Analysis of zz-www.sudokuwiki.org-0040-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=40
level: medium
position: .7...6.8..9.4...7...2...1.....2..9..5...1...6..4..8.......7.5...8...9.2..6.5...9. initial
Autosolve
position: .7...6.8..9.4...7..52...1.....2..9..5...1...6..4..8....4..7.5...85..9.2..6.5...9. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 1,3 => CTR => A1: 4 * PRF # C2: 1,3 => SOL * PRF # D3: 3,7 => SOL * DIS # F4: 3,7 => CTR => F4: 4,5 * DIS # B6: 2 => CTR => B6: 1,3 * DIS # G5: 2,3 => CTR => G5: 4,7,8 * PRF # G5: 3,4 => SOL * PRF # F5: 7 => SOL * CNT 8 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 1,3 => CTR => A1: 4 * PRF A1: 4 # C2: 1,3 => SOL * STA A1: 4 + C2: 1,3 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .7...6.8..9.4...7...2...1.....2..9..5...1...6..4..8.......7.5...8...9.2..6.5...9. | initial |
| .7...6.8..9.4...7..52...1.....2..9..5...1...6..4..8....4..7.5...85..9.2..6.5...9. | autosolve |
| 473196285891425673652783149736254918528917436914368752349872561185649327267531894 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) C1: 1,3 F3: 3,7 B4: 1,3 B5: 2,3 H5: 3,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,F2: 1.. / D1 = 1 => 13 pairs (_) / F2 = 1 => 9 pairs (_) B4,B6: 1.. / B4 = 1 => 5 pairs (_) / B6 = 1 => 4 pairs (_) B5,B6: 2.. / B5 = 2 => 5 pairs (_) / B6 = 2 => 0 pairs (X) A7,A9: 2.. / A7 = 2 => 13 pairs (_) / A9 = 2 => 5 pairs (_) B5,G5: 2.. / B5 = 2 => 5 pairs (_) / G5 = 2 => 0 pairs (X) A7,F7: 2.. / A7 = 2 => 13 pairs (_) / F7 = 2 => 5 pairs (_) A1,A3: 4.. / A1 = 4 => 6 pairs (_) / A3 = 4 => 0 pairs (X) I1,I2: 5.. / I1 = 5 => 12 pairs (_) / I2 = 5 => 6 pairs (_) H4,H6: 5.. / H4 = 5 => 0 pairs (X) / H6 = 5 => 5 pairs (_) E1,I1: 5.. / E1 = 5 => 6 pairs (_) / I1 = 5 => 12 pairs (_) E6,H6: 5.. / E6 = 5 => 0 pairs (X) / H6 = 5 => 5 pairs (_) F2,F4: 5.. / F2 = 5 => 0 pairs (*) / F4 = 5 => 0 pairs (X) G2,H3: 6.. / G2 = 6 => 11 pairs (_) / H3 = 6 => 22 pairs (_) H7,G8: 6.. / H7 = 6 => 11 pairs (_) / G8 = 6 => 22 pairs (_) A3,H3: 6.. / A3 = 6 => 11 pairs (_) / H3 = 6 => 22 pairs (_) D7,H7: 6.. / D7 = 6 => 22 pairs (_) / H7 = 6 => 11 pairs (_) C2,C4: 6.. / C2 = 6 => 20 pairs (_) / C4 = 6 => 7 pairs (_) G2,G8: 6.. / G2 = 6 => 11 pairs (_) / G8 = 6 => 22 pairs (_) H3,H7: 6.. / H3 = 6 => 22 pairs (_) / H7 = 6 => 11 pairs (_) D3,F3: 7.. / D3 = 7 => 0 pairs (*) / F3 = 7 => 0 pairs (X) I4,G5: 8.. / I4 = 8 => 0 pairs (*) / G5 = 8 => 0 pairs (X) D7,E9: 8.. / D7 = 8 => 12 pairs (_) / E9 = 8 => 10 pairs (_) C5,G5: 8.. / C5 = 8 => 0 pairs (*) / G5 = 8 => 0 pairs (X) D7,I7: 8.. / D7 = 8 => 12 pairs (_) / I7 = 