Analysis of zz-www.sudokuoftheday.co.uk-20060727-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006
level: medium
position: .5....7.6.7.....32..2..3.4.9......1....1..3.4..53.2..7.3.9.1....615.......9.2.16. initial
Autosolve
position: 35.21.7.617.....32.92..3.419.3....1....1..3.4.153.2..7.3.961....6153...95.9.2.163 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F1: 4,8 => CTR => F1: 9 * DIS # C2: 4 => CTR => C2: 6,8 * DIS # D3: 7 => CTR => D3: 6,8 * DIS # A5: 6,8 => CTR => A5: 7 * DIS # A6: 6,8 => CTR => A6: 4 * PRF # A6: 4 => SOL * DIS # G2: 5 => CTR => G2: 8,9 * DIS # F1: 4 => CTR => F1: 8,9 * DIS # G2: 5,8 => CTR => G2: 9 * DIS # E3: 5,8 => CTR => E3: 7 * PRF # B4: 2,8 => SOL * DIS # B4: 4 => CTR => B4: 2,8 * DIS # A6: 6 => CTR => A6: 4,8 * DIS # H7: 7 => CTR => H7: 2,5 * DIS # G6: 8,9 => CTR => G6: 6 * DIS # A7: 7,8 => CTR => A7: 2,4 * PRF # A8: 7,8 => SOL * PRF # A8: 4,8 => SOL * DIS # B4: 4,8 => CTR => B4: 2 * PRF # B4: 2 => SOL * PRF # A8: 4,8 => SOL * DIS # F1: 4,8 => CTR => F1: 9 * DIS # H7: 2,7 => CTR => H7: 5 * PRF # H7: 5 => SOL * PRF # A8: 4,8 => SOL * CNT 25 HDP CHAINS / 61 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F1: 4,8 => CTR => F1: 9 * DIS F1: 9 # D3: 7 => CTR => D3: 6,8 * DIS F1: 9 + D3: 6,8 # A5: 6,8 => CTR => A5: 7 * DIS F1: 9 + D3: 6,8 + A5: 7 # A6: 6,8 => CTR => A6: 4 * PRF F1: 9 + D3: 6,8 + A5: 7 + A6: 4 => SOL * STA F1: 9 + D3: 6,8 + A5: 7 + A6: 4 * CNT 5 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .5....7.6.7.....32..2..3.4.9......1....1..3.4..53.2..7.3.9.1....615.......9.2.16. | initial |
| 35.21.7.617.....32.92..3.419.3....1....1..3.4.153.2..7.3.961....6153...95.9.2.163 | autosolve |
| 354219786178456932692873541923647815786195324415382697237961458861534279549728163 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) C1: 4,8 A3: 6,8 H1: 8,9 G3: 5,8 B5: 2,8 E6: 4,8 I4: 5,8 H5: 2,5 H6: 8,9 C7: 7,8 B9: 4,8 F8: 4,8 I7: 5,8 H8: 2,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B4,B5: 2.. / B4 = 2 => 0 pairs (*) / B5 = 2 => 0 pairs (X) G4,H5: 2.. / G4 = 2 => 0 pairs (X) / H5 = 2 => 0 pairs (_) A7,A8: 2.. / A7 = 2 => 16 pairs (_) / A8 = 2 => 15 pairs (_) B4,G4: 2.. / B4 = 2 => 0 pairs (*) / G4 = 2 => 0 pairs (X) B5,H5: 2.. / B5 = 2 => 0 pairs (X) / H5 = 2 => 0 pairs (_) C1,C2: 4.. / C1 = 4 => 15 pairs (_) / C2 = 4 => 0 pairs (X) B4,A6: 4.. / B4 = 4 => 0 pairs (X) / A6 = 4 => 0 pairs (_) G7,G8: 4.. / G7 = 4 => 15 pairs (_) / G8 = 4 => 0 pairs (X) C1,F1: 4.. / C1 = 4 => 15 pairs (_) / F1 = 4 => 0 pairs (X) A6,E6: 4.. / A6 = 4 => 0 pairs (*) / E6 = 4 => 0 pairs (X) A7,G7: 4.. / A7 = 4 => 0 pairs (X) / G7 = 4 => 15 pairs (_) B4,B9: 4.. / B4 = 4 => 0 pairs (X) / B9 = 4 => 0 pairs (_) G2,G3: 5.. / G2 = 5 => 0 pairs (X) / G3 = 5 => 15 pairs (_) I4,H5: 5.. / I4 = 5 => 0 pairs (*) / H5 = 5 => 0 pairs (X) H7,I7: 5.. / H7 = 5 => 0 pairs (*) / I7 = 5 => 0 pairs (X) E3,G3: 5.. / E3 = 5 => 0 pairs (X) / G3 = 5 => 15 pairs (_) H5,H7: 5.. / H5 = 5 => 0 pairs (X) / H7 = 5 => 0 pairs (_) I4,I7: 5.. / I4 = 5 => 0 pairs (*) / I7 = 5 => 0 pairs (X) C2,A3: 6.. / C2 = 6 => 17 pairs (_) / A3 = 6 => 16 pairs (_) G4,G6: 6.. / G4 = 6 => 0 pairs (X) / G6 = 6 => 18 pairs (_) A3,D3: 6.. / A3 = 6 => 16 pairs (_) / D3 = 6 => 17 pairs (_) A6,G6: 6.. / A6 = 6 => 0 pairs (X) / G6 = 6 => 18 pairs (_) C2,C5: 6.. / C2 = 6 => 17 pairs (_) / C5 = 6 => 16 pairs (_) D3,E3: 7.. / D3 = 7 => 0 pairs (X) / E3 = 7 => 15 pairs (_) A5,C5: 7.. / A5 = 7 => 14 pairs (_) / C5 = 7 => 0 pairs (X) D9,F9: 7.. / D9 = 7 => 18 pairs (_) / F9 = 7 => 15 pairs (_) H7,H8: 7.. / H7 = 7 => 0 pairs (X) / H8 = 7 => 14 pairs (_) A8,H8: 7.. / A8 = 7 => 0 pairs (X) / H8 = 7 => 14 pairs (_) C5,C7: 7.. / C5 = 7 => 0 pairs (X) / C7 = 7 => 14 pairs (_) E3,E4: 7.. / E3 = 7 => 15 pairs (_) / E4 = 7 => 0 pairs (X) F4,F9: 7.. / F4 = 7 => 18 pairs (_) / F9 = 7 => 15 pairs (_) H1,H6: 8.. / H1 = 8 => 13 pairs (_) / H6 = 8 => 0 pairs (X) I4,I7: 8.. / I4 = 8 => 0 pairs (X) / I7 = 8 => 0 pairs (_) H1,G2: 9.. / H1 = 9 => 0 pairs (X) / G2 = 9 => 13 pairs (_) E5,F5: 9.. / E5 = 9 => 14 pairs (_) / F5 = 9 => 0 pairs (X) G6,H6: 9.. / G6 = 9 => 0 pairs (X) / H6 = 9 => 13 pairs (_) F1,H1: 9.. / F1 = 9 => 13 pairs (_) / H1 = 9 => 0 pairs (X) E2,E5: 9.. / E2 = 9 => 0 pairs (X) / E5 = 9 => 14 pairs (_) G2,G6: 9.. / G2 = 9 => 13 pairs (_) / G6 = 9 => 0 pairs (X) H1,H6: 9.. / H1 = 9 => 0 pairs (X) / H6 = 9 => 13 pairs (_) * DURATION: 0:00:50.722475 START: 01:19:43.685600 END: 01:20:34.408075 2019-05-01 * CP COUNT: (40) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B5,B9,C1,C7,E6,F8,G3,H1,H5,H6,H8,I4,I7) * 35.21.7.617.....32.92..3.419.3....1....1..3.4.153.2..7.3.961....6153...95.9.2.163 * PAIR C1: 4,8 BLK 1 C2: 4,8,6 # reduction candidate for 4,8 C2: 6 # 17 pairs C2: 4,8 # 16 pairs * PAIR C1: 4,8 ROW 1 F1: 4,8,9 # reduction candidate for 4,8 F1: 4,8 => CTR * 35.21.79617.....32.92..3.419.3...615...1.6324.153.2987.3.961..8.6153...95.9.2.163 F1: 9 # 13 pairs * PAIR A3: 6,8 BLK 1 C2: 6,8,4 # reduction candidate for 6,8 C2: 4 => CTR * 35.21.7.6174....32692..3.419.3....1...61..3.4.153.2697.37961....6153..795.9.2.163 C2: 6,8 # 15 pairs * PAIR A3: 6,8 ROW 3 D3: 6,8,7 # reduction candidate for 6,8 D3: 7 => CTR * 3542197861786549326927835419438762157.619.3.4815342697.37961....6153..79589427163 D3: 6,8 # 15 pairs * PAIR A3: 6,8 COL A A5: 6,8,7 # reduction candidate for 6,8 A5: 6,8 => CTR * 35421.786176...9328926735419.3....1868719.3.4.153.2..7.38961..5.6153.8.9549.2.163 A5: 7 # 14 pairs A6: 6,8,4 # reduction candidate for 6,8 A6: 6,8 => CTR * 35.21978617....932.92..3541943...218.2.198354815342697.37961825261534..9589.2.163 A6: 4 => SOLVED * 354219786178456932692873541923647815786195324415382697237961458861534279549728163 * PAIR H1: 8,9 BLK 3 G2: 8,9,5 # reduction