Analysis of zz-www.sudokuwiki.org-0120-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=120
level: medium
position: 39..1.2....6......4....63.9...9....5..97.48..6....3...7.28....3......9....4.3..81 initial
Autosolve
position: 39..1.2....63.....4....63.9...9....5..97.48..6....3.9.7.28....3......9..9.4.3..81 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H4: 2,6 => CTR => H4: 1,3,4,7 * DIS # G9: 5,6 => CTR => G9: 7 * CNT 2 HDP CHAINS / 25 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H4: 2,6 => CTR => H4: 1,3,4,7 * DIS H4: 1,3,4,7 # G9: 5,6 => CTR => G9: 7 * DIS H4: 1,3,4,7 + G9: 7 # B7: 5,6 => CTR => B7: 1 * PRF H4: 1,3,4,7 + G9: 7 + B7: 1 # B8: 3,8 => SOL * STA H4: 1,3,4,7 + G9: 7 + B7: 1 + B8: 3,8 * CNT 4 HDP CHAINS / 31 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 39..1.2....6......4....63.9...9....5..97.48..6....3...7.28....3......9....4.3..81 | initial |
| 39..1.2....63.....4....63.9...9....5..97.48..6....3.9.7.28....3......9..9.4.3..81 | autosolve |
| 395417268876392514421586379247968135139754826658123497712849653583671942964235781 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (4) D1: 4,5 D3: 2,5 I5: 2,6 B9: 5,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F4,D6: 1.. / F4 = 1 => 22 pairs (_) / D6 = 1 => 8 pairs (_) B7,F7: 1.. / B7 = 1 => 7 pairs (_) / F7 = 1 => 10 pairs (_) D6,D8: 1.. / D6 = 1 => 8 pairs (_) / D8 = 1 => 22 pairs (_) D9,F9: 2.. / D9 = 2 => 9 pairs (_) / F9 = 2 => 7 pairs (_) H8,I8: 2.. / H8 = 2 => 4 pairs (_) / I8 = 2 => 9 pairs (_) H4,H5: 3.. / H4 = 3 => 4 pairs (_) / H5 = 3 => 5 pairs (_) B8,C8: 3.. / B8 = 3 => 5 pairs (_) / C8 = 3 => 4 pairs (_) B5,H5: 3.. / B5 = 3 => 4 pairs (_) / H5 = 3 => 5 pairs (_) C4,C8: 3.. / C4 = 3 => 5 pairs (_) / C8 = 3 => 4 pairs (_) D1,E2: 4.. / D1 = 4 => 3 pairs (_) / E2 = 4 => 0 pairs (X) B4,B6: 4.. / B4 = 4 => 4 pairs (_) / B6 = 4 => 6 pairs (_) D1,D8: 4.. / D1 = 4 => 3 pairs (_) / D8 = 4 => 0 pairs (X) H1,I1: 6.. / H1 = 6 => 5 pairs (_) / I1 = 6 => 7 pairs (_) E4,E5: 6.. / E4 = 6 => 6 pairs (_) / E5 = 6 => 8 pairs (_) D8,D9: 6.. / D8 = 6 => 8 pairs (_) / D9 = 6 => 7 pairs (_) F9,G9: 7.. / F9 = 7 => 0 pairs (X) / G9 = 7 => 6 pairs (_) I1,I2: 8.. / I1 = 8 => 7 pairs (_) / I2 = 8 => 4 pairs (_) E2,F2: 9.. / E2 = 9 => 6 pairs (_) / F2 = 9 => 5 pairs (_) E7,F7: 9.. / E7 = 9 => 5 pairs (_) / F7 = 9 => 6 pairs (_) E2,E7: 9.. / E2 = 9 => 6 pairs (_) / E7 = 9 => 5 pairs (_) F2,F7: 9.. / F2 = 9 => 5 pairs (_) / F7 = 9 => 6 pairs (_) * DURATION: 0:00:25.340241 START: 05:41:29.179184 END: 05:41:54.519425 2017-05-01 * CP COUNT: (21) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,D1,D3,I5) * 39..1.2....63.....4....63.9...9....5..97.48..6....3.9.7.28....3......9..9.4.3..81 * PAIR D1: 4,5 BLK 2 E2: 4,5,2,7,8,9 # reduction candidate for 4,5 E2: 4,5 # 17 pairs E2: 2,7,8,9 # 3 pairs * PAIR D1: 4,5 ROW 1 H1: 4,5,6,7 # reduction candidate for 4,5 H1: 4,5 # 10 pairs H1: 6,7 # 5 pairs * PAIR D1: 4,5 COL D D8: 4,5,1,6 # reduction candidate for 4,5 D8: 4,5 # 18 pairs D8: 1,6 # 4 pairs * PAIR D3: 2,5 BLK 2 E2: 2,5,4,7,8,9 # reduction candidate for 2,5 E2: 2,5 # 12 pairs F2: 2,5,7,8,9 # reduction candidate for 2,5 F2: 2,5 # 11 pairs E3: 2,5,7,8 # reduction candidate for 2,5 E3: 2,5 # 13 pairs * PAIR D3: 2,5 ROW 3 B3: 2,5,1,7,8 # reduction candidate for 2,5 B3: 2,5 # 7 pairs B3: 1,7,8 # 4 pairs * PAIR D3: 2,5 COL D D6: 2,5,1 # reduction candidate for 2,5 D6: 2,5 # 22 pairs D9: 2,5,6 # reduction candidate for 2,5 D9: 2,5 # 8 pairs * PAIR I5: 2,6 BLK 6 H4: 2,6,1,3,4,7 # reduction candidate for 2,6 H4: 2,6 => CTR * 39.41.2..5.63.....4.1..63.9...9.14.51.97.483.64...31977128..6.3.631..9..954632781 H4: 1,3,4,7 # 4 pairs H5: 2,6,1,3 # reduction candidate for 2,6 H5: 2,6 # 15 pairs * PAIR I5: 2,6 ROW 5 E5: 2,6,5 # reduction candidate for 2,6 E5: 5 # 10 pairs E5: 2,6 # 7 pairs * PAIR I5: 2,6 COL I I8: 2,6,4,7 # reduction candidate for 2,6 I8: 2,6 # 7 pairs I8: 4,7 # 5 pairs * PAIR B9: 5,6 BLK 7 B7: 5,6,1 # reduction candidate for 5,6 B7: 5,6 # 10 pairs B8: 5,6,1,3,8 # reduction candidate for 5,6 B8: 5,6 # 9 pairs * PAIR B9: 5,6 ROW 9 D9: 5,6,2 # reduction candidate for 5,6 D9: 5,6 # 7 pairs G9: 5,6,7 # reduction candidate for 5,6 G9: 5,6 => CTR * 39.4182..2.6379..8478526319847962135.397548..6251.37947.289...3...64.9..9.4237.81 G9: 7 # 6 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0120-base-pr-000.dot * REASONING * DIS # H4: 2,6 => CTR => H4: 1,3,4,7 * DIS # G9: 5,6 => CTR => G9: 7 * CNT 2 HDP CHAINS / 25 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,D1,D3,I5) * 39..1.2....63.....4....63.9...9....5..97.48..6....3.9.7.28....3......9..9.4.3..81 * PAIR D1: 4,5 BLK 2 E2: 4,5,2,7,8,9 # reduction candidate for 4,5 E2: 4,5 # 17 pairs E2: 2,7,8,9 # 3 pairs * PAIR D1: 4,5 ROW 1 H1: 4,5,6,7 # reduction candidate for 4,5 H1: 4,5 # 10 pairs H1: 6,7 # 5 pairs * PAIR D1: 4,5 COL D D8: 4,5,1,6 # reduction candidate for 4,5 D8: 4,5 # 18 pairs D8: 1,6 # 4 pairs * PAIR D3: 2,5 BLK 2 E2: 2,5,4,7,8,9 # reduction candidate for 2,5 E2: 2,5 # 12 pairs F2: 2,5,7,8,9 # reduction candidate for 2,5 F2: 2,5 # 11 pairs E3: 2,5,7,8 # reduction candidate for 2,5 E3: 2,5 # 13 pairs * PAIR D3: 2,5 ROW 3 B3: 2,5,1,7,8 # reduction candidate for 2,5 B3: 2,5 # 7 pairs B3: 1,7,8 # 4 pairs * PAIR D3: 2,5 COL D D6: 2,5,1 # reduction candidate for 2,5 D6: 2,5 # 22 pairs D9: 2,5,6 # reduction candidate for 2,5 D9: 2,5 # 8 pairs * PAIR I5: 2,6 BLK 6 H4: 2,6,1,3,4,7 # reduction candidate for 2,6 H4: 2,6 => CTR * 39.41.2..5.63.....4.1..63.9...9.14.51.97.483.64...31977128..6.3.631..9..954632781 H5: 2,6,1,3 # reduction candidate for 2,6 H5: 2,6 # 15 pairs * RESTART * PAIR I5: 2,6 BLK 6 H5: 2,6,1,3 # reduction candidate for 2,6 H5: 2,6 # 15 pairs H5: 1,3 # 5 pairs * PAIR I5: 2,6 ROW 5 E5: 2,6,5 # reduction candidate for 2,6 E5: 5 # 10 pairs E5: 2,6 # 7 pairs * PAIR I5: 2,6 COL I I8: 2,6,4,7 # reduction candidate for 2,6 I8: 2,6 # 9 pairs I8: 4,7 # 5 pairs * PAIR B9: 5,6 BLK 7 B7: 5,6,1 # reduction candidate for 5,6 B7: 5,6 # 10 pairs B8: 5,6,1,3,8 # reduction candidate for 5,6 B8: 5,6 # 9 pairs * PAIR B9: 5,6 ROW 9 D9: 5,6,2 # reduction candidate for 5,6 D9: 5,6 # 7 