Analysis of zz-www.sudokuwiki.org-0268-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=268
level: medium
position: 1....4....34.6....6..7.2..4..6.5..4....6.8....2..4.9..5..4.6..7....9.16....3....2 initial
Autosolve
position: 1....46...34.6....6..7.2..4..6.5..4....6.8....2.14.9.65..4.6..7....9.16..6.3..4.2 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H1: 3,8 => CTR => H1: 2,5,7 * PRF # F4: 3,7 => SOL * DIS # C6: 3,7 => CTR => C6: 5,8 * DIS # H7: 3,8 => CTR => H7: 9 * CNT 4 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H1: 3,8 => CTR => H1: 2,5,7 * PRF H1: 2,5,7 # F4: 3,7 => SOL * STA H1: 2,5,7 + F4: 3,7 * CNT 2 HDP CHAINS / 13 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1....4....34.6....6..7.2..4..6.5..4....6.8....2..4.9..5..4.6..7....9.16....3....2 | initial |
| 1....46...34.6....6..7.2..4..6.5..4....6.8....2.14.9.65..4.6..7....9.16..6.3..4.2 | autosolve |
| 187534629234869715659712834876953241491628573325147986512486397743295168968371452 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) E1: 3,8 D4: 2,9 E5: 2,7 F6: 3,7 F8: 5,7 G7: 3,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F2,E3: 1.. / F2 = 1 => 10 pairs (_) / E3 = 1 => 13 pairs (_) E3,H3: 1.. / E3 = 1 => 13 pairs (_) / H3 = 1 => 10 pairs (_) B4,I4: 1.. / B4 = 1 => 11 pairs (_) / I4 = 1 => 12 pairs (_) F2,F9: 1.. / F2 = 1 => 10 pairs (_) / F9 = 1 => 13 pairs (_) C1,A2: 2.. / C1 = 2 => 14 pairs (_) / A2 = 2 => 6 pairs (_) D4,E5: 2.. / D4 = 2 => 7 pairs (_) / E5 = 2 => 0 pairs (*) E7,D8: 2.. / E7 = 2 => 7 pairs (_) / D8 = 2 => 0 pairs (*) C1,H1: 2.. / C1 = 2 => 14 pairs (_) / H1 = 2 => 6 pairs (_) D4,G4: 2.. / D4 = 2 => 7 pairs (_) / G4 = 2 => 0 pairs (*) C7,E7: 2.. / C7 = 2 => 0 pairs (*) / E7 = 2 => 0 pairs (X) A2,A8: 2.. / A2 = 2 => 6 pairs (_) / A8 = 2 => 14 pairs (_) D4,D8: 2.. / D4 = 2 => 7 pairs (_) / D8 = 2 => 0 pairs (*) E5,E7: 2.. / E5 = 2 => 0 pairs (*) / E7 = 2 => 0 pairs (X) E1,E3: 3.. / E1 = 3 => 6 pairs (_) / E3 = 3 => 10 pairs (_) F4,F6: 3.. / F4 = 3 => 0 pairs (*) / F6 = 3 => 0 pairs (X) A5,B5: 4.. / A5 = 4 => 8 pairs (_) / B5 = 4 => 11 pairs (_) A8,B8: 4.. / A8 = 4 => 11 pairs (_) / B8 = 4 => 8 pairs (_) A5,A8: 4.. / A5 = 4 => 8 pairs (_) / A8 = 4 => 11 pairs (_) B5,B8: 4.. / B5 = 4 => 11 pairs (_) / B8 = 4 => 8 pairs (_) I8,H9: 5.. / I8 = 5 => 19 pairs (_) / H9 = 5 => 10 pairs (_) C6,H6: 5.. / C6 = 5 => 7 pairs (_) / H6 = 5 => 0 pairs (X) F9,H9: 5.. / F9 = 5 => 19 pairs (_) / H9 = 5 => 10 pairs (_) E5,E9: 7.. / E5 = 7 => 7 pairs (_) / E9 = 7 => 0 pairs (*) B3,C3: 9.. / B3 = 9 => 