Analysis of zz-www.sudokuwiki.org-0026-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=26
level: medium
position: ..61.54..2..74...8....9.....8.....9.1...8...4.5.....2.....7....3...19..7..76.32.. initial
Autosolve
position: 8.61.54..2..746..8....9.....8.....9.1...8...4.5....82.....7....3...19..7..765328. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D3: 8 => CTR => D3: 2,3 * DIS # D3: 2,8 => CTR => D3: 3 * DIS # F7: 2,8 => CTR => F7: 4 * DIS # B5: 2,7 => CTR => B5: 3,6,9 * DIS # E4: 2 => CTR => E4: 3,6 * DIS # I6: 1 => CTR => I6: 3,6 * DIS # B9: 1 => CTR => B9: 4,9 * DIS # A6: 4,9 => CTR => A6: 6,7 * DIS # H8: 5,6 => CTR => H8: 4 * DIS # G4: 5,6 => CTR => G4: 1,3,7 * DIS # I7: 1,9 => CTR => I7: 3,5,6 * CNT 11 HDP CHAINS / 46 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D3: 8 => CTR => D3: 2,3 * DIS D3: 2,3 # B5: 2,7 => CTR => B5: 3,6,9 * DIS D3: 2,3 + B5: 3,6,9 # E4: 2 => CTR => E4: 3,6 * DIS D3: 2,3 + B5: 3,6,9 + E4: 3,6 # I6: 1 => CTR => I6: 3,6 * PRF D3: 2,3 + B5: 3,6,9 + E4: 3,6 + I6: 3,6 # B7: 2,6 => SOL * STA D3: 2,3 + B5: 3,6,9 + E4: 3,6 + I6: 3,6 + B7: 2,6 * CNT 5 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..61.54..2..74...8....9.....8.....9.1...8...4.5.....2.....7....3...19..7..76.32.. | initial |
| 8.61.54..2..746..8....9.....8.....9.1...8...4.5....82.....7....3...19..7..765328. | autosolve |
| 836125479219746358475398612682437195193582764754961823521874936368219547947653281 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) E1: 2,3 F3: 2,8 H1: 3,7 F5: 2,7 E6: 3,6 B8: 2,6 A9: 4,9 G8: 5,6 I9: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F4,F6: 1.. / F4 = 1 => 0 pairs (X) / F6 = 1 => 15 pairs (_) F6,I6: 1.. / F6 = 1 => 15 pairs (_) / I6 = 1 => 0 pairs (X) B9,I9: 1.. / B9 = 1 => 0 pairs (X) / I9 = 1 => 23 pairs (_) I1,I3: 2.. / I1 = 2 => 0 pairs (X) / I3 = 2 => 11 pairs (_) E1,I1: 2.. / E1 = 2 => 11 pairs (_) / I1 = 2 => 0 pairs (X) E1,E4: 2.. / E1 = 2 => 11 pairs (_) / E4 = 2 => 0 pairs (X) E1,D3: 3.. / E1 = 3 => 0 pairs (X) / D3 = 3 => 11 pairs (_) A9,B9: 4.. / A9 = 4 => 11 pairs (_) / B9 = 4 => 23 pairs (_) H7,H8: 4.. / H7 = 4 => 0 pairs (X) / H8 = 4 => 10 pairs (_) D8,H8: 4.. / D8 = 4 => 0 pairs (X) / H8 = 4 => 10 pairs (_) B3,B9: 4.. / B3 = 4 => 11 pairs (_) / B9 = 4 => 23 pairs (_) D4,D5: 5.. / D4 = 5 => 9 pairs (_) / D5 = 5 => 11 pairs (_) A3,A7: 5.. / A3 = 5 => 13 pairs (_) / A7 = 5 => 12 pairs (_) E4,E6: 6.. / E4 = 6 => 15 pairs (_) / E6 = 6 => 10 pairs (_) B1,H1: 7.. / B1 = 7 => 0 pairs (X) / H1 = 7 => 9 pairs (_) A6,F6: 7.. / A6 = 7 => 13 pairs (_) / F6 = 7 => 0 pairs (X) D3,F3: 8.. / D3 = 8 => 0 pairs (X) / F3 = 8 => 10 pairs (_) C7,C8: 8.. / C7 = 8 => 13 pairs (_) / C8 = 8 => 10 pairs (_) C8,D8: 8.. / C8 = 8 => 10 pairs (_) / D8 = 8 => 13 pairs (_) F3,F7: 8.. / F3 = 8 => 10 pairs (_) / F7 = 8 => 0 pairs (X) I1,G2: 9.. / I1 = 9 => 23 pairs (_) / G2 = 9 => 11 pairs (_) D5,D6: 9.. / D5 = 9 => 11 pairs (_) / D6 = 9 => 11 pairs (_) B1,I1: 9.. / B1 = 9 => 11 pairs (_) / I1 = 9 => 23 pairs (_) G2,G7: 9.. / G2 = 9 => 11 pairs (_) / G7 = 9 => 23 pairs (_) * DURATION: 0:00:31.458276 START: 03:55:31.377243 END: 03:56:02.835519 2017-05-01 * CP COUNT: (24) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B8,E1,E6,F3,F5,G8,H1,I9) * 8.61.54..2..746..8....9.....8.....9.1...8...4.5....82.....7....3...19..7..765328. * PAIR E1: 2,3 BLK 2 D3: 2,3,8 # reduction candidate for 2,3 D3: 8 => CTR * 8961354722..7469.8.7.892....8..2.79.1...87..475..6.82.....78...3.8.19..7.47653281 D3: 2,3 # 10 pairs * PAIR E1: 2,3 ROW 1 I1: 2,3,9 # reduction candidate for 2,3 I1: 9 # 23 pairs I1: 2,3 # 11 pairs * PAIR E1: 2,3 COL E E4: 2,3,6 # reduction candidate for 2,3 E4: 6 # 15 pairs E4: 2,3 # 10 pairs * PAIR F3: 2,8 BLK 2 D3: 2,8,3 # reduction candidate for 2,8 D3: 2,8 => CTR * 8961354722..7469.8.7..9.....8..2.79.1...87..475..6.82.....7....3...19..7.47653281 D3: 3 # 11 pairs * PAIR F3: 2,8 COL F F7: 2,8,4 # reduction candidate for 2,8 F7: 2,8 => CTR * 8961.547.23.746..8....9.....8....79.1...87..475....82.....7....3...19..7.17653289 F7: 4 # 15 pairs * PAIR H1: 3,7 BLK 3 G3: 3,7,1,5,6 # reduction candidate for 3,7 G3: 3,7 # 13 pairs H3: 3,7,1,5,6 # reduction candidate for 3,7 H3: 3,7 # 14 pairs * PAIR H1: 3,7 ROW 1 B1: 3,7,9 # reduction candidate for 3,7 B1: 3,7 # 23 pairs B1: 9 # 11 pairs * PAIR H1: 3,7 COL H H5: 3,7,5,6 # reduction candidate for 3,7 H5: 3,7 # 11 pairs H5: 5,6 # 10 pairs * PAIR F5: 2,7 BLK 5 F4: 2,7,1,4 # reduction candidate for 2,7 F4: 2,7 # 20 pairs F4: 1,4 # 10 pairs * PAIR F5: 2,7 ROW 5 B5: 2,7,3,6,9 # reduction candidate for 2,7 B5: 2,7 => CTR * 89612547323.7469.874.398..2682.3179517.582..495...7821....7....3...19..7417653289 B5: 3,6,9 # 11 pairs * PAIR E6: 3,6 BLK 5 E4: 3,6,2 # reduction candidate for 3,6 E4: 2 => CTR * 8.61354722..7469.8.7..9.....8..2.79.1...87..475..6.82.....7....3...19..7.47653281 E4: 3,6 # 11 pairs * PAIR E6: 3,6 ROW 6 I6: 3,6,1 # reduction candidate for 3,6 I6: 1 => CTR * 89612547323.7469.874.398..268243179517.582..495...7821....74...3...19.47417653289 I6: 3,6 # 15 pairs * PAIR B8: 2,6 BLK 7 B7: 2,6,1,9 # reduction candidate for 2,6 B7: 1,9 # 14 pairs B7: 2,6 # 13 pairs * PAIR B8: 2,6 COL B B5: 2,6,3,7,9 # reduction candidate for 2,6 B5: 2,6 # 14 pairs B5: 3,7,9 # 13 pairs * PAIR A9: 4,9 BLK 7 B9: 4,9,1 # reduction candidate for 4,9 B9: 1 => CTR * 89612547323.7469.874.398..2682.31795173.82..495..678215.9.7....3.8.19..7417653289 B9: 4,9 # 23 pairs * PAIR A9: 4,9 COL A A6: 4,9,6,7 # reduction candidate for 4,9 A6: 4,9 => CTR * 89612547323.7469.874.398..268243179517.582..495..67821....74...3...19.47417653289 A6: 6,7 # 11 pairs * PAIR G8: 5,6 BLK 9 G7: 5,6,1,3,9 # reduction candidate for 5,6 G7: 5,6 # 16 pairs H7: 5,6,1,3,4 # reduction candidate for 5,6 H7: 5,6 # 11 pairs I7: 5,6,1,3,9 # reduction candidate for 5,6 I7: 5,6 # 12 pairs H8: 5,6,4 # reduction