Analysis of zz-www.sudokuoftheday.co.uk-20060813-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006
level: medium
position: ..95..326.....21..56.......2....8..749....218..8.1.5....68..4..7..12..8.....4...1 initial
Autosolve
position: 1.95..3263....21..562..18..2.1..8..749....2186.821.5..9168..4.27..12..8.82..4.7.1 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 4 => CTR => B1: 7,8 * DIS # F6: 4,7 => CTR => F6: 3,9 * DIS # H3: 4,9 => CTR => H3: 7 * DIS # C5: 7 => CTR => C5: 3,5 * DIS # E4: 9 => CTR => E4: 3,5 * DIS # B8: 4 => CTR => B8: 3,5 * DIS # F6: 3,7 => CTR => F6: 4,9 * DIS # H4: 3,4 => CTR => H4: 6,9 * DIS # C8: 3,5 => CTR => C8: 4 * DIS # C5: 7 => CTR => C5: 3,5 * CNT 10 HDP CHAINS / 49 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B1: 4 => CTR => B1: 7,8 * DIS B1: 7,8 # E2: 6,9 => CTR => E2: 7,8 * DIS B1: 7,8 + E2: 7,8 # E4: 9 => CTR => E4: 3,5 * PRF B1: 7,8 + E2: 7,8 + E4: 3,5 # F9: 3,5 => SOL * STA B1: 7,8 + E2: 7,8 + E4: 3,5 + F9: 3,5 * CNT 4 HDP CHAINS / 13 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..95..326.....21..56.......2....8..749....218..8.1.5....68..4..7..12..8.....4...1 | initial |
| 1.95..3263....21..562..18..2.1..8..749....2186.821.5..9168..4.27..12..8.82..4.7.1 | autosolve |
| 189574326347682159562391874251438697493765218678219543916857432734126985825943761 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) C2: 4,7 E1: 7,8 F1: 4,7 I3: 4,9 B4: 3,5 B6: 3,7 G4: 6,9 C9: 3,5 H7: 3,5 G8: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D3,E3: 3.. / D3 = 3 => 15 pairs (_) / E3 = 3 => 12 pairs (_) I6,I8: 3.. / I6 = 3 => 17 pairs (_) / I8 = 3 => 19 pairs (_) D4,F6: 4.. / D4 = 4 => 11 pairs (_) / F6 = 4 => 0 pairs (X) B8,C8: 4.. / B8 = 4 => 0 pairs (X) / C8 = 4 => 13 pairs (_) B1,F1: 4.. / B1 = 4 => 0 pairs (X) / F1 = 4 => 11 pairs (_) D4,H4: 4.. / D4 = 4 => 11 pairs (_) / H4 = 4 => 0 pairs (X) C2,C8: 4.. / C2 = 4 => 0 pairs (X) / C8 = 4 => 13 pairs (_) F1,F6: 4.. / F1 = 4 => 11 pairs (_) / F6 = 4 => 0 pairs (X) H2,I2: 5.. / H2 = 5 => 20 pairs (_) / I2 = 5 => 11 pairs (_) B4,C5: 5.. / B4 = 5 => 12 pairs (_) / C5 = 5 => 23 pairs (_) B4,E4: 5.. / B4 = 5 => 12 pairs (_) / E4 = 5 => 23 pairs (_) B4,B8: 5.. / B4 = 5 => 12 pairs (_) / B8 = 5 => 23 pairs (_) I2,I8: 5.. / I2 = 5 => 11 pairs (_) / I8 = 5 => 20 pairs (_) D2,E2: 6.. / D2 = 6 => 12 pairs (_) / E2 = 6 => 10 pairs (_) G4,H4: 6.. / G4 = 6 => 10 pairs (_) / H4 = 6 => 10 pairs (_) G8,H9: 6.. / G8 = 6 => 10 pairs (_) / H9 = 6 => 10 pairs (_) F8,G8: 6.. / F8 = 6 => 10 pairs (_) / G8 = 6 => 10 pairs (_) E2,E5: 6.. / E2 = 6 => 10 pairs (_) / E5 = 6 => 12 pairs (_) G4,G8: 6.. / G4 = 6 => 10 pairs (_) / G8 = 6 => 10 pairs (_) H4,H9: 6.. / H4 = 6 => 10 pairs (_) / H9 = 6 => 10 pairs (_) H2,H3: 7.. / H2 = 7 => 0 pairs (X) / H3 = 7 => 11 pairs (_) C5,B6: 7.. / C5 = 7 => 0 pairs (X) / B6 = 7 => 13 pairs (_) E7,F7: 7.. / E7 = 7 => 13 pairs (_) / F7 = 7 => 16 pairs (_) B6,F6: 7.. / B6 = 7 => 13 pairs (_) / F6 = 7 => 0 pairs (X) C2,C5: 7.. / C2 = 7 => 13 pairs (_) / C5 = 7 => 0 pairs (X) B1,B2: 8.. / B1 = 8 => 16 pairs (_) / B2 = 8 => 10 pairs (_) E1,E2: 8.. / E1 = 8 => 10 pairs (_) / E2 = 8 => 16 pairs (_) B1,E1: 8.. / B1 = 8 => 16 pairs (_) / E1 = 8 => 10 pairs (_) B2,E2: 8.. / B2 = 8 => 10 pairs (_) / E2 = 8 => 16 pairs (_) G4,G8: 9.. / G4 = 9 => 10 pairs (_) / G8 = 9 => 10 pairs (_) * DURATION: 0:00:35.210777 START: 01:45:45.641972 END: 01:46:20.852749 2019-05-01 * CP COUNT: (30) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B6,C2,C9,E1,F1,G4,G8,H7,I3) * 1.95..3263....21..562..18..2.1..8..749....2186.821.5..9168..4.27..12..8.82..4.7.1 * PAIR C2: 4,7 BLK 1 B1: 4,7,8 # reduction candidate for 4,7 B1: 4,7 # 10 pairs B2: 4,7,8 # reduction candidate for 4,7 B2: 4,7 # 16 pairs * PAIR C2: 4,7 ROW 2 D2: 4,7,6,9 # reduction candidate for 4,7 D2: 4,7 # 15 pairs H2: 4,7,5,9 # reduction candidate for 4,7 H2: 4,7 # 15 pairs * PAIR E1: 7,8 BLK 2 E2: 7,8,6,9 # reduction candidate for 7,8 E2: 7,8 # 16 pairs E2: 6,9 # 11 pairs * PAIR E1: 7,8 ROW 1 B1: 7,8,4 # reduction candidate for 7,8 B1: 4 => CTR * 1495873263876921545624318792.19586474957632186782145..91687.4.27.412..8.82..4.761 B1: 7,8 # 11 pairs * PAIR F1: 4,7 BLK 2 D2: 4,7,6,9 # reduction candidate for 4,7 D2: 4,7 # 15 pairs D3: 4,7,3,9 # reduction candidate for 4,7 D3: 4,7 # 16 pairs * PAIR F1: 4,7 ROW 1 B1: 4,7,8 # reduction candidate for 4,7 B1: 8 # 16 pairs B1: 4,7 # 10 pairs * PAIR F1: 4,7 COL F F6: 4,7,3,9 # reduction candidate for 4,7 F6: 4,7 => CTR * 1.95..3263....21..562.318..2.1..86.749...32186.821.5..9168.54327.3126985825349761 F6: 3,9 # 16 pairs * PAIR I3: 4,9 BLK 3 H2: 4,9,5,7 # reduction candidate for 4,9 H2: 4,9 # 13 pairs I2: 4,9,5 # reduction candidate for 4,9 I2: 4,9 # 20 pairs H3: 4,9,7 # reduction candidate for 4,9 H3: 4,9 => CTR * 179584326384..21755627318..2514986374973562186382175..916873452745129.83823.4.7.1 H3: 7 # 11 pairs * PAIR I3: 4,9 ROW 3 D3: 4,9,3,7 # reduction candidate for 4,9 D3: 4,9 # 13 pairs D3: 3,7 # 12 pairs * PAIR I3: 4,9 COL I I6: 4,9,3 # reduction candidate for 4,9 I6: 4,9 # 19 pairs I6: 3 # 17 pairs * PAIR B4: 3,5 BLK 4 C5: 3,5,7 # reduction candidate for 3,5 C5: 7 => CTR * 179584326384..21.5562..18..251498637497.5.2186382175..916873452745126.83823.4.7.1 C5: 3,5 # 13 pairs * PAIR B4: 3,5 ROW 4 E4: 3,5,9 # reduction candidate for 3,5 E4: 9 => CTR * 1.95..3263....21..562.318..25149863749....2186.821.5..9168..4527..12698.825349761 E4: 3,5 # 18 pairs * PAIR B4: 3,5 COL B B8: 3,5,4 # reduction candidate for 3,5 B8: 4 => CTR * 179584326384..21.5562..18..251498637497.5.2186382175..916873452745126.83823.4.7.1 