candidate for 8,9 G2: 5 => CTR * 35.21.79617....5326927538419.3.7.615..61..3.4.153.2987.3.961..8.6153...95.9.27163 G2: 8,9 # 15 pairs * PAIR H1: 8,9 ROW 1 F1: 8,9,4 # reduction candidate for 8,9 F1: 4 => CTR * 35.214796174....32692..3.419.3....1...61..3.4.153.2..7.3.961....6153...95.9.2.163 F1: 8,9 # 15 pairs * PAIR G3: 5,8 BLK 3 G2: 5,8,9 # reduction candidate for 5,8 G2: 5,8 => CTR * 35.21.79617.....32.92..3.419.3...615...1.6324.153.2987.3.961..8.6153...95.9.2.163 G2: 9 # 13 pairs * PAIR G3: 5,8 ROW 3 E3: 5,8,7 # reduction candidate for 5,8 E3: 5,8 => CTR * 3542197861786549326927835419438762157.619.3.4815342697.37961....6153..79589427163 E3: 7 # 15 pairs * PAIR B5: 2,8 BLK 4 B4: 2,8,4 # reduction candidate for 2,8 B4: 2,8 => SOLVED * 354219786178456932692873541923647815786195324415382697237961458861534279549728163 B4: 4 => CTR * 35.21978617....932.92..3541943...218.2.198354815342697.37961825261534..9589.2.163 * PAIR E6: 4,8 BLK 5 D4: 4,8,6,7 # reduction candidate for 4,8 D4: 4,8 # 19 pairs E4: 4,8,5,7 # reduction candidate for 4,8 E4: 4,8 # 21 pairs F4: 4,8,5,6,7 # reduction candidate for 4,8 F4: 4,8 # 21 pairs * PAIR E6: 4,8 ROW 6 A6: 4,8,6 # reduction candidate for 4,8 A6: 6 => CTR * 35.21.7.617.....32.92..3.41943...21..2.1..354615342..7.3.961..5.6153...9589.2.163 A6: 4,8 # 18 pairs * PAIR E6: 4,8 COL E E2: 4,8,5,9 # reduction candidate for 4,8 E2: 4,8 # 19 pairs E2: 5,9 # 15 pairs * PAIR I4: 5,8 ROW 4 E4: 5,8,4,7 # reduction candidate for 5,8 E4: 5,8 # 18 pairs F4: 5,8,4,6,7 # reduction candidate for 5,8 F4: 5,8 # 19 pairs * PAIR H5: 2,5 COL H H7: 2,5,7 # reduction candidate for 2,5 H7: 7 => CTR * 35.21.7.617.....32.92..3.419.3...218.271..354.153.2697238961.7576153..295.9.2.163 H7: 2,5 # 14 pairs * PAIR H6: 8,9 BLK 6 G6: 8,9,6 # reduction candidate for 8,9 G6: 8,9 => CTR * 35.21.7.617.....32.92..3.419.3...61....1.6324615342..7.3.961....6153...95.9.2.163 G6: 6 # 18 pairs * PAIR C7: 7,8 BLK 7 A7: 7,8,2,4 # reduction candidate for 7,8 A7: 7,8 => CTR * 35421.78617....932.92..35419.3...218...1..3.4.153.2..7.3.961425261534879549.2.163 A7: 2,4 # 15 pairs A8: 7,8,2,4 # reduction candidate for 7,8 A8: 7,8 => SOLVED * 354219786178456932692873541923647815786195324415382697237961458861534279549728163 A8: 2,4 # 15 pairs * PAIR C7: 7,8 COL C C5: 7,8,6 # reduction candidate for 7,8 C5: 7,8 # 17 pairs C5: 6 # 16 pairs * PAIR B9: 4,8 BLK 7 A7: 4,8,2,7 # reduction candidate for 4,8 A7: 4,8 # 16 pairs A8: 4,8,2,7 # reduction candidate for 4,8 A8: 4,8 => SOLVED * 354219786178456932692873541923647815786195324415382697237961458861534279549728163 A8: 2,7 # 16 pairs * PAIR B9: 4,8 ROW 9 D9: 4,8,7 # reduction candidate for 4,8 D9: 4,8 # 15 pairs F9: 4,8,7 # reduction candidate for 4,8 F9: 4,8 # 18 pairs * PAIR B9: 4,8 COL B B4: 4,8,2 # reduction candidate for 4,8 B4: 4,8 => CTR * 35421978617....932.92..3541943...218.2.19.354815342697.37961825261538479589.2.163 