8 => 10 pairs (_) D3,D7: 8.. / D3 = 8 => 10 pairs (_) / D7 = 8 => 12 pairs (_) G5,G9: 8.. / G5 = 8 => 8 pairs (_) / G9 = 8 => 0 pairs (*) I1,I3: 9.. / I1 = 9 => 9 pairs (_) / I3 = 9 => 10 pairs (_) C5,A6: 9.. / C5 = 9 => 12 pairs (_) / A6 = 9 => 12 pairs (_) A7,C7: 9.. / A7 = 9 => 12 pairs (_) / C7 = 9 => 12 pairs (_) C5,D5: 9.. / C5 = 9 => 12 pairs (_) / D5 = 9 => 12 pairs (_) A6,A7: 9.. / A6 = 9 => 12 pairs (_) / A7 = 9 => 12 pairs (_) C5,C7: 9.. / C5 = 9 => 12 pairs (_) / C7 = 9 => 12 pairs (_) * DURATION: 0:00:43.419144 START: 04:12:27.690307 END: 04:13:11.109451 2017-05-01 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B5,C1,F3,H5) * .7...6.8..9.4...7..52...1.....2..9..5...1...6..4..8....4..7.5...85..9.2..6.5...9. * PAIR C1: 1,3 BLK 1 A1: 1,3,4 # reduction candidate for 1,3 A1: 1,3 => CTR * .7.9.6.8..9.4.1.7.452837169...2.59..52971.8.6..4398.5.94.6725.8.8514962.267583491 A1: 4 # 6 pairs A2: 1,3,6,8 # reduction candidate for 1,3 A2: 1,3 # 9 pairs C2: 1,3,6,8 # reduction candidate for 1,3 C2: 1,3 => SOLVED * 473196285891425673652783149736254918528917436914368752349872561185649327267531894 C2: 6,8 # 6 pairs * PAIR C1: 1,3 ROW 1 D1: 1,3,9 # reduction candidate for 1,3 D1: 9 # 19 pairs D1: 1,3 # 11 pairs * PAIR C1: 1,3 COL C C7: 1,3,9 # reduction candidate for 1,3 C7: 1,3 # 12 pairs C9: 1,3,7 # reduction candidate for 1,3 C9: 1,3 # 15 pairs * PAIR F3: 3,7 BLK 2 D3: 3,7,8,9 # reduction candidate for 3,7 D3: 3,7 => SOLVED * 473196285891425673652783149736254918528917436914368752349872561185649327267531894 D3: 8,9 # 8 pairs * PAIR F3: 3,7 COL F F4: 3,7,4,5 # reduction candidate for 3,7 F4: 3,7 => CTR * 473196285.9.425673652783149..62.79..5279148369.4..87.2.4987.561185..9.2..6.5...9. F4: 4,5 # 6 pairs F5: 3,7,4 # reduction candidate for 3,7 F5: 3,7 # 8 pairs * PAIR B4: 1,3 BLK 4 B6: 1,3,2 # reduction candidate for 1,3 B6: 2 => CTR * .7...6.8..9.4...7..52...1...1.2..9.8538917246924..8....4987.56..85..9.2..6.5..89. B6: 1,3 # 5 pairs * PAIR B4: 1,3 ROW 4 H4: 1,3,4,5 # reduction candidate for 1,3 H4: 1,3 # 6 pairs I4: 1,3,4,7,8 # reduction candidate for 1,3 I4: 1,3 # 14 pairs * PAIR B5: 2,3 BLK 4 B6: 2,3,1 # reduction candidate for 2,3 B6: 2,3 # 5 pairs B6: 1 # 4 pairs * PAIR B5: 2,3 ROW 5 G5: 2,3,4,7,8 # reduction candidate for 2,3 G5: 2,3 => CTR * .7...6.8..9.4...7..52...1.....2..9.85.8917.469.4..8....4987.56..85..9.2..6.5..89. G5: 4,7,8 # 5 pairs * PAIR H5: 3,4 BLK 6 H4: 3,4,1,5 # reduction candidate for 3,4 H4: 3,4 # 25 pairs I4: 3,4,1,7,8 # reduction candidate for 3,4 I4: 3,4 # 15 pairs G5: 3,4,2,7,8 # reduction candidate for 3,4 G5: 3,4 => SOLVED * 