Analysis of zz-www.sudokuwiki.org-0342-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=342
level: medium
position: .6.7.........8......5..9.1.8...6......9.25.3..7......4.....35.1....9..2...2...3.. initial
Autosolve
position: .6.7.........8......5..9.1.8...671....9.25.3..7.9....4...2.35.1....9..2...2...3.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E1: 3,4 => CTR => E1: 1,5 * DIS # A5: 1,4 => CTR => A5: 6 * DIS # D5: 8 => CTR => D5: 1,4 * DIS # C6: 6 => CTR => C6: 1,3 * CNT 4 HDP CHAINS / 32 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E1: 3,4 => CTR => E1: 1,5 * DIS E1: 1,5 # A5: 1,4 => CTR => A5: 6 * DIS E1: 1,5 + A5: 6 # C7: 4,7 => CTR => C7: 6,8 * PRF E1: 1,5 + A5: 6 + C7: 6,8 # C8: 6,8 => SOL * STA E1: 1,5 + A5: 6 + C7: 6,8 + C8: 6,8 * CNT 4 HDP CHAINS / 51 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .6.7.........8......5..9.1.8...6......9.25.3..7......4.....35.1....9..2...2...3.. | initial |
| .6.7.........8......5..9.1.8...671....9.25.3..7.9....4...2.35.1....9..2...2...3.. | autosolve |
| 361752948297184653485639712824367195619425837573918264946273581738591426152846379 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) D3: 3,6 E3: 3,4 B4: 2,5 C4: 3,4 B5: 1,4 A6: 2,5 D4: 3,4 E6: 1,3 F6: 1,8 H4: 5,9 E7: 4,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F1,F2: 2.. / F1 = 2 => 11 pairs (_) / F2 = 2 => 12 pairs (_) B4,A6: 2.. / B4 = 2 => 11 pairs (_) / A6 = 2 => 10 pairs (_) I4,G6: 2.. / I4 = 2 => 10 pairs (_) / G6 = 2 => 11 pairs (_) B4,I4: 2.. / B4 = 2 => 11 pairs (_) / I4 = 2 => 10 pairs (_) A6,G6: 2.. / A6 = 2 => 10 pairs (_) / G6 = 2 => 11 pairs (_) C4,C6: 3.. / C4 = 3 => 11 pairs (_) / C6 = 3 => 12 pairs (_) D4,E6: 3.. / D4 = 3 => 12 pairs (_) / E6 = 3 => 11 pairs (_) A8,B8: 3.. / A8 = 3 => 11 pairs (_) / B8 = 3 => 11 pairs (_) C4,D4: 3.. / C4 = 3 => 11 pairs (_) / D4 = 3 => 12 pairs (_) C6,E6: 3.. / C6 = 3 => 12 pairs (_) / E6 = 3 => 11 pairs (_) D4,D5: 4.. / D4 = 4 => 11 pairs (_) / D5 = 4 => 12 pairs (_) C4,D4: 4.. / C4 = 4 => 12 pairs (_) / D4 = 4 => 11 pairs (_) E1,D2: 5.. / E1 = 5 => 12 pairs (_) / D2 = 5 => 13 pairs (_) B4,A6: 5.. / B4 = 5 => 10 pairs (_) / A6 = 5 => 11 pairs (_) A6,H6: 5.. / A6 = 5 => 11 pairs (_) / H6 = 5 => 10 pairs (_) E1,E9: 5.. / E1 = 5 => 12 pairs (_) / E9 = 5 => 13 pairs (_) A5,C6: 6.. / A5 = 6 => 16 pairs (_) / C6 = 6 => 0 pairs (X) G5,I5: 7.. / G5 = 7 => 12 pairs (_) / I5 = 7 => 13 pairs (_) E7,E9: 7.. / E7 = 7 => 10 pairs (_) / E9 = 7 => 0 pairs (X) C1,B3: 8.. / C1 = 8 => 12 pairs (_) / B3 = 8 => 13 pairs (_) D5,F6: 8.. / D5 = 8 => 0 pairs (X) / F6 = 8 => 16 pairs (_) G1,G2: 