Analysis of zz-www.sudokuwiki.org-0090-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=90
level: medium
position: .....1.8.1...5...364.3.......8....4...28.39...7....6.......8.578...6...2.9.2..... initial
Autosolve
position: .....1.8.18..5...364.38...9..8....4..628.397..7....6.8..6..8.578...6..92.9.2..8.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E6: 1,4 => CTR => E6: 2,9 * CNT 1 HDP CHAINS / 31 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E6: 1,4 => CTR => E6: 2,9 * PRF E6: 2,9 # G3: 1,2 => SOL * STA E6: 2,9 + G3: 1,2 * CNT 2 HDP CHAINS / 40 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .....1.8.1...5...364.3.......8....4...28.39...7....6.......8.578...6...2.9.2..... | initial |
| .....1.8.18..5...364.38...9..8....4..628.397..7....6.8..6..8.578...6..92.9.2..8.. | autosolve |
| 723691584189452763645387129938716245562843971471529638216938457857164392394275816 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) C2: 7,9 C3: 5,7 F3: 2,7 I1: 4,6 H2: 2,6 H3: 1,2 A5: 4,5 E5: 1,4 G4: 2,3 I4: 1,5 I5: 1,5 H6: 2,3 I9: 4,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G3,H3: 1.. / G3 = 1 => 0 pairs (*) / H3 = 1 => 0 pairs (X) B4,C6: 1.. / B4 = 1 => 14 pairs (_) / C6 = 1 => 15 pairs (_) I4,I5: 1.. / I4 = 1 => 0 pairs (X) / I5 = 1 => 13 pairs (_) E5,I5: 1.. / E5 = 1 => 0 pairs (X) / I5 = 1 => 13 pairs (_) H3,H9: 1.. / H3 = 1 => 13 pairs (_) / H9 = 1 => 0 pairs (*) A1,B1: 2.. / A1 = 2 => 17 pairs (_) / B1 = 2 => 14 pairs (_) F2,F3: 2.. / F2 = 2 => 16 pairs (_) / F3 = 2 => 13 pairs (_) E4,E6: 2.. / E4 = 2 => 18 pairs (_) / E6 = 2 => 13 pairs (_) G4,H6: 2.. / G4 = 2 => 13 pairs (_) / H6 = 2 => 18 pairs (_) A7,B7: 2.. / A7 = 2 => 14 pairs (_) / B7 = 2 => 17 pairs (_) E4,G4: 2.. / E4 = 2 => 18 pairs (_) / G4 = 2 => 13 pairs (_) E6,H6: 2.. / E6 = 2 => 13 pairs (_) / H6 = 2 => 18 pairs (_) A1,A7: 2.. / A1 = 2 => 17 pairs (_) / A7 = 2 => 14 pairs (_) B1,B7: 2.. / B1 = 2 => 14 pairs (_) / B7 = 2 => 17 pairs (_) G4,H6: 3.. / G4 = 3 => 18 pairs (_) / H6 = 3 => 13 pairs (_) E7,E9: 3.. / E7 = 3 => 16 pairs (_) / E9 = 3 => 13 pairs (_) H6,H9: 3.. / H6 = 3 => 13 pairs (_) / H9 = 3 => 18 pairs (_) A5,E5: 4.. / A5 = 4 => 0 pairs (X) / E5 = 4 => 13 pairs (_) I1,I9: 4.. / I1 = 4 => 14 pairs (_) / I9 = 4 => 11 pairs (_) G1,G3: 5.. / G1 = 5 => 13 pairs (_) / G3 = 5 => 13 pairs (_) I4,I5: 5.. / I4 = 5 => 13 pairs (_) / I5 = 5 => 0 pairs (X) C3,G3: 5.. / C3 = 5 => 13 pairs (_) / G3 = 5 => 13 pairs (_) A5,I5: 5.. / A5 = 5 => 13 pairs (_) / I5 = 5 => 0 pairs (X) I1,H2: 6.. / I1 = 6 => 11 pairs (_) / H2 = 6 => 14 pairs (_) D4,F4: 6.. / D4 = 6 => 12 pairs (_) / F4 = 6 => 13 pairs (_) H9,I9: 6.. / H9 = 6 => 11 pairs (_) / I9 = 6 => 14 pairs (_) D1,I1: 6.. / D1 = 6 => 14 pairs (_) / I1 = 6 => 11 pairs (_) F2,F4: 6.. / F2 = 6 => 12 pairs (_) / F4 = 6 => 13 pairs (_) H2,H9: 6.. / H2 = 6 => 14 pairs (_) / H9 = 6 => 11 pairs (_) I1,I9: 6.. / I1 = 6 => 11 pairs (_) / I9 = 6 => 14 pairs (_) A1,A9: 7.. / A1 = 7 => 14 pairs (_) / A9 = 7 => 14 pairs (_) D7,E7: 9.. / D7 = 9 => 13 pairs (_) / E7 = 9 => 0 pairs (X) * DURATION: 0:00:47.286777 START: 05:04:41.846329 END: 05:05:29.133106 2017-05-01 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,C2,C3,E5,F3,G4,H2,H3,H6,I1,I4,I5,I9) * .....1.8.18..5...364.38...9..8....4..628.397..7....6.8..6..8.578...6..92.9.2..8.. * PAIR C2: 7,9 BLK 1 A1: 7,9,2,3,5 # reduction candidate for 7,9 A1: 7,9 # 14 pairs C1: 7,9,3,5 # reduction candidate for 7,9 C1: 7,9 # 18 pairs * PAIR C2: 7,9 ROW 2 D2: 7,9,4,6 # reduction candidate for 7,9 D2: 7,9 # 17 pairs F2: 7,9,2,4,6 # reduction candidate for 7,9 F2: 7,9 # 17 pairs * PAIR C3: 5,7 BLK 1 A1: 5,7,2,3,9 # reduction candidate for 5,7 A1: 5,7 # 14 pairs C1: 5,7,3,9 # reduction candidate for 5,7 C1: 5,7 # 18 pairs * PAIR C3: 5,7 ROW 3 G3: 5,7,1,2 # reduction candidate for 5,7 G3: 1,2 # 16 pairs G3: 5,7 # 13 pairs * PAIR C3: 5,7 COL C C8: 5,7,1,3,4 # reduction candidate for 5,7 C8: 5,7 # 16 pairs C9: 5,7,1,3,4 # reduction candidate for 5,7 C9: 5,7 # 17 pairs * PAIR F3: 2,7 BLK 2 F2: 2,7,4,6,9 # reduction candidate for 2,7 F2: 2,7 # 19 pairs F2: 4,6,9 # 13 pairs * PAIR F3: 2,7 ROW 3 G3: 2,7,1,5 # reduction candidate for 2,7 G3: 2,7 # 14 pairs G3: 1,5 # 14 pairs * PAIR I1: 4,6 ROW 1 D1: 4,6,7,9 # reduction candidate for 4,6 D1: 4,6 # 16 pairs D1: 7,9 # 12 pairs * PAIR H2: 2,6 ROW 2 F2: 2,6,4,7,9 # reduction candidate for 2,6 F2: 2,6 # 15 pairs F2: 4,7,9 # 13 pairs * PAIR H3: 1,2 BLK 3 G3: 1,2,5,7 # reduction candidate for 1,2 G3: 1,2 # 16 pairs G3: 5,7 # 13 pairs * PAIR A5: 4,5 BLK 4 A6: 4,5,3,9 # reduction candidate for 4,5 A6: 4,5 # 18 pairs C6: 4,5,1,3,9 # reduction candidate for 4,5 C6: 4,5 # 18 pairs * PAIR A5: 4,5 COL A A9: 4,5,3,7 # reduction candidate for 4,5 A9: 4,5 # 20 pairs A9: 3,7 # 14 pairs * PAIR E5: 1,4 BLK 5 D6: 1,4,5,9 # reduction candidate for 1,4 D6: 1,4 # 16 pairs E6: 1,4,2,9 # reduction candidate for 1,4 E6: 1,4 => CTR * 72369158418945..6364538..199.872634..628.397.37.5.962821693845783716..92.9.27.836 E6: 2,9 # 14 pairs * PAIR E5: 1,4 COL E E7: 1,4,3,9 # reduction candidate for 1,4 E7: 1,4 # 16 pairs E9: 1,4,3,7 # reduction candidate for 1,4 E9: 1,4 # 19 pairs * PAIR I4: 1,5 ROW 4 B4: 1,5,3 # reduction candidate for 1,5 B4: 1,5 # 15 pairs D4: 1,5,6,7,9 # reduction candidate for 1,5 D4: 1,5 # 21 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0090-base-pr-000.dot * REASONING * DIS # E6: 1,4 => CTR => E6: 2,9 * CNT 1 HDP