candidate for 5,6 H8: 5,6 => CTR * 8961.547223.746..8....9.....8....79.1...87..475....82.....7.143328419..7.17653289 H8: 4 # 10 pairs * PAIR G8: 5,6 COL G G3: 5,6,1,3,7 # reduction candidate for 5,6 G3: 5,6 # 11 pairs G4: 5,6,1,3,7 # reduction candidate for 5,6 G4: 5,6 => CTR * 89612547323.746..8....9.....8.....9.1...82..4.5....82.....7....3...19..7.17653289 G4: 1,3,7 # 9 pairs G5: 5,6,3,7 # reduction candidate for 5,6 G5: 5,6 # 10 pairs * PAIR I9: 1,9 BLK 9 G7: 1,9,3,5,6 # reduction candidate for 1,9 G7: 1,9 # 10 pairs I7: 1,9,3,5,6 # reduction candidate for 1,9 I7: 1,9 => CTR * 8961254732..7469.8.7.398..2.82.371951..582734753..182.....74...3...19.47.47653281 I7: 3,5,6 # 9 pairs * PAIR I9: 1,9 ROW 9 B9: 1,9,4 # reduction candidate for 1,9 B9: 4 # 23 pairs B9: 1,9 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0026-base-pr-000.dot * REASONING * DIS # D3: 8 => CTR => D3: 2,3 * DIS # D3: 2,8 => CTR => D3: 3 * DIS # F7: 2,8 => CTR => F7: 4 * DIS # B5: 2,7 => CTR => B5: 3,6,9 * DIS # E4: 2 => CTR => E4: 3,6 * DIS # I6: 1 => CTR => I6: 3,6 * DIS # B9: 1 => CTR => B9: 4,9 * DIS # A6: 4,9 => CTR => A6: 6,7 * DIS # H8: 5,6 => CTR => H8: 4 * DIS # G4: 5,6 => CTR => G4: 1,3,7 * DIS # I7: 1,9 => CTR => I7: 3,5,6 * CNT 11 HDP CHAINS / 46 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B8,E1,E6,F3,F5,G8,H1,I9) * 8.61.54..2..746..8....9.....8.....9.1...8...4.5....82.....7....3...19..7..765328. * PAIR E1: 2,3 BLK 2 D3: 2,3,8 # reduction candidate for 2,3 D3: 8 => CTR * 8961354722..7469.8.7.892....8..2.79.1...87..475..6.82.....78...3.8.19..7.47653281 * PAIR E1: 2,3 ROW 1 I1: 2,3,9 # reduction candidate for 2,3 I1: 9 # 23 pairs I1: 2,3 # 12 pairs * PAIR E1: 2,3 COL E E4: 2,3,6 # reduction candidate for 2,3 E4: 6 # 15 pairs E4: 2,3 # 11 pairs * PAIR H1: 3,7 BLK 3 G3: 3,7,1,5,6 # reduction candidate for 3,7 G3: 3,7 # 14 pairs H3: 3,7,1,5,6 # reduction candidate for 3,7 H3: 3,7 # 15 pairs * PAIR H1: 3,7 ROW 1 B1: 3,7,9 # reduction candidate for 3,7 B1: 3,7 # 23 pairs B1: 9 # 12 pairs * PAIR H1: 3,7 COL H H5: 3,7,5,6 # reduction candidate for 3,7 H5: 3,7 # 12 pairs H5: 5,6 # 11 pairs * PAIR F5: 2,7 BLK 5 F4: 2,7,1,4 # reduction candidate for 2,7 F4: 2,7 # 20 pairs F4: 1,4 # 11 pairs * PAIR F5: 2,7 ROW 5 B5: 2,7,3,6,9 # reduction candidate for 2,7 B5: 2,7 => CTR * 89612547323.7469.874.398..268243179517.582..495...7821....74...3...19.47417653289 * PAIR RESTART * PAIR F5: 2,7 BLK 5 F4: 2,7,1,4 # reduction candidate for 2,7 F4: 2,7 # 21 pairs F4: 1,4 # 13 pairs * PAIR E6: 3,6 BLK 5 E4: 3,6,2 # reduction candidate for 3,6 E4: 2 => CTR * 8.61354722..7469.8.7.298....8..2.79.1.2.87..475..6.82.....72...32..19..7.47653281 * PAIR E6: 3,6 ROW 6 I6: 3,6,1 # reduction candidate for 3,6 I6: 1 => CTR * 89612547323.746..8...398..2.8.....9.1...8...4.5....821....7....3...19..7.17653289 * PAIR RESTART * PAIR B8: 2,6 BLK 7 B7: 2,6,1 # reduction candidate for 2,6 B7: 2,6 => SOLVED * 