9.. / G1 = 9 => 11 pairs (_) / G2 = 9 => 11 pairs (_) H4,I4: 9.. / H4 = 9 => 11 pairs (_) / I4 = 9 => 11 pairs (_) A1,G1: 9.. / A1 = 9 => 11 pairs (_) / G1 = 9 => 11 pairs (_) I4,I9: 9.. / I4 = 9 => 11 pairs (_) / I9 = 9 => 11 pairs (_) * DURATION: 0:00:23.619740 START: 19:03:30.702514 END: 19:03:54.322254 2019-04-28 * CP COUNT: (25) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B4,B5,C4,D3,D4,E3,E6,E7,F6,H4) * .6.7.........8......5..9.1.8...671....9.25.3..7.9....4...2.35.1....9..2...2...3.. * PAIR D3: 3,6 BLK 2 D2: 3,6,1,5 # reduction candidate for 3,6 D2: 3,6 # 23 pairs D2: 1,5 # 12 pairs * PAIR D3: 3,6 ROW 3 I3: 3,6,2,7,8 # reduction candidate for 3,6 I3: 3,6 # 14 pairs I3: 2,7,8 # 11 pairs * PAIR E3: 3,4 BLK 2 E1: 3,4,1,5 # reduction candidate for 3,4 E1: 3,4 => CTR * .687.......758......56.9.1.8.43671..619425.3..73918..4..62735.1..189..2.7.215.3.. E1: 1,5 # 12 pairs * PAIR E3: 3,4 ROW 3 A3: 3,4,2,7 # reduction candidate for 3,4 A3: 3,4 # 13 pairs B3: 3,4,2,8 # reduction candidate for 3,4 B3: 3,4 # 13 pairs * PAIR B4: 2,5 ROW 4 I4: 2,5,9 # reduction candidate for 2,5 I4: 9 # 11 pairs I4: 2,5 # 11 pairs * PAIR B5: 1,4 BLK 4 A5: 1,4,6 # reduction candidate for 1,4 A5: 1,4 => CTR * .6.7.2.....7.86...285349.1.8234671....9825.3.576931284..82735.1..1.9..2.7.2...3.. A5: 6 # 16 pairs * PAIR B5: 1,4 ROW 5 D5: 1,4,8 # reduction candidate for 1,4 D5: 8 => CTR * .6.7.2.....7.86...285349.1.8234671....9825.3.576931284..82735.1..1.9..2.7.2...3.. D5: 1,4 # 16 pairs * PAIR B5: 1,4 COL B B2: 1,4,2,3,9 # reduction candidate for 1,4 B2: 1,4 # 13 pairs B8: 1,4,3,5,8 # reduction candidate for 1,4 B8: 1,4 # 14 pairs B9: 1,4,5,8,9 # reduction candidate for 1,4 B9: 1,4 # 13 pairs * PAIR E6: 1,3 ROW 6 C6: 1,3,6 # reduction candidate for 1,3 C6: 6 => CTR * .6.7.2.....7.86...285349.1.8234671....9825.3.576931284..82735.1..1.9..2.7.2...3.. C6: 1,3 # 16 pairs * PAIR E6: 1,3 COL E E1: 1,3,4,5 # reduction candidate for 1,3 E1: 1,3 # 13 pairs E1: 4,5 # 12 pairs * PAIR F6: 1,8 BLK 5 D5: 1,8,4 # reduction candidate for 1,8 D5: 4 # 12 pairs D5: 1,8 # 11 pairs * PAIR F6: 1,8 COL F F8: 1,8,4,6 # reduction candidate for 1,8 F8: 1,8 # 16 pairs F9: 1,8,4,6 # reduction candidate for 1,8 F9: 1,8 # 16 pairs * PAIR H4: 5,9 BLK 6 I4: 5,9,2 # reduction candidate for 5,9 I4: 5,9 # 11 pairs I4: 2 # 10 pairs * PAIR E7: 4,7 BLK 8 E9: 4,7,1,5 # reduction candidate for 4,7 E9: 4,7 # 21 pairs E9: 1,5 # 12 pairs * PAIR E7: 4,7 ROW 7 A7: 4,7,6,9 # reduction candidate for 4,7 A7: 4,7 # 14 pairs C7: 4,7,6,8 # reduction candidate for 4,7 C7: 4,7 # 14 pairs H7: 4,7,6,8,9 # reduction candidate for 