Analysis of zz-www.sudokuoftheday.co.uk-20060322-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006
level: medium
position: .8.....6.2...38..99..51.8.7.....53.24.........3....6.57.9.83....2........6.7.1... initial
Autosolve
position: .8.....6.2...38..994.51.8.76....53.24..3......3....6.57.9.83....2........6.7.1... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D8: 4,6 => CTR => D8: 9 * DIS # G1: 1,5 => CTR => G1: 2,4 * DIS # B2: 1,5 => CTR => B2: 7 * DIS # C2: 1,5 => CTR => C2: 6,7 * DIS # H8: 1,5 => CTR => H8: 3,7,8,9 * DIS # G7: 1,5 => CTR => G7: 2,4 * DIS # B2: 1,5 => CTR => B2: 7 * CNT 7 HDP CHAINS / 41 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D8: 4,6 => CTR => D8: 9 * DIS D8: 9 # G1: 1,5 => CTR => G1: 2,4 * PRF D8: 9 + G1: 2,4 # C4: 1,8 => SOL * STA D8: 9 + G1: 2,4 + C4: 1,8 * CNT 3 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .8.....6.2...38..99..51.8.7.....53.24.........3....6.57.9.83....2........6.7.1... | initial |
| .8.....6.2...38..994.51.8.76....53.24..3......3....6.57.9.83....2........6.7.1... | autosolve |
| 185297463276438519943516827691875342452369781837142695719683254328954176564721938 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) C3: 3,6 D2: 4,6 F3: 2,6 H2: 1,5 H3: 2,3 A6: 1,8 C6: 2,7 D4: 1,8 D6: 1,8 I5: 1,8 B7: 1,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D4,D6: 1.. / D4 = 1 => 11 pairs (_) / D6 = 1 => 13 pairs (_) A6,D6: 1.. / A6 = 1 => 11 pairs (_) / D6 = 1 => 13 pairs (_) G1,H3: 2.. / G1 = 2 => 0 pairs (X) / H3 = 2 => 21 pairs (_) C5,C6: 2.. / C5 = 2 => 15 pairs (_) / C6 = 2 => 13 pairs (_) D7,E9: 2.. / D7 = 2 => 0 pairs (X) / E9 = 2 => 21 pairs (_) F3,H3: 2.. / F3 = 2 => 0 pairs (X) / H3 = 2 => 21 pairs (_) D1,D7: 2.. / D1 = 2 => 21 pairs (_) / D7 = 2 => 0 pairs (X) I1,H3: 3.. / I1 = 3 => 21 pairs (_) / H3 = 3 => 0 pairs (X) C3,H3: 3.. / C3 = 3 => 21 pairs (_) / H3 = 3 => 0 pairs (X) H4,H6: 4.. / H4 = 4 => 13 pairs (_) / H6 = 4 => 11 pairs (_) C8,C9: 4.. / C8 = 4 => 16 pairs (_) / C9 = 4 => 12 pairs (_) D2,G2: 4.. / D2 = 4 => 21 pairs (_) / G2 = 4 => 0 pairs (X) E4,H4: 4.. / E4 = 4 => 11 pairs (_) / H4 = 4 => 13 pairs (_) B5,C5: 5.. / B5 = 5 => 13 pairs (_) / C5 = 5 => 14 pairs (_) E8,E9: 5.. / E8 = 5 => 11 pairs (_) / E9 = 5 => 0 pairs (X) C2,C3: 6.. / C2 = 6 => 21 pairs (_) / C3 = 6 => 0 pairs (X) D2,F3: 6.. / D2 = 6 => 0 pairs (X) / F3 = 6 => 21 pairs (_) E5,F5: 6.. / E5 = 6 => 11 pairs (_) / F5 = 6 => 0 pairs (X) I7,I8: 6.. / I7 = 6 => 12 pairs (_) / I8 = 6 => 21 pairs (_) C2,D2: 6.. / C2 = 6 => 21 pairs (_) / D2 = 6 => 0 pairs (X) C3,F3: 6.. / C3 = 6 => 0 pairs (X) / F3 = 6 => 21 pairs (_) D7,I7: 6.. / D7 = 6 => 21 pairs (_) / I7 = 6 => 12 pairs (_) E5,E8: 6.. / E5 = 6 => 11 pairs (_) / E8 = 6 => 0 pairs (X) B2,C2: 7.. / B2 = 7 => 12 pairs (_) / C2 = 7 => 0 pairs (X) E1,F1: 7.. / E1 = 7 => 12 pairs (_) / F1 = 7 => 11 pairs (_) G8,H8: 7.. / G8 = 7 => 12 pairs (_) / H8 = 7 => 12 pairs (_) G5,G8: 7.. / G5 = 7 => 12 pairs (_) / G8 = 7 => 12 pairs (_) D4,D6: 8.. / D4 = 8 => 13 pairs (_) / D6 = 8 => 11 pairs (_) A6,D6: 8.. / A6 = 8 => 13 pairs (_) / D6 = 8 => 11 pairs (_) B4,B5: 9.. / B4 = 9 => 12 pairs (_) / B5 = 9 => 19 pairs (_) D1,D8: 9.. / D1 = 9 => 0 pairs (X) / D8 = 9 => 17 pairs (_) * DURATION: 0:00:30.280413 START: 21:48:38.245771 END: 21:49:08.526184 2019-04-30 * CP COUNT: (31) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B7,C3,C6,D2,D4,D6,F3,H2,H3,I5) * .8.....6.2...38..994.51.8.76....53.24..3......3....6.57.9.83....2........6.7.1... * PAIR D2: 4,6 COL D D7: 4,6,2 # reduction candidate for 4,6 D7: 4,6 # 21 pairs D8: 4,6,9 # reduction candidate for 4,6 D8: 4,6 => CTR * .8.9...642..438..994.5168.76....53.24..3......3....6.57.92834.6.2........6.7.1... D8: 9 # 17 pairs * PAIR F3: 2,6 COL F F5: 2,6,7,9 # reduction candidate for 2,6 F5: 7,9 # 16 pairs F5: 2,6 # 13 pairs * PAIR H2: 1,5 BLK 3 G1: 1,5,2,4 # reduction candidate for 1,5 G1: 1,5 => CTR * .8.....632...384.99435168276....53.24..3......3....6.57.9.83....2........6.7.1... G1: 2,4 # 21 pairs G2: 1,5,4 # reduction candidate for 1,5 G2: 1,5 # 21 pairs * PAIR H2: 1,5 ROW 2 B2: 1,5,7 # reduction candidate for 1,5 B2: 1,5 => CTR * .8.....6.2.76384.99465128376....53.24..3......32...6.57.9283....2........6.7.1... B2: 7 # 12 pairs C2: 1,5,6,7 # reduction candidate for 1,5 C2: 1,5 => CTR * .8.....6.27.6384.99465128376....53.24..3......3....6.57.9283....2........6.7.1... C2: 6,7 # 12 pairs * PAIR H2: 1,5 COL H H7: 1,5,2 # reduction candidate for 1,5 H7: 1,5 # 14 pairs H8: 1,5,3,7,8,9 # reduction candidate for 1,5 H8: 1,5 => CTR * .8.2...6.2...38..994651.8376....53.24..3......3....6.57.9.83.2..2....7...6.721... H8: 3,7,8,9 # 11 pairs * PAIR H3: 2,3 COL H H9: 2,3,5,8,9 # reduction candidate for 2,3 H9: 2,3 # 15 pairs H9: 5,8,9 # 11 pairs * PAIR A6: 1,8 BLK 4 C4: 1,8,7 # reduction candidate for 1,8 C4: 1,8 # 13 pairs C5: 1,8,2,5,7 # reduction candidate for 1,8 C5: 1,8 # 20 pairs * PAIR A6: 1,8 COL A A8: 1,8,3,5 # reduction candidate for 1,8 A8: 1,8 # 14 pairs A8: 3,5 # 12 pairs * PAIR C6: 2,7 BLK 4 C5: 2,7,1,5,8 # reduction candidate for 2,7 C5: 2,7 # 16 pairs C5: 1,5,8 # 13 pairs * PAIR C6: 2,7 ROW 6 E6: 2,7,4,9 # reduction candidate for 2,7 E6: 2,7 # 14 pairs F6: 2,7,4,9 # reduction candidate for 2,7 F6: 2,7 # 14 pairs * PAIR D4: 1,8 ROW 4 C4: 1,8,7 # reduction candidate for 1,8 C4: 1,8 # 13 pairs H4: 1,8,4,7,9 # reduction candidate for 1,8 H4: 1,8 # 19 pairs * PAIR I5: 1,8 BLK 6 H4: 1,8,4,7,9 # reduction candidate for 1,8 H4: 1,8 # 19 pairs H5: 1,8,7,9 # reduction candidate for 1,8 H5: 1,8 # 13 pairs * PAIR I5: 1,8 ROW 5 C5: 1,8,2,5,7 # reduction candidate for 1,8 C5: 1,8 # 20 pairs C5: 2,5,7 # 11 pairs * PAIR I5: 1,8 COL I I8: 1,8,3,4,6 # reduction candidate for 1,8 I8: 1,8 # 15 pairs I8: 3,4,6 # 11 pairs * PAIR B7: 1,5 BLK 7 A8: 1,5,3,8 # reduction candidate for 1,5 A8: 1,5 # 13 pairs C8: 1,5,3,4,8 # reduction candidate for 1,5 C8: 1,5 # 16 pairs * PAIR B7: 1,5 ROW 7 G7: 1,5,2,4 # reduction candidate for 1,5 G7: 1,5 => CTR * .8.2...6.2...38..994.5168276....53.24..3......3....6.57.9.83....2........6.7.1... G7: 2,4 # 12 pairs H7: 1,5,2 # reduction candidate for 1,5 H7: 1,5 # 14 pairs * PAIR B7: 1,5 COL B B2: 1,5,7 # reduction candidate for 1,5 B2: 1,5 => CTR * .8.....6.2.76384.99465128376....53.24..3......32...6.57.9283....2........6.7.1... B2: 7 # 12 pairs B5: 