CHAINS / 31 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,C2,C3,E5,F3,G4,H2,H3,H6,I1,I4,I5,I9) * .....1.8.18..5...364.38...9..8....4..628.397..7....6.8..6..8.578...6..92.9.2..8.. * PAIR C2: 7,9 BLK 1 A1: 7,9,2,3,5 # reduction candidate for 7,9 A1: 7,9 # 14 pairs C1: 7,9,3,5 # reduction candidate for 7,9 C1: 7,9 # 18 pairs * PAIR C2: 7,9 ROW 2 D2: 7,9,4,6 # reduction candidate for 7,9 D2: 7,9 # 17 pairs F2: 7,9,2,4,6 # reduction candidate for 7,9 F2: 7,9 # 17 pairs * PAIR C3: 5,7 BLK 1 A1: 5,7,2,3,9 # reduction candidate for 5,7 A1: 5,7 # 14 pairs C1: 5,7,3,9 # reduction candidate for 5,7 C1: 5,7 # 18 pairs * PAIR C3: 5,7 ROW 3 G3: 5,7,1,2 # reduction candidate for 5,7 G3: 1,2 # 16 pairs G3: 5,7 # 13 pairs * PAIR C3: 5,7 COL C C8: 5,7,1,3,4 # reduction candidate for 5,7 C8: 5,7 # 16 pairs C9: 5,7,1,3,4 # reduction candidate for 5,7 C9: 5,7 # 17 pairs * PAIR F3: 2,7 BLK 2 F2: 2,7,4,6,9 # reduction candidate for 2,7 F2: 2,7 # 19 pairs F2: 4,6,9 # 13 pairs * PAIR F3: 2,7 ROW 3 G3: 2,7,1,5 # reduction candidate for 2,7 G3: 2,7 # 14 pairs G3: 1,5 # 14 pairs * PAIR I1: 4,6 ROW 1 D1: 4,6,7,9 # reduction candidate for 4,6 D1: 4,6 # 16 pairs D1: 7,9 # 12 pairs * PAIR H2: 2,6 ROW 2 F2: 2,6,4,7,9 # reduction candidate for 2,6 F2: 2,6 # 15 pairs F2: 4,7,9 # 13 pairs * PAIR H3: 1,2 BLK 3 G3: 1,2,5,7 # reduction candidate for 1,2 G3: 1,2 # 16 pairs G3: 5,7 # 13 pairs * PAIR A5: 4,5 BLK 4 A6: 4,5,3,9 # reduction candidate for 4,5 A6: 4,5 # 18 pairs C6: 4,5,1,3,9 # reduction candidate for 4,5 C6: 4,5 # 18 pairs * PAIR A5: 4,5 COL A A9: 4,5,3,7 # reduction candidate for 4,5 A9: 4,5 # 20 pairs A9: 3,7 # 14 pairs * PAIR E5: 1,4 BLK 5 D6: 1,4,5,9 # reduction candidate for 1,4 D6: 1,4 # 16 pairs E6: 1,4,2,9 # reduction candidate for 1,4 E6: 1,4 => CTR * 72369158418945..6364538..199.872634..628.397.37.5.962821693845783716..92.9.27.836 * RESTART * PAIR E5: 1,4 BLK 5 D6: 1,4,5,9 # reduction candidate for 1,4 D6: 5,9 # 17 pairs D6: 1,4 # 16 pairs * PAIR E5: 1,4 COL E E7: 1,4,3,9 # reduction candidate for 1,4 E7: 1,4 # 16 pairs E9: 1,4,3,7 # reduction candidate for 1,4 E9: 1,4 # 19 pairs * PAIR I4: 1,5 ROW 4 B4: 1,5,3 # reduction candidate for 1,5 B4: 1,5 # 19 pairs D4: 1,5,6,7,9 # reduction candidate for 1,5 D4: 1,5 # 21 pairs * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A5,C2,C3,E5,E6,F3,G4,H2,H3,H6,I1,I4,I5,I9) * .....1.8.18..5...364.38...9..8....4..628.397..7....6.8..6..8.578...6..92.9.2..8.. * PAIR C2: 7,9 BLK 1 A1: 7,9,2,3,5 # reduction candidate for 7,9 A1: 7,9 # 15 pairs C1: 7,9,3,5 # reduction candidate for 7,9 C1: 7,9 # 19 pairs * PAIR C2: 7,9 ROW 2 D2: 7,9,4,6 # reduction candidate for 7,9 D2: 7,9 # 13 pairs F2: 7,9,2,4,6 # reduction candidate for 7,9 F2: 