B4: 2 => SOLVED * 354219786178456932692873541923647815786195324415382697237961458861534279549728163 * PAIR F8: 4,8 BLK 8 D9: 4,8,7 # reduction candidate for 4,8 D9: 4,8 # 15 pairs F9: 4,8,7 # reduction candidate for 4,8 F9: 4,8 # 18 pairs * PAIR F8: 4,8 ROW 8 A8: 4,8,2,7 # reduction candidate for 4,8 A8: 4,8 => SOLVED * 354219786178456932692873541923647815786195324415382697237961458861534279549728163 A8: 2,7 # 16 pairs G8: 4,8,2 # reduction candidate for 4,8 G8: 4,8 # 16 pairs * PAIR F8: 4,8 COL F F1: 4,8,9 # reduction candidate for 4,8 F1: 4,8 => CTR * 35.21.79617.....32.92..3.419.3...615...1.6324.153.2987.3.961..8.6153...95.9.2.163 F1: 9 # 13 pairs F2: 4,8,5,6,9 # reduction candidate for 4,8 F2: 4,8 # 20 pairs F4: 4,8,5,6,7 # reduction candidate for 4,8 F4: 4,8 # 21 pairs * PAIR H8: 2,7 BLK 9 H7: 2,7,5 # reduction candidate for 2,7 H7: 2,7 => CTR * 35.21978617....932.92..3541943...218.2.19.354815342697.37961825261538479589.2.163 H7: 5 => SOLVED * 354219786178456932692873541923647815786195324415382697237961458861534279549728163 * PAIR H8: 2,7 ROW 8 A8: 2,7,4,8 # reduction candidate for 2,7 A8: 4,8 => SOLVED * 354219786178456932692873541923647815786195324415382697237961458861534279549728163 A8: 2,7 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060727-absurd-base-pr-000.dot * REASONING * DIS # F1: 4,8 => CTR => F1: 9 * DIS # C2: 4 => CTR => C2: 6,8 * DIS # D3: 7 => CTR => D3: 6,8 * DIS # A5: 6,8 => CTR => A5: 7 * DIS # A6: 6,8 => CTR => A6: 4 * PRF # A6: 4 => SOL * DIS # G2: 5 => CTR => G2: 8,9 * DIS # F1: 4 => CTR => F1: 8,9 * DIS # G2: 5,8 => CTR => G2: 9 * DIS # E3: 5,8 => CTR => E3: 7 * PRF # B4: 2,8 => SOL * DIS # B4: 4 => CTR => B4: 2,8 * DIS # A6: 6 => CTR => A6: 4,8 * DIS # H7: 7 => CTR => H7: 2,5 * DIS # G6: 8,9 => CTR => G6: 6 * DIS # A7: 7,8 => CTR => A7: 2,4 * PRF # A8: 7,8 => SOL * PRF # A8: 4,8 => SOL * DIS # B4: 4,8 => CTR => B4: 2 * PRF # B4: 2 => SOL * PRF # A8: 4,8 => SOL * DIS # F1: 4,8 => CTR => F1: 9 * DIS # H7: 2,7 => CTR => H7: 5 * PRF # H7: 5 => SOL * PRF # A8: 4,8 => SOL * CNT 25 HDP CHAINS / 61 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B5,B9,C1,C7,E6,F8,G3,H1,H5,H6,H8,I4,I7) * 35.21.7.617.....32.92..3.419.3....1....1..3.4.153.2..7.3.961....6153...95.9.2.163 * PAIR C1: 4,8 BLK 1 C2: 4,8,6 # reduction candidate for 4,8 C2: 6 # 17 pairs C2: 4,8 # 16 pairs * PAIR C1: 4,8 ROW 1 F1: 4,8,9 # reduction candidate for 4,8 F1: 4,8 => CTR * 35.21.79617.....32.92..3.419.3...615...1.6324.153.2987.3.961..8.6153...95.9.2.163 * PAIR RESTART * PAIR A3: 6,8 ROW 3 D3: 6,8,7 # reduction candidate for 6,8 D3: 7 => CTR * 354219786178.5.932692783541943.7.218726198354815342697.37961825261534.795.9.27163 * PAIR A3: 6,8 COL A A5: 6,8,7 # reduction candidate for 6,8 A5: 6,8 => CTR * 354219786176...9328926735419.3....186871953.4.153.2.97.38961..5.6153.8.9549.2.163 A6: 