Analysis of zz-www.sudokuwiki.org-0046-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=46
level: medium
position: .32.5..9.8.....6....74.6..2.8....5.....1.9.....3....6.7..6.31....4.....6.6..2.83. initial
Autosolve
position: 632.5..9.84....6....74.63.2.8....5.....1.9.....3....6.7.86.31..3.4.....6.6..2.83. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D6: 7,8 => CTR => D6: 2,5 * PRF # I1: 4,7 => SOL * CNT 2 HDP CHAINS / 13 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D6: 7,8 => CTR => D6: 2,5 * PRF D6: 2,5 # I1: 4,7 => SOL * STA D6: 2,5 + I1: 4,7 * CNT 2 HDP CHAINS / 15 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .32.5..9.8.....6....74.6..2.8....5.....1.9.....3....6.7..6.31....4.....6.6..2.83. | initial |
| 632.5..9.84....6....74.63.2.8....5.....1.9.....3....6.7.86.31..3.4.....6.6..2.83. | autosolve |
| 632851497849372615517496382981764523256139748473285961728643159394518276165927834 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) D1: 7,8 G1: 4,7 B5: 5,7 C5: 5,6 E7: 4,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F1,I1: 1.. / F1 = 1 => 7 pairs (_) / I1 = 1 => 20 pairs (_) D2,F2: 2.. / D2 = 2 => 0 pairs (X) / F2 = 2 => 6 pairs (_) B7,B8: 2.. / B7 = 2 => 7 pairs (_) / B8 = 2 => 8 pairs (_) B7,H7: 2.. / B7 = 2 => 7 pairs (_) / H7 = 2 => 8 pairs (_) D2,E2: 3.. / D2 = 3 => 12 pairs (_) / E2 = 3 => 5 pairs (_) I4,I5: 3.. / I4 = 3 => 12 pairs (_) / I5 = 3 => 5 pairs (_) E5,I5: 3.. / E5 = 3 => 12 pairs (_) / I5 = 3 => 5 pairs (_) D2,D4: 3.. / D2 = 3 => 12 pairs (_) / D4 = 3 => 5 pairs (_) G1,I1: 4.. / G1 = 4 => 5 pairs (_) / I1 = 4 => 0 pairs (X) E7,F9: 4.. / E7 = 4 => 7 pairs (_) / F9 = 4 => 0 pairs (X) F9,I9: 4.. / F9 = 4 => 0 pairs (X) / I9 = 4 => 7 pairs (_) D6,F6: 5.. / D6 = 5 => 12 pairs (_) / F6 = 5 => 5 pairs (_) C4,C5: 6.. / C4 = 6 => 0 pairs (X) / C5 = 6 => 5 pairs (_) E4,E5: 6.. / E4 = 6 => 5 pairs (_) / E5 = 6 => 0 pairs (X) C4,E4: 6.. / C4 = 6 => 0 pairs (X) / E4 = 6 => 5 pairs (_) C5,E5: 6.. / C5 = 6 => 5 pairs (_) / E5 = 6 => 0 pairs (X) B5,B6: 7.. / B5 = 7 => 6 pairs (_) / B6 = 7 => 10 pairs (_) I1,H3: 8.. / I1 = 8 => 0 pairs (X) / H3 = 8 => 13 pairs (_) E3,H3: 8.. / E3 = 8 => 0 pairs (X) / H3 = 8 => 13 pairs (_) H3,H5: 8.. / H3 = 8 => 13 pairs (_) / H5 = 8 => 0 pairs (X) G6,G8: 9.. / G6 = 9 => 7 pairs (_) / G8 = 9 => 6 pairs (_) * DURATION: 0:00:27.107096 START: 04:20:14.370803 END: 04:20:41.477899 2017-05-01 * CP COUNT: (21) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,C5,D1,E7,G1) * 632.5..9.84....6....74.63.2.8....5.....1.9.....3....6.7.86.31..3.4.....6.6..2.83. * PAIR D1: 7,8 BLK 2 F1: 7,8,1 # reduction candidate for 7,8 F1: 7,8 # 20 pairs F1: 1 # 7 pairs * PAIR D1: 7,8 ROW 1 I1: 7,8,1,4 # reduction candidate for 7,8 I1: 1,4 # 14 pairs I1: 7,8 # 8 pairs * PAIR D1: 7,8 COL D D6: 7,8,2,5 # reduction candidate for 7,8 D6: 7,8 => CTR * 632.5.49.84...26....74.6382.8.2.451.2..1.974.4.3..526.7.86431..3.4...976.6.927834 D6: 2,5 # 6 pairs D8: 7,8,5,9 # reduction candidate for 7,8 D8: 7,8 # 11 pairs * PAIR G1: 4,7 BLK 3 I1: 4,7,1,8 # reduction candidate for 4,7 I1: 4,7 => SOLVED * 632851497849372615517496382981764523256139748473285961728643159394518276165927834 I1: 1,8 # 7 pairs * PAIR G1: 4,7 COL G G5: 4,7,2 # reduction candidate for 4,7 G5: 4,7 # 8 pairs G6: 4,7,2,9 # reduction candidate for 4,7 G6: 4,7 # 8 pairs * PAIR E7: 4,9 ROW 7 I7: 4,9,5 # reduction candidate for 4,9 I7: 5 # 9 pairs I7: 4,9 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0046-base-pr-000.dot * REASONING * DIS # D6: 7,8 => CTR => D6: 2,5 * PRF # I1: 4,7 => SOL * CNT 2 HDP CHAINS / 13 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,C5,D1,E7,G1) * 632.5..9.84....6....74.63.2.8....5.....1.9.....3....6.7.86.31..3.4.....6.6..2.83. * PAIR D1: 7,8 BLK 2 F1: 7,8,1 # reduction candidate for 7,8 F1: 7,8 # 20 pairs F1: 1 # 7 pairs * PAIR D1: 7,8 ROW 1 I1: 7,8,1,4 # reduction candidate for 7,8 I1: 1,4 # 14 pairs I1: 7,8 # 8 pairs * PAIR D1: 7,8 COL D D6: 7,8,2,5 # reduction candidate for 7,8 D6: 7,8 => CTR * 632.5.49.84...26....74.6382.8.2.451.2..1.974.4.3..526.7.86431..3.4...976.6.927834 D8: 7,8,5,9 # reduction candidate for 7,8 D8: 7,8 # 11 pairs * RESTART * PAIR D1: 7,8 COL D D8: 7,8,5,9 # reduction candidate for 7,8 D8: 5,9 # 17 pairs D8: 7,8 # 11 pairs * PAIR RESTART * PAIR D1: 7,8 BLK 2 F1: 7,8,1 # reduction candidate for 7,8 F1: 7,8 # 21 pairs F1: 1 # 8 pairs * PAIR D1: 7,8 ROW 1 I1: 7,8,1,4 # reduction candidate for 7,8 I1: 1,4 # 15 pairs I1: 7,8 # 9 pairs * PAIR D1: 7,8 COL D D8: 7,8,5,9 # reduction candidate for 7,8 D8: 5,9 # 17 pairs D8: 7,8 # 11 pairs * PAIR G1: 4,7 BLK 3 I1: 4,7,1,8 # reduction candidate for 4,7 I1: 4,7 => SOLVED * 632851497849372615517496382981764523256139748473285961728643159394518276165927834 * DURATION: 0:00:13.079119 START: 04:20:51.252690 END: 04:21:04.331809 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0046-base-pr-001.dot * REASONING * DIS # D6: 7,8 => CTR => D6: 2,5 * PRF D6: 2,5 # I1: 4,7 => SOL * STA D6: 2,5 + I1: 4,7 * CNT 2 HDP CHAINS / 15 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=46
Solution
position: 632851497849372615517496382981764523256139748473285961728643159394518276165927834 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 # F1: 7,8 => UNS * INC # F1: 1 => UNS * INC # I1: 7,8 => UNS * INC # I1: 1,4 => UNS * DIS # D6: 7,8 => CTR => D6: 2,5 * INC # D6: 2,5 => UNS * INC # D8: 7,8 => UNS * PRF # I1: 4,7 => SOL * INC # I1: 1,8 => UNS * INC # G5: 4,7 => UNS * INC # G6: 4,7 => UNS * INC # I7: 4,9 => UNS * INC # I7: 5 => UNS * CNT 13 HDP CHAINS / 13 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F1: 7,8 => UNS * INC # F1: 1 => UNS * INC # I1: 7,8 => UNS * INC # I1: 1,4 => UNS * DIS # D6: 7,8 => CTR => D6: 2,5 * INC D6: 2,5 # D8: 7,8 => UNS * INC D6: 2,5 # D8: 7,8 => UNS * INC D6: 2,5 # D8: 5,9 => UNS * INC D6: 2,5 # F1: 7,8 => UNS * INC D6: 2,5 # F1: 1 => UNS * INC D6: 2,5 # I1: 7,8 => UNS * INC D6: 2,5 # I1: 1,4 => UNS * INC D6: 2,5 # D8: 7,8 => UNS * INC D6: 2,5 # D8: 5,9 => UNS * PRF D6: 2,5 # I1: 4,7 => SOL * STA D6: 2,5 + I1: 4,7 * CNT 15 HDP CHAINS / 15 HYP OPENED