B8: 3,5 # 13 pairs * PAIR B6: 3,7 BLK 4 C5: 3,7,5 # reduction candidate for 3,7 C5: 5 # 23 pairs C5: 3,7 # 12 pairs * PAIR B6: 3,7 ROW 6 F6: 3,7,4,9 # reduction candidate for 3,7 F6: 3,7 => CTR * 1.95.43263....21..562..18..2.149863749....2186.821.5..9168..4527..126983823.4.7.1 F6: 4,9 # 14 pairs * PAIR G4: 6,9 BLK 6 H4: 6,9,3,4 # reduction candidate for 6,9 H4: 3,4 => CTR * 1.95..3263....21..562.318..2.1..86.749....2186.821.5..9168..4327..126985825349761 H4: 6,9 # 14 pairs * PAIR C9: 3,5 BLK 7 B8: 3,5,4 # reduction candidate for 3,5 B8: 3,5 # 13 pairs C8: 3,5,4 # reduction candidate for 3,5 C8: 3,5 => CTR * 179584326384..21.5562..18..251498637497.5.2186382175..916873452745126.83823.4.7.1 C8: 4 # 13 pairs * PAIR C9: 3,5 ROW 9 F9: 3,5,6,9 # reduction candidate for 3,5 F9: 3,5 # 15 pairs H9: 3,5,6,9 # reduction candidate for 3,5 H9: 3,5 # 10 pairs * PAIR C9: 3,5 COL C C5: 3,5,7 # reduction candidate for 3,5 C5: 7 => CTR * 179584326384..21.5562..18..251498637497.5.2186382175..916873452745126.83823.4.7.1 C5: 3,5 # 13 pairs * PAIR H7: 3,5 BLK 9 I8: 3,5,9 # reduction candidate for 3,5 I8: 3,5 # 13 pairs H9: 3,5,6,9 # reduction candidate for 3,5 H9: 3,5 # 10 pairs * PAIR H7: 3,5 ROW 7 E7: 3,5,7 # reduction candidate for 3,5 E7: 3,5 # 16 pairs F7: 3,5,7 # reduction candidate for 3,5 F7: 3,5 # 13 pairs * PAIR G8: 6,9 BLK 9 H9: 6,9,3,5 # reduction candidate for 6,9 H9: 6,9 # 13 pairs H9: 3,5 # 10 pairs * PAIR G8: 6,9 ROW 8 F8: 6,9,3,5 # reduction candidate for 6,9 F8: 6,9 # 13 pairs F8: 3,5 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060813-absurd-base-pr-000.dot * REASONING * DIS # B1: 4 => CTR => B1: 7,8 * DIS # F6: 4,7 => CTR => F6: 3,9 * DIS # H3: 4,9 => CTR => H3: 7 * DIS # C5: 7 => CTR => C5: 3,5 * DIS # E4: 9 => CTR => E4: 3,5 * DIS # B8: 4 => CTR => B8: 3,5 * DIS # F6: 3,7 => CTR => F6: 4,9 * DIS # H4: 3,4 => CTR => H4: 6,9 * DIS # C8: 3,5 => CTR => C8: 4 * DIS # C5: 7 => CTR => C5: 3,5 * CNT 10 HDP CHAINS / 49 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B6,C2,C9,E1,F1,G4,G8,H7,I3) * 1.95..3263....21..562..18..2.1..8..749....2186.821.5..9168..4.27..12..8.82..4.7.1 * PAIR C2: 4,7 BLK 1 B1: 4,7,8 # reduction candidate for 4,7 B1: 4,7 # 10 pairs B2: 4,7,8 # reduction candidate for 4,7 B2: 4,7 # 16 pairs * PAIR C2: 4,7 ROW 2 D2: 4,7,6,9 # reduction candidate for 4,7 D2: 4,7 # 15 pairs H2: 4,7,5,9 # reduction candidate for 4,7 H2: 4,7 # 15 pairs * PAIR E1: 7,8 BLK 2 E2: 7,8,6,9 # reduction candidate for 7,8 E2: 7,8 # 16 pairs E2: 6,9 # 11 pairs * PAIR E1: 7,8 ROW 1 B1: 7,8,4 # reduction candidate for 7,8 B1: 4 => CTR * 1495873263876921545624318792.19586474957632186782145..91687.4.27.412..8.82..4.761 * PAIR RESTART * PAIR E1: 7,8 BLK 2 E2: 7,8,6,9 # reduction candidate for 7,8 E2: 6,9 => CTR * 