1,5,7,9 # reduction candidate for 1,5 B5: 1,5 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060322-absurd-base-pr-000.dot * REASONING * DIS # D8: 4,6 => CTR => D8: 9 * DIS # G1: 1,5 => CTR => G1: 2,4 * DIS # B2: 1,5 => CTR => B2: 7 * DIS # C2: 1,5 => CTR => C2: 6,7 * DIS # H8: 1,5 => CTR => H8: 3,7,8,9 * DIS # G7: 1,5 => CTR => G7: 2,4 * DIS # B2: 1,5 => CTR => B2: 7 * CNT 7 HDP CHAINS / 41 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B7,C3,C6,D2,D4,D6,F3,H2,H3,I5) * .8.....6.2...38..994.51.8.76....53.24..3......3....6.57.9.83....2........6.7.1... * PAIR D2: 4,6 COL D D7: 4,6,2 # reduction candidate for 4,6 D7: 4,6 # 21 pairs D8: 4,6,9 # reduction candidate for 4,6 D8: 4,6 => CTR * .8.9...642..438..994.5168.76....53.24..3......3....6.57.92834.6.2........6.7.1... * RESTART * PAIR RESTART * PAIR F3: 2,6 COL F F5: 2,6,7,9 # reduction candidate for 2,6 F5: 7,9 # 26 pairs F5: 2,6 # 20 pairs * PAIR H2: 1,5 BLK 3 G1: 1,5,2,4 # reduction candidate for 1,5 G1: 1,5 => CTR * .8.2...642..438..994.5168.76....53.24..3......3....6.57.9.83....2.9......6.7.1... * RESTART * PAIR A6: 1,8 BLK 4 C4: 1,8,7 # reduction candidate for 1,8 C4: 1,8 => SOLVED * 185297463276438519943516827691875342452369781837142695719683254328954176564721938 * DURATION: 0:00:05.387721 START: 21:49:29.663295 END: 21:49:35.051016 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060322-absurd-base-pr-001.dot * REASONING * DIS # D8: 4,6 => CTR => D8: 9 * DIS D8: 9 # G1: 1,5 => CTR => G1: 2,4 * PRF D8: 9 + G1: 2,4 # C4: 1,8 => SOL * STA D8: 9 + G1: 2,4 + C4: 1,8 * CNT 3 HDP CHAINS / 6 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006, 20060322, absurd
Solution
position: 185297463276438519943516827691875342452369781837142695719683254328954176564721938 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 # D7: 4,6 => UNS * DIS # D8: 4,6 => CTR => D8: 9 * INC # D8: 9 => UNS * INC # F5: 2,6 => UNS * INC # F5: 7,9 => UNS * DIS # G1: 1,5 => CTR => G1: 2,4 * INC # G1: 2,4 => UNS * INC # G2: 1,5 => UNS * DIS # B2: 1,5 => CTR => B2: 7 * INC # B2: 7 => UNS * DIS # C2: 1,5 => CTR => C2: 6,7 * INC # C2: 6,7 => UNS * INC # H7: 1,5 => UNS * DIS # H8: 1,5 => CTR => H8: 3,7,8,9 * INC # H8: 3,7,8,9 => UNS * INC # H9: 2,3 => UNS * INC # H9: 5,8,9 => UNS * INC # C4: 1,8 => UNS * INC # C5: 1,8 => UNS * INC # A8: 1,8 => UNS * INC # A8: 3,5 => UNS * INC # C5: 2,7 => UNS * INC # C5: 1,5,8 => UNS * INC # E6: 2,7 => UNS * INC # F6: 2,7 => UNS * INC # C4: 1,8 => UNS * INC # H4: 1,8 => UNS * INC # H4: 1,8 => UNS * INC # H5: 1,8 => UNS * INC # C5: 1,8 => UNS * INC # C5: 2,5,7 => UNS * INC # I8: 1,8 => UNS * INC # I8: 3,4,6 => UNS * INC # A8: 1,5 => UNS * INC # C8: 1,5 => UNS * DIS # G7: 1,5 => CTR => G7: 2,4 * INC # G7: 2,4 => UNS * INC # H7: 1,5 => UNS * DIS # B2: 1,5 => CTR => B2: 7 * INC # B2: 7 => UNS * INC # B5: 1,5 => UNS * CNT 41 HDP CHAINS / 41 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D7: 4,6 => UNS * DIS # D8: 4,6 => CTR => D8: 9 * INC D8: 9 # F5: 2,6 => UNS * INC D8: 9 # F5: 7,9 => UNS * DIS D8: 9 # G1: 1,5 => CTR => G1: 2,4 * PRF D8: 9 + G1: 2,4 # C4: 1,8 => SOL * STA D8: 9 + G1: 2,4 + C4: 1,8 * CNT 6 HDP CHAINS / 6 HYP OPENED