6,8,4 # reduction candidate for 6,8 A6: 6,8 => CTR * 35421978617....932692873541943.8.21.72.19.354.15342697.37961.2526153..79589.2.163 A6: 4 => SOLVED * 354219786178456932692873541923647815786195324415382697237961458861534279549728163 * DURATION: 0:00:06.392271 START: 01:21:17.174449 END: 01:21:23.566720 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060727-absurd-base-pr-001.dot * REASONING * DIS # F1: 4,8 => CTR => F1: 9 * DIS F1: 9 # D3: 7 => CTR => D3: 6,8 * DIS F1: 9 + D3: 6,8 # A5: 6,8 => CTR => A5: 7 * DIS F1: 9 + D3: 6,8 + A5: 7 # A6: 6,8 => CTR => A6: 4 * PRF F1: 9 + D3: 6,8 + A5: 7 + A6: 4 => SOL * STA F1: 9 + D3: 6,8 + A5: 7 + A6: 4 * CNT 5 HDP CHAINS / 7 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060727, absurd
Solution
position: 354219786178456932692873541923647815786195324415382697237961458861534279549728163 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 # C2: 4,8 => UNS * INC # C2: 6 => UNS * DIS # F1: 4,8 => CTR => F1: 9 * INC # F1: 9 => UNS * INC # C2: 6,8 => UNS * DIS # C2: 4 => CTR => C2: 6,8 * INC # D3: 6,8 => UNS * DIS # D3: 7 => CTR => D3: 6,8 * DIS # A5: 6,8 => CTR => A5: 7 * INC # A5: 7 => UNS * DIS # A6: 6,8 => CTR => A6: 4 * PRF # A6: 4 => SOL * INC # G2: 8,9 => UNS * DIS # G2: 5 => CTR => G2: 8,9 * INC # F1: 8,9 => UNS * DIS # F1: 4 => CTR => F1: 8,9 * DIS # G2: 5,8 => CTR => G2: 9 * INC # G2: 9 => UNS * DIS # E3: 5,8 => CTR => E3: 7 * INC # E3: 7 => UNS * PRF # B4: 2,8 => SOL * DIS # B4: 4 => CTR => B4: 2,8 * INC # D4: 4,8 => UNS * INC # E4: 4,8 => UNS * INC # F4: 4,8 => UNS * INC # A6: 4,8 => UNS * DIS # A6: 6 => CTR => A6: 4,8 * INC # E2: 4,8 => UNS * INC # E2: 5,9 => UNS * INC # E4: 5,8 => UNS * INC # F4: 5,8 => UNS * INC # H7: 2,5 => UNS * DIS # H7: 7 => CTR => H7: 2,5 * DIS # G6: 8,9 => CTR => G6: 6 * INC # G6: 6 => UNS * DIS # A7: 7,8 => CTR => A7: 2,4 * INC # A7: 2,4 => UNS * PRF # A8: 7,8 => SOL * INC # A8: 2,4 => UNS * INC # C5: 7,8 => UNS * INC # C5: 6 => UNS * INC # A7: 4,8 => UNS * PRF # A8: 4,8 => SOL * INC # A8: 2,7 => UNS * INC # D9: 4,8 => UNS * INC # F9: 4,8 => UNS * DIS # B4: 4,8 => CTR => B4: 2 * PRF # B4: 2 => SOL * INC # D9: 4,8 => UNS * INC # F9: 4,8 => UNS * PRF # A8: 4,8 => SOL * INC # A8: 2,7 => UNS * INC # G8: 4,8 => UNS * DIS # F1: 4,8 => CTR => F1: 9 * INC # F1: 9 => UNS * INC # F2: 4,8 => UNS * INC # F4: 4,8 => UNS * DIS # H7: 2,7 => CTR => H7: 5 * PRF # H7: 5 => SOL * INC # A8: 2,7 => UNS * PRF # A8: 4,8 => SOL * CNT 61 HDP CHAINS / 61 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C2: 4,8 => UNS * INC # C2: 6 => UNS * DIS # F1: 4,8 => CTR => F1: 9 * INC F1: 9 # D3: 6,8 => UNS * DIS F1: 9 # D3: 7 => CTR => D3: 6,8 * DIS F1: 9 + D3: 6,8 # A5: 6,8 => CTR => A5: 7 * DIS F1: 9 + D3: 6,8 + A5: 7 # A6: 6,8 => CTR => A6: 4 * PRF F1: 9 + D3: 6,8 + A5: 7 + A6: 4 => SOL * STA F1: 9 + D3: 6,8 + A5: 7 + A6: 4 * CNT 8 HDP CHAINS / 7 HYP OPENED