4,7 H7: 4,7 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0342-base-pr-000.dot * REASONING * DIS # E1: 3,4 => CTR => E1: 1,5 * DIS # A5: 1,4 => CTR => A5: 6 * DIS # D5: 8 => CTR => D5: 1,4 * DIS # C6: 6 => CTR => C6: 1,3 * CNT 4 HDP CHAINS / 32 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B4,B5,C4,D3,D4,E3,E6,E7,F6,H4) * .6.7.........8......5..9.1.8...671....9.25.3..7.9....4...2.35.1....9..2...2...3.. * PAIR D3: 3,6 BLK 2 D2: 3,6,1,5 # reduction candidate for 3,6 D2: 3,6 # 23 pairs D2: 1,5 # 12 pairs * PAIR D3: 3,6 ROW 3 I3: 3,6,2,7,8 # reduction candidate for 3,6 I3: 3,6 # 14 pairs I3: 2,7,8 # 11 pairs * PAIR E3: 3,4 BLK 2 E1: 3,4,1,5 # reduction candidate for 3,4 E1: 3,4 => CTR * .687.......758......56.9.1.8.43671..619425.3..73918..4..62735.1..189..2.7.215.3.. * PAIR E3: 3,4 ROW 3 A3: 3,4,2,7 # reduction candidate for 3,4 A3: 3,4 # 14 pairs B3: 3,4,2,8 # reduction candidate for 3,4 B3: 3,4 # 14 pairs * PAIR B4: 2,5 ROW 4 I4: 2,5,9 # reduction candidate for 2,5 I4: 9 # 12 pairs I4: 2,5 # 12 pairs * PAIR B5: 1,4 BLK 4 A5: 1,4,6 # reduction candidate for 1,4 A5: 1,4 => CTR * .6.7.2.....7.86...285349.1.8234671....9825.3.576931284..82735.1..1.9..2.7.2...3.. * PAIR B5: 1,4 COL B B2: 1,4,2,3,9 # reduction candidate for 1,4 B2: 1,4 # 21 pairs B8: 1,4,3,5,8 # reduction candidate for 1,4 B8: 1,4 # 20 pairs B9: 1,4,5,8,9 # reduction candidate for 1,4 B9: 1,4 # 19 pairs * PAIR H4: 5,9 BLK 6 I4: 5,9,2 # reduction candidate for 5,9 I4: 5,9 # 14 pairs I4: 2 # 13 pairs * PAIR E7: 4,7 BLK 8 E9: 4,7,1,5 # reduction candidate for 4,7 E9: 4,7 # 21 pairs E9: 1,5 # 15 pairs * PAIR E7: 4,7 ROW 7 A7: 4,7,9 # reduction candidate for 4,7 A7: 4,7 # 20 pairs C7: 4,7,6,8 # reduction candidate for 4,7 C7: 4,7 => CTR * .687...4..9..8..7.7.5..9.1.85..671926.9.25.3.27.9.8654987243561..6891427..2.76389 H7: 4,7,6,8,9 # reduction candidate for 4,7 H7: 4,7 # 25 pairs * PAIR RESTART * PAIR E7: 4,7 BLK 8 E9: 4,7,1,5 # reduction candidate for 4,7 E9: 4,7 # 21 pairs E9: 1,5 # 16 pairs * PAIR E7: 4,7 ROW 7 A7: 4,7,9 # reduction candidate for 4,7 A7: 4,7 # 20 pairs H7: 4,7,6,8,9 # reduction candidate for 4,7 H7: 4,7 # 25 pairs * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A6,B4,B5,C4,C6,C7,D3,D4,D5,E1,E3,E6,E7,G5,G6,H4,H6,I5) * .6.7.........8......5..9.1.8...671..6.9.25.3..7.9.8..4...2.35.1....9..2...2...3.. * PAIR E1: 1,5 BLK 2 D2: 1,5,3,6 # reduction candidate for 1,5 D2: 3,6 # 24 pairs D2: 1,5 # 20 pairs * PAIR E1: 1,5 COL E E9: 1,5,4,7 # reduction candidate for 1,5 E9: 4,7 # 21 pairs E9: 1,5 # 16 pairs * PAIR D3: 3,6 BLK 2 D2: 3,6,1,5 # reduction candidate for 3,6 D2: 