Analysis of zz-www.sudokuwiki.org-0073-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=73
level: medium
position: ..9..8..1....5.93..6.9.....8..4....7.2.....6.6....3..9.....9.2..72.3....4..8..5.. initial
Autosolve
position: ..93.8..1....5.93..6.9.....8..4....7.2.....6.6....3..9.....9.2..72.3....4..8..5.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F4: 1,5 => CTR => F4: 2,6 * DIS # G7: 3,6 => CTR => G7: 1,4,7 * CNT 2 HDP CHAINS / 17 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F4: 1,5 => CTR => F4: 2,6 * PRF F4: 2,6 # H6: 1,5 => SOL * STA F4: 2,6 + H6: 1,5 * CNT 2 HDP CHAINS / 12 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..9..8..1....5.93..6.9.....8..4....7.2.....6.6....3..9.....9.2..72.3....4..8..5.. | initial |
| ..93.8..1....5.93..6.9.....8..4....7.2.....6.6....3..9.....9.2..72.3....4..8..5.. | autosolve |
| 759328641148657932263941785835496217924715368617283459386579124572134896491862573 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (3) B1: 4,5 H4: 1,5 I9: 3,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I2,I3: 2.. / I2 = 2 => 4 pairs (_) / I3 = 2 => 0 pairs (X) G4,G6: 2.. / G4 = 2 => 3 pairs (_) / G6 = 2 => 0 pairs (X) E9,F9: 2.. / E9 = 2 => 4 pairs (_) / F9 = 2 => 3 pairs (_) A1,E1: 2.. / A1 = 2 => 4 pairs (_) / E1 = 2 => 4 pairs (_) D2,D6: 2.. / D2 = 2 => 0 pairs (X) / D6 = 2 => 3 pairs (_) A3,C3: 3.. / A3 = 3 => 4 pairs (_) / C3 = 3 => 9 pairs (_) E7,F8: 4.. / E7 = 4 => 23 pairs (_) / F8 = 4 => 5 pairs (_) I3,I5: 5.. / I3 = 5 => 5 pairs (_) / I5 = 5 => 0 pairs (X) G1,I2: 6.. / G1 = 6 => 3 pairs (_) / I2 = 6 => 0 pairs (X) E4,F4: 6.. / E4 = 6 => 14 pairs (_) / F4 = 6 => 3 pairs (_) C7,C9: 6.. / C7 = 6 => 9 pairs (_) / C9 = 6 => 4 pairs (_) E1,G1: 6.. / E1 = 6 => 0 pairs (X) / G1 = 6 => 3 pairs (_) G7,H9: 7.. / G7 = 7 => 8 pairs (_) / H9 = 7 => 9 pairs (_) E5,E6: 8.. / E5 = 8 => 5 pairs (_) / E6 = 8 => 3 pairs (_) B7,C7: 8.. / B7 = 8 => 6 pairs (_) / C7 = 8 => 4 pairs (_) B2,B7: 8.. / B2 = 8 => 4 pairs (_) / B7 = 8 => 6 pairs (_) B4,A5: 9.. / B4 = 9 => 14 pairs (_) / A5 = 9 => 5 pairs (_) E4,E5: 9.. / E4 = 9 => 5 pairs (_) / E5 = 9 => 14 pairs (_) A8,B9: 9.. / A8 = 9 => 14 pairs (_) / B9 = 9 => 5 pairs (_) H8,H9: 9.. / H8 = 9 => 5 pairs (_) / H9 = 9 => 14 pairs (_) B4,E4: 9.. / B4 = 9 => 14 pairs (_) / E4 = 9 => 5 pairs (_) A5,E5: 9.. / A5 = 9 => 5 pairs (_) / E5 = 9 => 14 pairs (_) A8,H8: 9.. / A8 = 9 => 14 pairs (_) / H8 = 9 => 5 pairs (_) B9,H9: 9.. / B9 = 9 => 5 pairs (_) / H9 = 9 => 14 pairs (_) A5,A8: 9.. / A5 = 9 => 5 pairs (_) / A8 = 9 => 14 pairs (_) B4,B9: 9.. / B4 = 9 => 14 pairs (_) / B9 = 9 => 5 pairs (_) * DURATION: 0:00:29.856891 START: 04:43:38.961919 END: 04:44:08.818810 2017-05-01 * CP COUNT: (26) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,H4,I9) * ..93.8..1....5.93..6.9.....8..4....7.2.....6.6....3..9.....9.2..72.3....4..8..5.. * PAIR B1: 4,5 BLK 1 C3: 4,5,1,3,7,8 # reduction candidate for 4,5 C3: 4,5 # 7 pairs C3: 1,3,7,8 # 3 pairs * PAIR B1: 4,5 ROW 1 H1: 4,5,7 # reduction candidate for 4,5 H1: 7 # 9 pairs H1: 4,5 # 6 pairs * PAIR B1: 4,5 COL B B6: 4,5,1 # reduction candidate for 4,5 B6: 1 # 6 pairs B6: 4,5 # 5 pairs * PAIR H4: 1,5 BLK 6 H6: 1,5,4,8 # reduction candidate for 1,5 H6: 1,5 # 8 pairs H6: 4,8 # 4 pairs * PAIR H4: 1,5 ROW 4 B4: 1,5,3,9 # reduction candidate for 1,5 B4: 1,5 # 10 pairs C4: 1,5,3 # reduction candidate for 1,5 C4: 1,5 # 7 pairs F4: 1,5,2,6 # reduction candidate for 1,5 F4: 1,5 => CTR * ..93.86.1....5.93.36.9....589346.2.7.24.9.3686.7283..9..5..972.972.3....4.68..593 F4: 2,6 # 4 pairs * PAIR I9: 3,6 BLK 9 G7: 3,6,1,4,7 # reduction candidate for 3,6 G7: 3,6 => CTR * ..9368..1....5.936.6.94...28..4962.792...5.636....3..9.....9.2457263419849.8..57. G7: 1,4,7 # 3 pairs I7: 3,6,4 # reduction candidate for 3,6 I7: 3,6 # 23 pairs * PAIR I9: 3,6 ROW 9 C9: 3,6,1 # reduction candidate for 3,6 C9: 1 # 12 pairs C9: 3,6 # 5 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0073-base-pr-000.dot * REASONING * DIS # F4: 1,5 => CTR => F4: 2,6 * DIS # G7: 3,6 => CTR => G7: 1,4,7 * CNT 2 HDP CHAINS / 17 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,H4,I9) * ..93.8..1....5.93..6.9.....8..4....7.2.....6.6....3..9.....9.2..72.3....4..8..5.. * PAIR B1: 4,5 BLK 1 C3: 4,5,1,3,7,8 # reduction candidate for 4,5 C3: 4,5 # 7 pairs C3: 1,3,7,8 # 3 pairs * PAIR B1: 4,5 ROW 1 H1: 4,5,7 # reduction candidate for 4,5 H1: 7 # 9 pairs H1: 4,5 # 6 pairs * PAIR B1: 4,5 COL B B6: 4,5,1 # reduction candidate for 4,5 B6: 1 # 6 pairs B6: 4,5 # 5 pairs * PAIR H4: 1,5 BLK 6 H6: 1,5,4,8 # reduction candidate for 1,5 H6: 1,5 # 8 pairs H6: 4,8 # 4 pairs * PAIR H4: 1,5 ROW 4 B4: 1,5,3,9 # reduction candidate for 1,5 B4: 1,5 # 10 pairs C4: 1,5,3 # reduction candidate for 1,5 C4: 1,5 # 7 pairs F4: 1,5,2,6 # reduction candidate for 1,5 F4: 1,5 => CTR * ..93.86.1....5.93.36.9....589346.2.7.24.9.3686.7283..9..5..972.972.3....4.68..593 * PAIR RESTART * PAIR H4: 1,5 BLK 6 H6: 1,5,4,8 # reduction candidate for 1,5 H6: 1,5 => SOLVED * 759328641148657932263941785835496217924715368617283459386579124572134896491862573 * DURATION: 0:00:08.942085 START: 04:44:20.299307 END: 04:44:29.241392 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0073-base-pr-001.dot * REASONING * DIS # F4: 1,5 => CTR => F4: 2,6 * PRF F4: 2,6 # H6: 1,5 => SOL * STA F4: 2,6 + H6: 1,5 * CNT 2 HDP CHAINS / 12 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=73
Solution
position: 759328641148657932263941785835496217924715368617283459386579124572134896491862573 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 # C3: 4,5 => UNS * INC # C3: 1,3,7,8 => UNS * INC # H1: 4,5 => UNS * INC # H1: 7 => UNS * INC # B6: 4,5 => UNS * INC # B6: 1 => UNS * INC # H6: 1,5 => UNS * INC # H6: 4,8 => UNS * INC # B4: 1,5 => UNS * INC # C4: 1,5 => UNS * DIS # F4: 1,5 => CTR => F4: 2,6 * INC # F4: 2,6 => UNS * DIS # G7: 3,6 => CTR => G7: 1,4,7 * INC # G7: 1,4,7 => UNS * INC # I7: 3,6 => UNS * INC # C9: 3,6 => UNS * INC # C9: 1 => UNS * CNT 17 HDP CHAINS / 17 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C3: 4,5 => UNS * INC # C3: 1,3,7,8 => UNS * INC # H1: 4,5 => UNS * INC # H1: 7 => UNS * INC # B6: 4,5 => UNS * INC # B6: 1 => UNS * INC # H6: 1,5 => UNS * INC # H6: 4,8 => UNS * INC # B4: 1,5 => UNS * INC # C4: 1,5 => UNS * DIS # F4: 1,5 => CTR => F4: 2,6 * PRF F4: 2,6 # H6: 1,5 => SOL * STA F4: 2,6 + H6: 1,5 * CNT 12 HDP CHAINS / 12 HYP OPENED