (X) E5,I5: 6.. / E5 = 6 => 10 pairs (_) / I5 = 6 => 0 pairs (*) A4,A5: 7.. / A4 = 7 => 16 pairs (_) / A5 = 7 => 10 pairs (_) A5,I5: 7.. / A5 = 7 => 10 pairs (_) / I5 = 7 => 16 pairs (_) B3,C3: 8.. / B3 = 8 => 0 pairs (X) / C3 = 8 => 11 pairs (_) E1,E2: 9.. / E1 = 9 => 10 pairs (_) / E2 = 9 => 0 pairs (X) A9,C9: 9.. / A9 = 9 => 15 pairs (_) / C9 = 9 => 11 pairs (_) B2,B4: 9.. / B2 = 9 => 11 pairs (_) / B4 = 9 => 0 pairs (X) * DURATION: 0:00:37.354550 START: 04:31:13.978951 END: 04:31:51.333501 2017-05-01 * CP COUNT: (26) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B5,C6,D4,E5,F6,G6,H7,I6) * .7.....8.4..8....25..4..9......23.5...39.412.62.78..9...7..9..11....8..9.6.....3. * PAIR A5: 7,8 BLK 4 A4: 7,8,9 # reduction candidate for 7,8 A4: 9 => SOLVED * 271396584496875312538412967914623758783954126625781493357269841142538679869147235 A4: 7,8 # 15 pairs * PAIR A5: 7,8 ROW 5 I5: 7,8,6 # reduction candidate for 7,8 I5: 6 => SOLVED * 271396584496875312538412967914623758783954126625781493357269841142538679869147235 I5: 7,8 # 10 pairs * PAIR B5: 5,8 COL B B7: 5,8,3,4 # reduction candidate for 5,8 B7: 5,8 # 13 pairs B7: 3,4 # 10 pairs * PAIR E5: 5,6 COL E E7: 5,6,3,4 # reduction candidate for 5,6 E7: 5,6 # 10 pairs E8: 5,6,3,4,7 # reduction candidate for 5,6 E8: 5,6 # 12 pairs * PAIR F6: 1,5 COL F F1: 1,5,2,6 # reduction candidate for 1,5 F1: 1,5 # 12 pairs F2: 1,5,6,7 # reduction candidate for 1,5 F2: 1,5 # 12 pairs F9: 1,5,2,7 # reduction candidate for 1,5 F9: 1,5 # 13 pairs * PAIR G6: 3,4 COL G G1: 3,4,5,6 # reduction candidate for 3,4 G1: 5,6 # 11 pairs G1: 3,4 # 10 pairs * PAIR I6: 3,4 COL I I1: 3,4,5,6 # reduction candidate for 3,4 I1: 3,4 # 14 pairs I1: 5,6 # 10 pairs * PAIR H7: 4,6 BLK 9 H8: 4,6,7 # reduction candidate for 4,6 H8: 7 # 13 pairs H8: 4,6 # 13 pairs * PAIR H7: 4,6 ROW 7 E7: 4,6,3,5 # reduction candidate for 4,6 E7: 4,6 # 10 pairs E7: 3,5 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0061-base-pr-000.dot * REASONING * PRF # A4: 9 => SOL * PRF # I5: 6 => SOL * CNT 2 HDP CHAINS / 19 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B5,C6,D4,E5,F6,G6,H7,I6) * .7.....8.4..8....25..4..9......23.5...39.412.62.78..9...7..9..11....8..9.6.....3. * PAIR A5: 7,8 BLK 4 A4: 7,8,9 # reduction candidate for 7,8 A4: 9 => SOLVED * 271396584496875312538412967914623758783954126625781493357269841142538679869147235 * DURATION: 0:00:03.228521 START: 04:32:06.099165 END: 04:32:09.327686 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0061-base-pr-001.dot * REASONING * PRF # A4: 9 => SOL * STA A4: 9 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=61
Solution
position: 271396584496875312538412967914623758783954126625781493357269841142538679869147235 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 # A4: 7,8 => UNS * PRF # A4: 9 => SOL * INC # I5: 7,8 => UNS * PRF # I5: 6 => SOL * INC # B7: 5,8 => UNS * INC # B7: 3,4 => UNS * INC # E7: 5,6 => UNS * INC # E8: 5,6 => UNS * INC # F1: 1,5 => UNS * INC # F2: 1,5 => UNS * INC # F9: 1,5 => UNS * INC # G1: 3,4 => UNS * INC # G1: 5,6 => UNS * INC # I1: 3,4 => UNS * INC # I1: 5,6 => UNS * INC # H8: 4,6 => UNS * INC # H8: 7 => UNS * INC # E7: 4,6 => UNS * INC # E7: 3,5 => UNS * CNT 19 HDP CHAINS / 19 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A4: 7,8 => UNS * PRF # A4: 9 => SOL * STA A4: 9 * CNT 2 HDP CHAINS / 2 HYP OPENED