7,9 # 18 pairs * PAIR C3: 5,7 BLK 1 A1: 5,7,2,3,9 # reduction candidate for 5,7 A1: 5,7 # 15 pairs C1: 5,7,3,9 # reduction candidate for 5,7 C1: 5,7 # 22 pairs * PAIR C3: 5,7 ROW 3 G3: 5,7,1,2 # reduction candidate for 5,7 G3: 1,2 => SOLVED * 723691584189452763645387129938716245562843971471529638216938457857164392394275816 * DURATION: 0:00:33.127631 START: 05:05:54.021853 END: 05:06:27.149484 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0090-base-pr-001.dot * REASONING * DIS # E6: 1,4 => CTR => E6: 2,9 * PRF E6: 2,9 # G3: 1,2 => SOL * STA E6: 2,9 + G3: 1,2 * CNT 2 HDP CHAINS / 40 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=90
Solution
position: 723691584189452763645387129938716245562843971471529638216938457857164392394275816 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 # A1: 7,9 => UNS * INC # C1: 7,9 => UNS * INC # D2: 7,9 => UNS * INC # F2: 7,9 => UNS * INC # A1: 5,7 => UNS * INC # C1: 5,7 => UNS * INC # G3: 5,7 => UNS * INC # G3: 1,2 => UNS * INC # C8: 5,7 => UNS * INC # C9: 5,7 => UNS * INC # F2: 2,7 => UNS * INC # F2: 4,6,9 => UNS * INC # G3: 2,7 => UNS * INC # G3: 1,5 => UNS * INC # D1: 4,6 => UNS * INC # D1: 7,9 => UNS * INC # F2: 2,6 => UNS * INC # F2: 4,7,9 => UNS * INC # G3: 1,2 => UNS * INC # G3: 5,7 => UNS * INC # A6: 4,5 => UNS * INC # C6: 4,5 => UNS * INC # A9: 4,5 => UNS * INC # A9: 3,7 => UNS * INC # D6: 1,4 => UNS * DIS # E6: 1,4 => CTR => E6: 2,9 * INC # E6: 2,9 => UNS * INC # E7: 1,4 => UNS * INC # E9: 1,4 => UNS * INC # B4: 1,5 => UNS * INC # D4: 1,5 => UNS * CNT 31 HDP CHAINS / 31 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 7,9 => UNS * INC # C1: 7,9 => UNS * INC # D2: 7,9 => UNS * INC # F2: 7,9 => UNS * INC # A1: 5,7 => UNS * INC # C1: 5,7 => UNS * INC # G3: 5,7 => UNS * INC # G3: 1,2 => UNS * INC # C8: 5,7 => UNS * INC # C9: 5,7 => UNS * INC # F2: 2,7 => UNS * INC # F2: 4,6,9 => UNS * INC # G3: 2,7 => UNS * INC # G3: 1,5 => UNS * INC # D1: 4,6 => UNS * INC # D1: 7,9 => UNS * INC # F2: 2,6 => UNS * INC # F2: 4,7,9 => UNS * INC # G3: 1,2 => UNS * INC # G3: 5,7 => UNS * INC # A6: 4,5 => UNS * INC # C6: 4,5 => UNS * INC # A9: 4,5 => UNS * INC # A9: 3,7 => UNS * INC # D6: 1,4 => UNS * DIS # E6: 1,4 => CTR => E6: 2,9 * INC E6: 2,9 # D6: 1,4 => UNS * INC E6: 2,9 # D6: 5,9 => UNS * INC E6: 2,9 # E7: 1,4 => UNS * INC E6: 2,9 # E9: 1,4 => UNS * INC E6: 2,9 # B4: 1,5 => UNS * INC E6: 2,9 # D4: 1,5 => UNS * INC E6: 2,9 # A1: 7,9 => UNS * INC E6: 2,9 # C1: 7,9 => UNS * INC E6: 2,9 # D2: 7,9 => UNS * INC E6: 2,9 # F2: 7,9 => UNS * INC E6: 2,9 # A1: 5,7 => UNS * INC E6: 2,9 # C1: 5,7 => UNS * INC E6: 2,9 # G3: 5,7 => UNS * PRF E6: 2,9 # G3: 1,2 => SOL * STA E6: 2,9 + G3: 1,2 * CNT 40 HDP CHAINS / 40 HYP OPENED