pairs G9: 5,6,7 # reduction candidate for 5,6 G9: 5,6 => CTR * 39.4182..2.6379..8478526319847962135.397548..6251.37947.289...3...64.9..9.4237.81 * RESTART * PAIR B9: 5,6 ROW 9 D9: 5,6,2 # reduction candidate for 5,6 D9: 2 # 16 pairs D9: 5,6 # 7 pairs * PAIR RESTART * PAIR B9: 5,6 BLK 7 B7: 5,6,1 # reduction candidate for 5,6 B7: 5,6 => CTR * 39..1726...6349..84.1286359.479.8635.397648126851.34977.2891.43.13.75926954632781 B8: 5,6,3,8 # reduction candidate for 5,6 B8: 5,6 # 11 pairs * RESTART * PAIR B9: 5,6 BLK 7 B8: 5,6,3,8 # reduction candidate for 5,6 B8: 3,8 => SOLVED * 395417268876392514421586379247968135139754826658123497712849653583671942964235781 * DURATION: 0:00:23.375618 START: 05:42:11.492687 END: 05:42:34.868305 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0120-base-pr-001.dot * REASONING * DIS # H4: 2,6 => CTR => H4: 1,3,4,7 * DIS H4: 1,3,4,7 # G9: 5,6 => CTR => G9: 7 * DIS H4: 1,3,4,7 + G9: 7 # B7: 5,6 => CTR => B7: 1 * PRF H4: 1,3,4,7 + G9: 7 + B7: 1 # B8: 3,8 => SOL * STA H4: 1,3,4,7 + G9: 7 + B7: 1 + B8: 3,8 * CNT 4 HDP CHAINS / 31 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=120
Solution
position: 395417268876392514421586379247968135139754826658123497712849653583671942964235781 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 # E2: 4,5 => UNS * INC # E2: 2,7,8,9 => UNS * INC # H1: 4,5 => UNS * INC # H1: 6,7 => UNS * INC # D8: 4,5 => UNS * INC # D8: 1,6 => UNS * INC # E2: 2,5 => UNS * INC # F2: 2,5 => UNS * INC # E3: 2,5 => UNS * INC # B3: 2,5 => UNS * INC # B3: 1,7,8 => UNS * INC # D6: 2,5 => UNS * INC # D9: 2,5 => UNS * DIS # H4: 2,6 => CTR => H4: 1,3,4,7 * INC # H4: 1,3,4,7 => UNS * INC # H5: 2,6 => UNS * INC # E5: 2,6 => UNS * INC # E5: 5 => UNS * INC # I8: 2,6 => UNS * INC # I8: 4,7 => UNS * INC # B7: 5,6 => UNS * INC # B8: 5,6 => UNS * INC # D9: 5,6 => UNS * DIS # G9: 5,6 => CTR => G9: 7 * INC # G9: 7 => UNS * CNT 25 HDP CHAINS / 25 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E2: 4,5 => UNS * INC # E2: 2,7,8,9 => UNS * INC # H1: 4,5 => UNS * INC # H1: 6,7 => UNS * INC # D8: 4,5 => UNS * INC # D8: 1,6 => UNS * INC # E2: 2,5 => UNS * INC # F2: 2,5 => UNS * INC # E3: 2,5 => UNS * INC # B3: 2,5 => UNS * INC # B3: 1,7,8 => UNS * INC # D6: 2,5 => UNS * INC # D9: 2,5 => UNS * DIS # H4: 2,6 => CTR => H4: 1,3,4,7 * INC H4: 1,3,4,7 # H5: 2,6 => UNS * INC H4: 1,3,4,7 # H5: 2,6 => UNS * INC H4: 1,3,4,7 # H5: 1,3 => UNS * INC H4: 1,3,4,7 # E5: 2,6 => UNS * INC H4: 1,3,4,7 # E5: 5 => UNS * INC H4: 1,3,4,7 # I8: 2,6 => UNS * INC H4: 1,3,4,7 # I8: 4,7 => UNS * INC H4: 1,3,4,7 # B7: 5,6 => UNS * INC H4: 1,3,4,7 # B8: 5,6 => UNS * INC H4: 1,3,4,7 # D9: 5,6 => UNS * DIS H4: 1,3,4,7 # G9: 5,6 => CTR => G9: 7 * INC H4: 1,3,4,7 + G9: 7 # D9: 5,6 => UNS * INC H4: 1,3,4,7 + G9: 7 # D9: 2 => UNS * DIS H4: 1,3,4,7 + G9: 7 # B7: 5,6 => CTR => B7: 1 * INC H4: 1,3,4,7 + G9: 7 + B7: 1 # B8: 5,6 => UNS * INC H4: 1,3,4,7 + G9: 7 + B7: 1 # B8: 5,6 => UNS * PRF H4: 1,3,4,7 + G9: 7 + B7: 1 # B8: 3,8 => SOL * STA H4: 1,3,4,7 + G9: 7 + B7: 1 + B8: 3,8 * CNT 31 HDP CHAINS / 31 HYP OPENED