836125479219746358475398612682437195193582764754961823521874936368219547947653281 * DURATION: 0:00:18.448034 START: 03:56:35.779938 END: 03:56:54.227972 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0026-base-pr-001.dot * REASONING * DIS # D3: 8 => CTR => D3: 2,3 * DIS D3: 2,3 # B5: 2,7 => CTR => B5: 3,6,9 * DIS D3: 2,3 + B5: 3,6,9 # E4: 2 => CTR => E4: 3,6 * DIS D3: 2,3 + B5: 3,6,9 + E4: 3,6 # I6: 1 => CTR => I6: 3,6 * PRF D3: 2,3 + B5: 3,6,9 + E4: 3,6 + I6: 3,6 # B7: 2,6 => SOL * STA D3: 2,3 + B5: 3,6,9 + E4: 3,6 + I6: 3,6 + B7: 2,6 * CNT 5 HDP CHAINS / 22 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=26
Solution
position: 836125479219746358475398612682437195193582764754961823521874936368219547947653281 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 # D3: 2,3 => UNS * DIS # D3: 8 => CTR => D3: 2,3 * INC # I1: 2,3 => UNS * INC # I1: 9 => UNS * INC # E4: 2,3 => UNS * INC # E4: 6 => UNS * DIS # D3: 2,8 => CTR => D3: 3 * INC # D3: 3 => UNS * DIS # F7: 2,8 => CTR => F7: 4 * INC # F7: 4 => UNS * INC # G3: 3,7 => UNS * INC # H3: 3,7 => UNS * INC # B1: 3,7 => UNS * INC # B1: 9 => UNS * INC # H5: 3,7 => UNS * INC # H5: 5,6 => UNS * INC # F4: 2,7 => UNS * INC # F4: 1,4 => UNS * DIS # B5: 2,7 => CTR => B5: 3,6,9 * INC # B5: 3,6,9 => UNS * INC # E4: 3,6 => UNS * DIS # E4: 2 => CTR => E4: 3,6 * INC # I6: 3,6 => UNS * DIS # I6: 1 => CTR => I6: 3,6 * INC # B7: 2,6 => UNS * INC # B7: 1,9 => UNS * INC # B5: 2,6 => UNS * INC # B5: 3,7,9 => UNS * INC # B9: 4,9 => UNS * DIS # B9: 1 => CTR => B9: 4,9 * DIS # A6: 4,9 => CTR => A6: 6,7 * INC # A6: 6,7 => UNS * INC # G7: 5,6 => UNS * INC # H7: 5,6 => UNS * INC # I7: 5,6 => UNS * DIS # H8: 5,6 => CTR => H8: 4 * INC # H8: 4 => UNS * INC # G3: 5,6 => UNS * DIS # G4: 5,6 => CTR => G4: 1,3,7 * INC # G4: 1,3,7 => UNS * INC # G5: 5,6 => UNS * INC # G7: 1,9 => UNS * DIS # I7: 1,9 => CTR => I7: 3,5,6 * INC # I7: 3,5,6 => UNS * INC # B9: 1,9 => UNS * INC # B9: 4 => UNS * CNT 46 HDP CHAINS / 46 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D3: 2,3 => UNS * DIS # D3: 8 => CTR => D3: 2,3 * INC D3: 2,3 # I1: 2,3 => UNS * INC D3: 2,3 # I1: 9 => UNS * INC D3: 2,3 # E4: 2,3 => UNS * INC D3: 2,3 # E4: 6 => UNS * INC D3: 2,3 # G3: 3,7 => UNS * INC D3: 2,3 # H3: 3,7 => UNS * INC D3: 2,3 # B1: 3,7 => UNS * INC D3: 2,3 # B1: 9 => UNS * INC D3: 2,3 # H5: 3,7 => UNS * INC D3: 2,3 # H5: 5,6 => UNS * INC D3: 2,3 # F4: 2,7 => UNS * INC D3: 2,3 # F4: 1,4 => UNS * DIS D3: 2,3 # B5: 2,7 => CTR => B5: 3,6,9 * INC D3: 2,3 + B5: 3,6,9 # F4: 2,7 => UNS * INC D3: 2,3 + B5: 3,6,9 # F4: 1,4 => UNS * INC D3: 2,3 + B5: 3,6,9 # E4: 3,6 => UNS * DIS D3: 2,3 + B5: 3,6,9 # E4: 2 => CTR => E4: 3,6 * INC D3: 2,3 + B5: 3,6,9 + E4: 3,6 # I6: 3,6 => UNS * DIS D3: 2,3 + B5: 3,6,9 + E4: 3,6 # I6: 1 => CTR => I6: 3,6 * PRF D3: 2,3 + B5: 3,6,9 + E4: 3,6 + I6: 3,6 # B7: 2,6 => SOL * STA D3: 2,3 + B5: 3,6,9 + E4: 3,6 + I6: 3,6 + B7: 2,6 * CNT 22 HDP CHAINS / 22 HYP OPENED