3,6 # 24 pairs D2: 1,5 # 20 pairs * PAIR D3: 3,6 ROW 3 I3: 3,6,2,7,8 # reduction candidate for 3,6 I3: 3,6 # 21 pairs I3: 2,7,8 # 18 pairs * PAIR E3: 3,4 ROW 3 A3: 3,4,2,7 # reduction candidate for 3,4 A3: 3,4 # 21 pairs B3: 3,4,2,8 # reduction candidate for 3,4 B3: 3,4 # 22 pairs * PAIR B4: 2,5 ROW 4 I4: 2,5,9 # reduction candidate for 2,5 I4: 2,5 # 18 pairs I4: 9 # 15 pairs * PAIR B5: 1,4 COL B B2: 1,4,2,3,9 # reduction candidate for 1,4 B2: 1,4 # 21 pairs B8: 1,4,3,5,8 # reduction candidate for 1,4 B8: 1,4 # 21 pairs B9: 1,4,5,8,9 # reduction candidate for 1,4 B9: 1,4 # 20 pairs * PAIR H4: 5,9 BLK 6 I4: 5,9,2 # reduction candidate for 5,9 I4: 5,9 # 14 pairs I4: 2 # 14 pairs * PAIR G5: 7,8 COL G G3: 7,8,2,4,6 # reduction candidate for 7,8 G3: 7,8 # 20 pairs G8: 7,8,4,6 # reduction candidate for 7,8 G8: 7,8 # 20 pairs * PAIR I5: 7,8 COL I I3: 7,8,2,3,6 # reduction candidate for 7,8 I3: 7,8 # 19 pairs I8: 7,8,6 # reduction candidate for 7,8 I8: 7,8 # 20 pairs I9: 7,8,6,9 # reduction candidate for 7,8 I9: 7,8 # 17 pairs * PAIR G6: 2,6 COL G G2: 2,6,4,7,9 # reduction candidate for 2,6 G2: 2,6 # 19 pairs G3: 2,6,4,7,8 # reduction candidate for 2,6 G3: 2,6 # 19 pairs * PAIR H6: 5,6 COL H H2: 5,6,4,7 # reduction candidate for 5,6 H2: 5,6 # 22 pairs H2: 4,7 # 19 pairs * PAIR C7: 6,8 BLK 7 C8: 6,8,1,4,7 # reduction candidate for 6,8 C8: 6,8 => SOLVED * 361752948297184653485639712824367195619425837573918264946273581738591426152846379 * DURATION: 0:00:33.651285 START: 19:04:11.953653 END: 19:04:45.604938 2019-04-28 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0342-base-pr-001.dot * REASONING * DIS # E1: 3,4 => CTR => E1: 1,5 * DIS E1: 1,5 # A5: 1,4 => CTR => A5: 6 * DIS E1: 1,5 + A5: 6 # C7: 4,7 => CTR => C7: 6,8 * PRF E1: 1,5 + A5: 6 + C7: 6,8 # C8: 6,8 => SOL * STA E1: 1,5 + A5: 6 + C7: 6,8 + C8: 6,8 * CNT 4 HDP CHAINS / 51 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=342
Solution
position: 361752948297184653485639712824367195619425837573918264946273581738591426152846379 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 # D2: 3,6 => UNS * INC # D2: 1,5 => UNS * INC # I3: 3,6 => UNS * INC # I3: 2,7,8 => UNS * DIS # E1: 3,4 => CTR => E1: 1,5 * INC # E1: 1,5 => UNS * INC # A3: 3,4 => UNS * INC # B3: 3,4 => UNS * INC # I4: 2,5 => UNS * INC # I4: 9 => UNS * DIS # A5: 1,4 => CTR => A5: 6 * INC # A5: 6 => UNS * INC # D5: 1,4 => UNS * DIS # D5: 8 => CTR => D5: 1,4 * INC # B2: 1,4 => UNS * INC # B8: 1,4 => UNS * INC # B9: 1,4 => UNS * INC # C6: 1,3 => UNS * DIS # C6: 6 => CTR => C6: 1,3 * INC # E1: 1,3 => UNS * INC # E1: 4,5 => UNS * INC # D5: 