179584326384..21.5562..18..251498637497.5.2186382175..916873452745126.83823.4.7.1 * PAIR B4: 3,5 ROW 4 E4: 3,5,9 # reduction candidate for 3,5 E4: 9 => CTR * 1895743263476821..562..18742514986374937652186782135499168.74.27.412..8.82..4.7.1 * PAIR RESTART * PAIR C9: 3,5 ROW 9 F9: 3,5,6 # reduction candidate for 3,5 F9: 3,5 => SOLVED * 189574326347682159562391874251438697493765218678219543916857432734126985825943761 * DURATION: 0:00:09.954893 START: 01:46:52.000587 END: 01:47:01.955480 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060813-absurd-base-pr-001.dot * REASONING * DIS # B1: 4 => CTR => B1: 7,8 * DIS B1: 7,8 # E2: 6,9 => CTR => E2: 7,8 * DIS B1: 7,8 + E2: 7,8 # E4: 9 => CTR => E4: 3,5 * PRF B1: 7,8 + E2: 7,8 + E4: 3,5 # F9: 3,5 => SOL * STA B1: 7,8 + E2: 7,8 + E4: 3,5 + F9: 3,5 * CNT 4 HDP CHAINS / 13 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060813, absurd
Solution
position: 189574326347682159562391874251438697493765218678219543916857432734126985825943761 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 # B1: 4,7 => UNS * INC # B2: 4,7 => UNS * INC # D2: 4,7 => UNS * INC # H2: 4,7 => UNS * INC # E2: 7,8 => UNS * INC # E2: 6,9 => UNS * INC # B1: 7,8 => UNS * DIS # B1: 4 => CTR => B1: 7,8 * INC # D2: 4,7 => UNS * INC # D3: 4,7 => UNS * INC # B1: 4,7 => UNS * INC # B1: 8 => UNS * DIS # F6: 4,7 => CTR => F6: 3,9 * INC # F6: 3,9 => UNS * INC # H2: 4,9 => UNS * INC # I2: 4,9 => UNS * DIS # H3: 4,9 => CTR => H3: 7 * INC # H3: 7 => UNS * INC # D3: 4,9 => UNS * INC # D3: 3,7 => UNS * INC # I6: 4,9 => UNS * INC # I6: 3 => UNS * INC # C5: 3,5 => UNS * DIS # C5: 7 => CTR => C5: 3,5 * INC # E4: 3,5 => UNS * DIS # E4: 9 => CTR => E4: 3,5 * INC # B8: 3,5 => UNS * DIS # B8: 4 => CTR => B8: 3,5 * INC # C5: 3,7 => UNS * INC # C5: 5 => UNS * DIS # F6: 3,7 => CTR => F6: 4,9 * INC # F6: 4,9 => UNS * INC # H4: 6,9 => UNS * DIS # H4: 3,4 => CTR => H4: 6,9 * INC # B8: 3,5 => UNS * DIS # C8: 3,5 => CTR => C8: 4 * INC # C8: 4 => UNS * INC # F9: 3,5 => UNS * INC # H9: 3,5 => UNS * INC # C5: 3,5 => UNS * DIS # C5: 7 => CTR => C5: 3,5 * INC # I8: 3,5 => UNS * INC # H9: 3,5 => UNS * INC # E7: 3,5 => UNS * INC # F7: 3,5 => UNS * INC # H9: 6,9 => UNS * INC # H9: 3,5 => UNS * INC # F8: 6,9 => UNS * INC # F8: 3,5 => UNS * CNT 49 HDP CHAINS / 49 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 4,7 => UNS * INC # B2: 4,7 => UNS * INC # D2: 4,7 => UNS * INC # H2: 4,7 => UNS * INC # E2: 7,8 => UNS * INC # E2: 6,9 => UNS * INC # B1: 7,8 => UNS * DIS # B1: 4 => CTR => B1: 7,8 * INC B1: 7,8 # E2: 7,8 => UNS * DIS B1: 7,8 # E2: 6,9 => CTR => E2: 7,8 * INC B1: 7,8 + E2: 7,8 # E4: 3,5 => UNS * DIS B1: 7,8 + E2: 7,8 # E4: 9 => CTR => E4: 3,5 * PRF B1: 7,8 + E2: 7,8 + E4: 3,5 # F9: 3,5 => SOL * STA B1: 7,8 + E2: 7,8 + E4: 3,5 + F9: 3,5 * CNT 13 HDP CHAINS / 13 HYP OPENED