473196285891425673652783149736254918528917436914368752349872561185649327267531894 G5: 2,7,8 # 5 pairs * PAIR H5: 3,4 ROW 5 F5: 3,4,7 # reduction candidate for 3,4 F5: 7 => SOLVED * 473196285891425673652783149736254918528917436914368752349872561185649327267531894 F5: 3,4 # 8 pairs * PAIR H5: 3,4 COL H H3: 3,4,6 # reduction candidate for 3,4 H3: 6 # 22 pairs H3: 3,4 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0040-base-pr-000.dot * REASONING * DIS # A1: 1,3 => CTR => A1: 4 * PRF # C2: 1,3 => SOL * PRF # D3: 3,7 => SOL * DIS # F4: 3,7 => CTR => F4: 4,5 * DIS # B6: 2 => CTR => B6: 1,3 * DIS # G5: 2,3 => CTR => G5: 4,7,8 * PRF # G5: 3,4 => SOL * PRF # F5: 7 => SOL * CNT 8 HDP CHAINS / 30 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B5,C1,F3,H5) * .7...6.8..9.4...7..52...1.....2..9..5...1...6..4..8....4..7.5...85..9.2..6.5...9. * PAIR C1: 1,3 BLK 1 A1: 1,3,4 # reduction candidate for 1,3 A1: 1,3 => CTR * .7.9.6.8..9.4.1.7.452837169...2.59..52971.8.6..4398.5.94.6725.8.8514962.267583491 A2: 1,3,6,8 # reduction candidate for 1,3 A2: 1,3 # 9 pairs C2: 1,3,6,8 # reduction candidate for 1,3 C2: 1,3 => SOLVED * 473196285891425673652783149736254918528917436914368752349872561185649327267531894 * DURATION: 0:00:04.177925 START: 04:13:34.793385 END: 04:13:38.971310 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0040-base-pr-001.dot * REASONING * DIS # A1: 1,3 => CTR => A1: 4 * PRF A1: 4 # C2: 1,3 => SOL * STA A1: 4 + C2: 1,3 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=40
Solution
position: 473196285891425673652783149736254918528917436914368752349872561185649327267531894 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:
* DIS # A1: 1,3 => CTR => A1: 4 * INC # A1: 4 => UNS * INC # A2: 1,3 => UNS * PRF # C2: 1,3 => SOL * INC # C2: 6,8 => UNS * INC # D1: 1,3 => UNS * INC # D1: 9 => UNS * INC # C7: 1,3 => UNS * INC # C9: 1,3 => UNS * PRF # D3: 3,7 => SOL * INC # D3: 8,9 => UNS * DIS # F4: 3,7 => CTR => F4: 4,5 * INC # F4: 4,5 => UNS * INC # F5: 3,7 => UNS * INC # B6: 1,3 => UNS * DIS # B6: 2 => CTR => B6: 1,3 * INC # H4: 1,3 => UNS * INC # I4: 1,3 => UNS * INC # B6: 2,3 => UNS * INC # B6: 1 => UNS * DIS # G5: 2,3 => CTR => G5: 4,7,8 * INC # G5: 4,7,8 => UNS * INC # H4: 3,4 => UNS * INC # I4: 3,4 => UNS * PRF # G5: 3,4 => SOL * INC # G5: 2,7,8 => UNS * INC # F5: 3,4 => UNS * PRF # F5: 7 => SOL * INC # H3: 3,4 => UNS * INC # H3: 6 => UNS * CNT 30 HDP CHAINS / 30 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 1,3 => CTR => A1: 4 * INC A1: 4 # A2: 1,3 => UNS * PRF A1: 4 # C2: 1,3 => SOL * STA A1: 4 + C2: 1,3 * CNT 3 HDP CHAINS / 3 HYP OPENED