1,8 => UNS * INC # D5: 4 => UNS * INC # F8: 1,8 => UNS * INC # F9: 1,8 => UNS * INC # I4: 5,9 => UNS * INC # I4: 2 => UNS * INC # E9: 4,7 => UNS * INC # E9: 1,5 => UNS * INC # A7: 4,7 => UNS * INC # C7: 4,7 => UNS * INC # H7: 4,7 => UNS * CNT 32 HDP CHAINS / 32 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D2: 3,6 => UNS * INC # D2: 1,5 => UNS * INC # I3: 3,6 => UNS * INC # I3: 2,7,8 => UNS * DIS # E1: 3,4 => CTR => E1: 1,5 * INC E1: 1,5 # A3: 3,4 => UNS * INC E1: 1,5 # B3: 3,4 => UNS * INC E1: 1,5 # I4: 2,5 => UNS * INC E1: 1,5 # I4: 9 => UNS * DIS E1: 1,5 # A5: 1,4 => CTR => A5: 6 * INC E1: 1,5 + A5: 6 # B2: 1,4 => UNS * INC E1: 1,5 + A5: 6 # B8: 1,4 => UNS * INC E1: 1,5 + A5: 6 # B9: 1,4 => UNS * INC E1: 1,5 + A5: 6 # I4: 5,9 => UNS * INC E1: 1,5 + A5: 6 # I4: 2 => UNS * INC E1: 1,5 + A5: 6 # E9: 4,7 => UNS * INC E1: 1,5 + A5: 6 # E9: 1,5 => UNS * INC E1: 1,5 + A5: 6 # A7: 4,7 => UNS * DIS E1: 1,5 + A5: 6 # C7: 4,7 => CTR => C7: 6,8 * INC E1: 1,5 + A5: 6 + C7: 6,8 # H7: 4,7 => UNS * INC E1: 1,5 + A5: 6 + C7: 6,8 # E9: 4,7 => UNS * INC E1: 1,5 + A5: 6 + C7: 6,8 # E9: 1,5 => UNS * INC E1: 1,5 + A5: 6 + C7: 6,8 # A7: 4,7 => UNS * INC E1: 1,5 + A5: 6 + C7: 6,8 # H7: 4,7 => UNS * INC E1: 1,5 + A5: 6 + C7: 6,8 # D2: 1,5 => UNS * INC E1: 1,5 + A5: 6 + C7: 6,8 # D2: 3,6 => UNS * INC E1: 1,5 + A5: 6 + C7: 6,8 # E9: 1,5 => UNS * INC E1: 1,5 + A5: 6 + C7: 6,8 # E9: 4,7 => UNS * INC E1: 1,5 + A5: 6 + C7: 6,8 # D2: 3,6 => UNS * INC E1: 1,5 + A5: 6 + C7: 6,8 # D2: 1,5 => UNS * INC E1: 1,5 + A5: 6 + C7: 6,8 # I3: 3,6 => UNS * INC E1: 1,5 + A5: 6 + C7: 6,8 # I3: 2,7,8 => UNS * INC E1: 1,5 + A5: 6 + C7: 6,8 # A3: 3,4 => UNS * INC E1: 1,5 + A5: 6 + C7: 6,8 # B3: 3,4 => UNS * INC E1: 1,5 + A5: 6 + C7: 6,8 # I4: 2,5 => UNS * INC E1: 1,5 + A5: 6 + C7: 6,8 # I4: 9 => UNS * INC E1: 1,5 + A5: 6 + C7: 6,8 # B2: 1,4 => UNS * INC E1: 1,5 + A5: 6 + C7: 6,8 # B8: 1,4 => UNS * INC E1: 1,5 + A5: 6 + C7: 6,8 # B9: 1,4 => UNS * INC E1: 1,5 + A5: 6 + C7: 6,8 # I4: 5,9 => UNS * INC E1: 1,5 + A5: 6 + C7: 6,8 # I4: 2 => UNS * INC E1: 1,5 + A5: 6 + C7: 6,8 # G3: 7,8 => UNS * INC E1: 1,5 + A5: 6 + C7: 6,8 # G8: 7,8 => UNS * INC E1: 1,5 + A5: 6 + C7: 6,8 # I3: 7,8 => UNS * INC E1: 1,5 + A5: 6 + C7: 6,8 # I8: 7,8 => UNS * INC E1: 1,5 + A5: 6 + C7: 6,8 # I9: 7,8 => UNS * INC E1: 1,5 + A5: 6 + C7: 6,8 # G2: 2,6 => UNS * INC E1: 1,5 + A5: 6 + C7: 6,8 # G3: 2,6 => UNS * INC E1: 1,5 + A5: 6 + C7: 6,8 # H2: 5,6 => UNS * INC E1: 1,5 + A5: 6 + C7: 6,8 # H2: 4,7 => UNS * PRF E1: 1,5 + A5: 6 + C7: 6,8 # C8: 6,8 => SOL * STA E1: 1,5 + A5: 6 + C7: 6,8 + C8: 6,8 * CNT 51 HDP CHAINS / 51 HYP OPENED