Analysis of zz-www.sudokuwiki.org-0124-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=124
level: medium
position: ..9.........4.52..45.1....89.3.....5...3.8...8.....7.67....9.13..18.2.........4.. initial
Autosolve
position: ..9.........4.52..45.1....89.3.....5...3.8...8..9..7367....9.13..18.2.........4.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C7: 5,6 => CTR => C7: 2,4,8 * DIS # B7: 4,6 => CTR => B7: 2,8 * DIS # C7: 4,6 => CTR => C7: 2,5,8 * DIS # H9: 7,9 => CTR => H9: 2,5,6,8 * DIS # I9: 7,9 => CTR => I9: 2 * CNT 5 HDP CHAINS / 24 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C7: 5,6 => CTR => C7: 2,4,8 * DIS C7: 2,4,8 # G7: 8 => CTR => G7: 5,6 * DIS C7: 2,4,8 + G7: 5,6 # I2: 1 => CTR => I2: 7,9 * DIS C7: 2,4,8 + G7: 5,6 + I2: 7,9 # H8: 5 => CTR => H8: 7,9 * PRF C7: 2,4,8 + G7: 5,6 + I2: 7,9 + H8: 7,9 # B1: 2,6 => SOL * STA C7: 2,4,8 + G7: 5,6 + I2: 7,9 + H8: 7,9 + B1: 2,6 * CNT 5 HDP CHAINS / 21 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..9.........4.52..45.1....89.3.....5...3.8...8.....7.67....9.13..18.2.........4.. | initial |
| ..9.........4.52..45.1....89.3.....5...3.8...8..9..7367....9.13..18.2.........4.. | autosolve |
| 269783154138495267457126398913267845674358921825914736782649513541832679396571482 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) F6: 1,4 G4: 1,8 G5: 1,9 D7: 5,6 E7: 4,6 I8: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E9,F9: 1.. / E9 = 1 => 8 pairs (_) / F9 = 1 => 8 pairs (_) B7,C7: 2.. / B7 = 2 => 9 pairs (_) / C7 = 2 => 16 pairs (_) H9,I9: 2.. / H9 = 2 => 0 pairs (X) / I9 = 2 => 6 pairs (_) C3,E3: 2.. / C3 = 2 => 0 pairs (X) / E3 = 2 => 12 pairs (_) A1,A5: 2.. / A1 = 2 => 12 pairs (_) / A5 = 2 => 0 pairs (X) D1,D4: 2.. / D1 = 2 => 0 pairs (X) / D4 = 2 => 12 pairs (_) I5,I9: 2.. / I5 = 2 => 0 pairs (X) / I9 = 2 => 6 pairs (_) G1,G3: 3.. / G1 = 3 => 17 pairs (_) / G3 = 3 => 7 pairs (_) H1,I1: 4.. / H1 = 4 => 12 pairs (_) / I1 = 4 => 8 pairs (_) F4,F6: 4.. / F4 = 4 => 8 pairs (_) / F6 = 4 => 7 pairs (_) E7,E8: 4.. / E7 = 4 => 8 pairs (_) / E8 = 4 => 0 pairs (X) B8,E8: 4.. / B8 = 4 => 8 pairs (_) / E8 = 4 => 0 pairs (X) I1,I5: 4.. / I1 = 4 => 8 pairs (_) / I5 = 4 => 12 pairs (_) G1,H1: 5.. / G1 = 5 => 9 pairs (_) / H1 = 5 => 8 pairs (_) E5,E6: 5.. / E5 = 5 => 8 pairs (_) / E6 = 5 => 12 pairs (_) D7,D9: 5.. / D7 = 5 => 7 pairs (_) / D9 = 5 => 14 pairs (_) C6,E6: 5.. / C6 = 5 => 8 pairs (_) / E6 = 5 => 12 pairs (_) E1,E2: 8.. / E1 = 8 => 6 pairs (_) / E2 = 8 => 0 pairs (X) G4,H4: 8.. / G4 = 8 => 12 pairs (_) / H4 = 8 => 0 pairs (X) G7,H9: 8.. / G7 = 8 => 0 pairs (X) / H9 = 8 => 12 pairs (_) B1,E1: 8.. / B1 = 8 => 0 pairs (X) / E1 = 8 => 6 pairs (_) G4,G7: 8.. / G4 = 8 => 12 pairs (_) / G7 = 8 => 0 pairs (X) H4,H9: 8.. / H4 = 8 => 0 pairs (X) / H9 = 8 => 12 pairs (_) E2,E3: 9.. / E2 = 9 => 8 pairs (_) / E3 = 9 => 0 pairs (X) B8,B9: 9.. / B8 = 9 => 0 pairs (X) / B9 = 9 => 7 pairs (_) * DURATION: 0:00:35.054941 START: 05:47:27.727761 END: 05:48:02.782702 2017-05-01 * CP COUNT: (25) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D7,E7,F6,G4,G5,I8) * ..9.........4.52..45.1....89.3.....5...3.8...8..9..7367....9.13..18.2.........4.. * PAIR F6: 1,4 BLK 5 F4: 1,4,6,7 # reduction candidate for 1,4 F4: 6,7 # 8 pairs F4: 1,4 # 8 pairs * PAIR F6: 1,4 ROW 6 B6: 1,4,2 # reduction candidate for 1,4 B6: 2 # 16 pairs B6: 1,4 # 9 pairs * PAIR G5: 1,9 BLK 6 I5: 1,9,2,4 # reduction candidate for 1,9 I5: 1,9 # 14 pairs I5: 2,4 # 7 pairs * PAIR D7: 5,6 BLK 8 D9: 5,6,7 # reduction candidate for 5,6 D9: 5,6 # 12 pairs D9: 7 # 9 pairs * PAIR D7: 5,6 ROW 7 C7: 5,6,2,4,8 # reduction candidate for 5,6 C7: 5,6 => CTR * ..9.........4.52..45.1....89.3...185...3.89..81.9.473672..49813.418.2....98..14.. C7: 2,4,8 # 6 pairs G7: 5,6,8 # reduction candidate for 5,6 G7: 5,6 # 12 pairs * PAIR E7: 4,6 BLK 8 E8: 4,6,3,7 # reduction candidate for 4,6 E8: 4,6 # 13 pairs E8: 3,7 # 9 pairs * PAIR E7: 4,6 ROW 7 B7: 4,6,2,8 # reduction candidate for 4,6 B7: 4,6 => CTR * 2.9.8.......4952..45.12..989.32.4185...3.89..8249517367.2549813.41832..9.98.1.4.. B7: 2,8 # 7 pairs C7: 4,6,2,5,8 # reduction candidate for 4,6 C7: 4,6 => CTR * 2.968...1138495267456127398943276185..73189.48129547367245698133.18426.....7314.. C7: 2,5,8 # 7 pairs * PAIR I8: 7,9 BLK 9 H8: 7,9,5,6 # reduction candidate for 7,9 H8: 7,9 # 8 pairs H9: 7,9,2,5,6,8 # reduction candidate for 7,9 H9: 7,9 => CTR * 2.9783541.8.49526.45.12.3989.32..185...3.89248..9..7367....9813..18.2659.98...472 H9: 2,5,6,8 # 6 pairs I9: 7,9,2 # reduction candidate for 7,9 I9: 7,9 => CTR * 219.8...463849527145712..989.32..1851..3.89428..9147367.4569813391842..7586.3142. I9: 2 # 6 pairs * PAIR I8: 7,9 COL I I2: 7,9,1 # reduction candidate for 7,9 I2: 1 # 13 pairs I2: 7,9 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0124-base-pr-000.dot * REASONING * DIS # C7: 5,6 => CTR => C7: 2,4,8 * DIS # B7: 4,6 => CTR => B7: 2,8 * DIS # C7: 4,6 => CTR => C7: 2,5,8 * DIS # H9: 7,9 => CTR => H9: 2,5,6,8 * DIS # I9: 7,9 => CTR => I9: 2 * CNT 5 HDP CHAINS / 24 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D7,E7,F6,G4,G5,I8) * ..9.........4.52..45.1....89.3.....5...3.8...8..9..7367....9.13..18.2.........4.. * PAIR F6: 1,4 BLK 5 F4: 1,4,6,7 # reduction candidate for 1,4 F4: 6,7 # 8 pairs F4: 1,4 # 8 pairs * PAIR F6: 1,4 ROW 6 B6: 1,4,2 # reduction candidate for 1,4 B6: 2 # 16 pairs B6: 1,4 # 9 pairs * PAIR G5: 1,9 BLK 6 I5: 1,9,2,4 # reduction candidate for 1,9 I5: 1,9 # 14 pairs I5: 2,4 # 7 pairs * PAIR D7: 5,6 BLK 8 D9: 5,6,7 # reduction candidate for 5,6 D9: 5,6 # 12 pairs D9: 7 # 9 pairs * PAIR D7: 5,6 ROW 7 C7: 5,6,2,4,8 # reduction candidate for 5,6 C7: 5,6 => CTR * ..9.........4.52..45.1....89.3...185...3.89..81.9.473672..49813.418.2....98..14.. G7: 5,6,8 # reduction candidate for 5,6 G7: 5,6 # 12 pairs * RESTART * PAIR D7: 5,6 ROW 7 G7: 5,6,8 # reduction candidate for 5,6 G7: 8 => CTR * 2.968...1138495267456127398943276185.673189.4812954736724569813391842......7314.. * PAIR RESTART * PAIR D7: 5,6 BLK 8 D9: 5,6,7 # reduction candidate for 5,6 D9: 5,6 # 17 pairs D9: 7 # 15 