8 pairs (_) / C3 = 9 => 9 pairs (_) I1,I2: 9.. / I1 = 9 => 7 pairs (_) / I2 = 9 => 8 pairs (_) D4,F4: 9.. / D4 = 9 => 0 pairs (*) / F4 = 9 => 0 pairs (X) H7,H9: 9.. / H7 = 9 => 8 pairs (_) / H9 = 9 => 0 pairs (X) D1,I1: 9.. / D1 = 9 => 8 pairs (_) / I1 = 9 => 7 pairs (_) A5,A9: 9.. / A5 = 9 => 15 pairs (_) / A9 = 9 => 8 pairs (_) F2,F4: 9.. / F2 = 9 => 0 pairs (*) / F4 = 9 => 0 pairs (X) * DURATION: 0:00:30.414139 START: 14:14:16.397546 END: 14:14:46.811685 2019-04-28 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D4,E1,E5,F6,F8,G7) * 1....46...34.6....6..7.2..4..6.5..4....6.8....2.14.9.65..4.6..7....9.16..6.3..4.2 * PAIR E1: 3,8 BLK 2 E3: 3,8,1 # reduction candidate for 3,8 E3: 1 # 13 pairs E3: 3,8 # 10 pairs * PAIR E1: 3,8 ROW 1 H1: 3,8,2,5,7 # reduction candidate for 3,8 H1: 3,8 => CTR * 172..463.834.6127.6..7328143.625974.4..6785237251439865..42639724389716596.31.4.2 H1: 2,5,7 # 6 pairs I1: 3,8,5,9 # reduction candidate for 3,8 I1: 3,8 # 10 pairs * PAIR E5: 2,7 ROW 5 G5: 2,7,3,5 # reduction candidate for 2,7 G5: 2,7 # 7 pairs H5: 2,7,1,3,5 # reduction candidate for 2,7 H5: 2,7 # 10 pairs * PAIR F6: 3,7 BLK 5 F4: 3,7,9 # reduction candidate for 3,7 F4: 3,7 => SOLVED * 187534629234869715659712834876953241491628573325147986512486397743295168968371452 F4: 9 # 7 pairs * PAIR F6: 3,7 ROW 6 A6: 3,7,8 # reduction candidate for 3,7 A6: 3,7 # 9 pairs C6: 3,7,5,8 # reduction candidate for 3,7 C6: 3,7 => CTR * 17...46..234.61.7.6..7.2.1431625974894.678...8271439565..426..7...89716576.3154.2 C6: 5,8 # 7 pairs H6: 3,7,5,8 # reduction candidate for 3,7 H6: 3,7 # 12 pairs * PAIR F8: 5,7 BLK 8 F9: 5,7,1 # reduction candidate for 5,7 F9: 1 # 13 pairs F9: 5,7 # 10 pairs * PAIR G7: 3,8 BLK 9 H7: 3,8,9 # reduction candidate for 3,8 H7: 3,8 => CTR * 1....46..234.61...6..7.2.14..6.59.4.94.6.8....2.1439.65..4.6..74.329.165.6.3.5492 H7: 9 # 8 pairs I8: 3,8,5 # reduction candidate for 3,8 I8: 3,8 # 10 pairs * PAIR G7: 3,8 ROW 7 C7: 3,8,1,2,9 # reduction candidate for 3,8 C7: 3,8 # 16 pairs C7: 1,2,9 # 7 pairs * PAIR G7: 3,8 COL G G3: 3,8,5 # reduction candidate for 3,8 G3: 3,8 # 8 pairs G4: 3,8,2,7 # reduction candidate for 3,8 G4: 3,8 # 21 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0268-base-pr-000.dot * REASONING * DIS # H1: 3,8 => CTR => H1: 2,5,7 * PRF # F4: 3,7 => SOL * DIS # C6: 3,7 => CTR => C6: 5,8 * DIS # H7: 3,8 => CTR => H7: 9 * CNT 4 HDP CHAINS / 22 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D4,E1,E5,F6,F8,G7) * 1....46...34.6....6..7.2..4..6.5..4....6.8....2.14.9.65..4.6..7....9.16..6.3..4.2 * PAIR E1: 3,8 BLK 2 E3: 3,8,1 # reduction candidate for 3,8 E3: 1 # 13 pairs E3: 3,8 # 10 pairs * PAIR E1: 3,8 ROW 1 H1: 3,8,2,5,7 # reduction candidate for 3,8 H1: 3,8 => CTR * 172..463.834.6127.6..7328143.625974.4..6785237251439865..42639724389716596.31.4.2 I1: 3,8,5,9 # reduction candidate for 3,8 I1: 3,8 # 10 pairs * RESTART * PAIR E1: 3,8 ROW 1 I1: 3,8,5,9 # reduction candidate for 3,8 I1: 3,8 # 10 pairs I1: 5,9 # 7 pairs * PAIR RESTART * PAIR E1: 3,8 BLK 2 E3: 3,8,1 # reduction candidate for 3,8 E3: 1 # 14 pairs E3: 3,8 # 10 pairs * PAIR E1: 3,8 ROW 1 I1: 3,8,5,9 # reduction candidate for 3,8 I1: 3,8 # 10 pairs I1: 5,9 # 7 pairs * PAIR E5: 2,7 ROW 5 G5: 2,7,3,5 # reduction candidate for 2,7 G5: 2,7 # 8 pairs H5: 2,7,1,3,5 # reduction candidate for 2,7 H5: 2,7 # 10 pairs * PAIR F6: 3,7 BLK 5 F4: 3,7,9 # reduction candidate for 3,7 F4: 3,7 => SOLVED * 187534629234869715659712834876953241491628573325147986512486397743295168968371452 * DURATION: 0:00:08.098779 START: 14:14:58.963248 END: 14:15:07.062027 2019-04-28 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0268-base-pr-001.dot * REASONING * DIS # H1: 3,8 => CTR => H1: 2,5,7 * PRF H1: 2,5,7 # F4: 3,7 => SOL * STA H1: 2,5,7 + F4: 3,7 * CNT 2 HDP CHAINS / 13 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=268
Solution
position: 187534629234869715659712834876953241491628573325147986512486397743295168968371452 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 # E3: 3,8 => UNS * INC # E3: 1 => UNS * DIS # H1: 3,8 => CTR => H1: 2,5,7 * INC # H1: 2,5,7 => UNS * INC # I1: 3,8 => UNS * INC # G5: 2,7 => UNS * INC # H5: 2,7 => UNS * PRF # F4: 3,7 => SOL * INC # F4: 9 => UNS * INC # A6: 3,7 => UNS * DIS # C6: 3,7 => CTR => C6: 5,8 * INC # C6: 5,8 => UNS * INC # H6: 3,7 => UNS * INC # F9: 5,7 => UNS * INC # F9: 1 => UNS * DIS # H7: 3,8 => CTR => H7: 9 * INC # H7: 9 => UNS * INC # I8: 3,8 => UNS * INC # C7: 3,8 => UNS * INC # C7: 1,2,9 => UNS * INC # G3: 3,8 => UNS * INC # G4: 3,8 => UNS * CNT 22 HDP CHAINS / 22 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E3: 3,8 => UNS * INC # E3: 1 => UNS * DIS # H1: 3,8 => CTR => H1: 2,5,7 * INC H1: 2,5,7 # I1: 3,8 => UNS * INC H1: 2,5,7 # I1: 3,8 => UNS * INC H1: 2,5,7 # I1: 5,9 => UNS * INC H1: 2,5,7 # E3: 3,8 => UNS * INC H1: 2,5,7 # E3: 1 => UNS * INC H1: 2,5,7 # I1: 3,8 => UNS * INC H1: 2,5,7 # I1: 5,9 => UNS * INC H1: 2,5,7 # G5: 2,7 => UNS * INC H1: 2,5,7 # H5: 2,7 => UNS * PRF H1: 2,5,7 # F4: 3,7 => SOL * STA H1: 2,5,7 + F4: 3,7 * CNT 13 HDP CHAINS / 13 HYP OPENED