pairs * PAIR I8: 7,9 BLK 9 H8: 7,9,5,6 # reduction candidate for 7,9 H8: 7,9 # 18 pairs H8: 5,6 # 15 pairs * PAIR I8: 7,9 COL I I2: 7,9,1 # reduction candidate for 7,9 I2: 1 => CTR * 1.9......6..4.52.145.1....89.3...8.52..3.81..81.9247367...49.13.418.2....96...482 * PAIR RESTART * PAIR I8: 7,9 BLK 9 H8: 7,9,5 # reduction candidate for 7,9 H8: 5 => CTR * ..92..5411..4.52.945219.3.8913..48252..3.81948.49517367..549613.418.2957.9..1.482 * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A1,B6,B7,C7,C9,D7,E8,F3,F6,G7,G8,H4,H5,H8,I2,I8) * ..9...1541..4.52..45.1..3.89.3...8.5...3.89.18..9..7367...49.13.418.2....9....482 * PAIR A1: 2,6 BLK 1 B1: 2,6,3,7,8 # reduction candidate for 2,6 B1: 2,6 => SOLVED * 269783154138495267457126398913267845674358921825914736782649513541832679396571482 * DURATION: 0:00:19.257566 START: 05:48:19.688077 END: 05:48:38.945643 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0124-base-pr-001.dot * REASONING * DIS # C7: 5,6 => CTR => C7: 2,4,8 * DIS C7: 2,4,8 # G7: 8 => CTR => G7: 5,6 * DIS C7: 2,4,8 + G7: 5,6 # I2: 1 => CTR => I2: 7,9 * DIS C7: 2,4,8 + G7: 5,6 + I2: 7,9 # H8: 5 => CTR => H8: 7,9 * PRF C7: 2,4,8 + G7: 5,6 + I2: 7,9 + H8: 7,9 # B1: 2,6 => SOL * STA C7: 2,4,8 + G7: 5,6 + I2: 7,9 + H8: 7,9 + B1: 2,6 * CNT 5 HDP CHAINS / 21 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=124
Solution
position: 269783154138495267457126398913267845674358921825914736782649513541832679396571482 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 # F4: 1,4 => UNS * INC # F4: 6,7 => UNS * INC # B6: 1,4 => UNS * INC # B6: 2 => UNS * INC # I5: 1,9 => UNS * INC # I5: 2,4 => UNS * INC # D9: 5,6 => UNS * INC # D9: 7 => UNS * DIS # C7: 5,6 => CTR => C7: 2,4,8 * INC # C7: 2,4,8 => UNS * INC # G7: 5,6 => UNS * INC # E8: 4,6 => UNS * INC # E8: 3,7 => UNS * DIS # B7: 4,6 => CTR => B7: 2,8 * INC # B7: 2,8 => UNS * DIS # C7: 4,6 => CTR => C7: 2,5,8 * INC # C7: 2,5,8 => UNS * INC # H8: 7,9 => UNS * DIS # H9: 7,9 => CTR => H9: 2,5,6,8 * INC # H9: 2,5,6,8 => UNS * DIS # I9: 7,9 => CTR => I9: 2 * INC # I9: 2 => UNS * INC # I2: 7,9 => UNS * INC # I2: 1 => UNS * CNT 24 HDP CHAINS / 24 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F4: 1,4 => UNS * INC # F4: 6,7 => UNS * INC # B6: 1,4 => UNS * INC # B6: 2 => UNS * INC # I5: 1,9 => UNS * INC # I5: 2,4 => UNS * INC # D9: 5,6 => UNS * INC # D9: 7 => UNS * DIS # C7: 5,6 => CTR => C7: 2,4,8 * INC C7: 2,4,8 # G7: 5,6 => UNS * INC C7: 2,4,8 # G7: 5,6 => UNS * DIS C7: 2,4,8 # G7: 8 => CTR => G7: 5,6 * INC C7: 2,4,8 + G7: 5,6 # D9: 5,6 => UNS * INC C7: 2,4,8 + G7: 5,6 # D9: 7 => UNS * INC C7: 2,4,8 + G7: 5,6 # H8: 7,9 => UNS * INC C7: 2,4,8 + G7: 5,6 # H8: 5,6 => UNS * INC C7: 2,4,8 + G7: 5,6 # I2: 7,9 => UNS * DIS C7: 2,4,8 + G7: 5,6 # I2: 1 => CTR => I2: 7,9 * INC C7: 2,4,8 + G7: 5,6 + I2: 7,9 # H8: 7,9 => UNS * DIS C7: 2,4,8 + G7: 5,6 + I2: 7,9 # H8: 5 => CTR => H8: 7,9 * PRF C7: 2,4,8 + G7: 5,6 + I2: 7,9 + H8: 7,9 # B1: 2,6 => SOL * STA C7: 2,4,8 + G7: 5,6 + I2: 7,9 + H8: 7,9 + B1: 2,6 * CNT 21 HDP CHAINS / 21 HYP OPENED