Analysis of zz-www.sudokuoftheday.co.uk-20060805-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: ......93.5.7.......1.4....7........96...7.1...21.....8.59.62.14..4.83.....69..5.. initial
Autosolve
position: .....793.5.7...4...1.4....7........96...7.1...21.....8359762814174583.9.2869..573 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A4: 7 => CTR => A4: 4,8 * DIS # I1: 2,6 => CTR => I1: 1,5 * DIS # B5: 3,4 => CTR => B5: 9 * DIS # E4: 3,4 => CTR => E4: 1,2,5 * DIS # H4: 2,5 => CTR => H4: 4,6 * DIS # I1: 2,6 => CTR => I1: 1,5 * CNT 6 HDP CHAINS / 35 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A4: 7 => CTR => A4: 4,8 * DIS A4: 4,8 # C3: 3 => CTR => C3: 2,8 * PRF A4: 4,8 + C3: 2,8 # H3: 2,8 => SOL * STA A4: 4,8 + C3: 2,8 + H3: 2,8 * CNT 3 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ......93.5.7.......1.4....7........96...7.1...21.....8.59.62.14..4.83.....69..5.. | initial |
| .....793.5.7...4...1.4....7........96...7.1...21.....8359762814174583.9.2869..573 | autosolve |
| 468127935537896421912435687843251769695378142721649358359762814174583296286914573 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) A1: 4,8 B1: 4,6 C1: 2,8 A3: 8,9 H2: 2,8 G3: 2,6 B4: 3,4 D6: 3,6 G4: 3,7 I5: 2,5 G6: 3,7 E9: 1,4 F9: 1,4 G8: 2,6 I8: 2,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I1,I2: 1.. / I1 = 1 => 17 pairs (_) / I2 = 1 => 15 pairs (_) E9,F9: 1.. / E9 = 1 => 14 pairs (_) / F9 = 1 => 13 pairs (_) C1,C3: 2.. / C1 = 2 => 16 pairs (_) / C3 = 2 => 14 pairs (_) G8,I8: 2.. / G8 = 2 => 13 pairs (_) / I8 = 2 => 17 pairs (_) G3,G8: 2.. / G3 = 2 => 17 pairs (_) / G8 = 2 => 13 pairs (_) B2,C3: 3.. / B2 = 3 => 14 pairs (_) / C3 = 3 => 19 pairs (_) G4,G6: 3.. / G4 = 3 => 0 pairs (X) / G6 = 3 => 15 pairs (_) C3,E3: 3.. / C3 = 3 => 19 pairs (_) / E3 = 3 => 14 pairs (_) A1,B1: 4.. / A1 = 4 => 16 pairs (_) / B1 = 4 => 0 pairs (X) E9,F9: 4.. / E9 = 4 => 13 pairs (_) / F9 = 4 => 14 pairs (_) I1,H3: 5.. / I1 = 5 => 15 pairs (_) / H3 = 5 => 16 pairs (_) C4,C5: 5.. / C4 = 5 => 16 pairs (_) / C5 = 5 => 20 pairs (_) E1,I1: 5.. / E1 = 5 => 16 pairs (_) / I1 = 5 => 15 pairs (_) I1,I5: 5.. / I1 = 5 => 15 pairs (_) / I5 = 5 => 16 pairs (_) B1,B2: 6.. / B1 = 6 => 16 pairs (_) / B2 = 6 => 0 pairs (X) H4,H6: 6.. / H4 = 6 => 17 pairs (_) / H6 = 6 => 0 pairs (X) G8,I8: 6.. / G8 = 6 => 17 pairs (_) / I8 = 6 => 13 pairs (_) F3,G3: 6.. / F3 = 6 => 17 pairs (_) / G3 = 6 => 13 pairs (_) G3,G8: 6.. / G3 = 6 => 13 pairs (_) / G8 = 6 => 17 pairs (_) A4,A6: 7.. / A4 = 7 => 0 pairs (X) / A6 = 7 => 15 pairs (_) G4,G6: 7.. / G4 = 7 => 15 pairs (_) / G6 = 7 => 0 pairs (X) A4,G4: 7.. / A4 = 7 => 0 pairs (X) / G4 = 7 => 15 pairs (_) A6,G6: 7.. / A6 = 7 => 15 pairs (_) / G6 = 7 => 0 pairs (X) H2,H3: 8.. / H2 = 8 => 15 pairs (_) / H3 = 8 => 0 pairs (*) B2,A3: 9.. / B2 = 9 => 0 pairs (X) / A3 = 9 => 16 pairs (_) B5,A6: 9.. / B5 = 9 => 16 pairs (_) / A6 = 9 => 0 pairs (X) B5,F5: 9.. / B5 = 9 => 16 pairs (_) / F5 = 9 => 0 pairs (X) A3,A6: 9.. / A3 = 9 => 16 pairs (_) / A6 = 9 => 0 pairs (X) B2,B5: 9.. / B2 = 9 => 0 pairs (X) / B5 = 9 => 16 pairs (_) * DURATION: 0:00:35.350194 START: 01:34:52.769054 END: 01:35:28.119248 2019-05-01 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B1,B4,C1,D6,E9,F9,G3,G4,G6,G8,H2,I5,I8) * .....793.5.7...4...1.4....7........96...7.1...21.....8359762814174583.9.2869..573 * PAIR A1: 4,8 COL A A4: 4,8,7 # reduction candidate for 4,8 A4: 7 => CTR * 462857931597.2.4868134962577456183296382791459213..768359762814174583.9.2869..573 A4: 4,8 # 15 pairs * PAIR C1: 2,8 BLK 1 C3: 2,8,3 # reduction candidate for 2,8 C3: 3 # 19 pairs C3: 2,8 # 14 pairs * PAIR C1: 2,8 ROW 1 D1: 2,8,1,6 # reduction candidate for 2,8 D1: 2,8 # 19 pairs D1: 1,6 # 18 pairs * PAIR A3: 8,9 ROW 3 F3: 8,9,5,6 # reduction candidate for 8,9 F3: 5,6 # 16 pairs F3: 8,9 # 15 pairs * PAIR H2: 2,8 BLK 3 H3: 2,8,5 # reduction candidate for 2,8 H3: 5 # 16 pairs H3: 2,8 # 15 pairs * PAIR H2: 2,8 ROW 2 D2: 2,8,1,3,6 # reduction candidate for 2,8 D2: 2,8 # 17 pairs D2: 1,3,6 # 15 pairs * PAIR G3: 2,6 BLK 3 I1: 2,6,1,5 # reduction candidate for 2,6 I1: 2,6 => CTR * 468157932537.2948191243865784521...9693874125.21.95..8359762814174583296286941573 I1: 1,5 # 16 pairs I2: 2,6,1 # reduction candidate for 2,6 I2: 2,6 # 17 pairs * PAIR B4: 3,4 BLK 4 B5: 3,4,9 # reduction candidate for 3,4 B5: 3,4 => CTR * 462857931597.2.4868134962577456183296382791459213..768359762814174583.9.2869..573 B5: 9 # 16 pairs * PAIR B4: 3,4 ROW 4 E4: 3,4,1,2,5 # reduction candidate for 3,4 E4: 3,4 => CTR * 46...793.537...4..91.43...7845...7.96.3.7.1..721...3.8359762814174583.9.2869..573 E4: 1,2,5 # 15 pairs * PAIR D6: 3,6 BLK 5 D4: 3,6,1,2,8 # reduction candidate for 3,6 D4: 3,6 # 20 pairs D4: 1,2,8 # 15 pairs * PAIR D6: 3,6 COL D D2: 3,6,1,2,8 # reduction candidate for 3,6 D2: 3,6 # 19 pairs D2: 1,2,8 # 15 pairs * PAIR I5: 2,5 BLK 6 H4: 2,5,4,6 # reduction candidate for 2,5 H4: 2,5 => CTR * 4628.793.59723.4..81349...774....3.963..7914.9213..768359762814174583.9.2869..573 H4: 4,6 # 17 pairs H5: 2,5,4 # reduction candidate for 2,5 H5: 2,5 # 22 pairs * PAIR I5: 2,5 COL I I1: 2,5,1,6 # reduction candidate for 2,5 I1: 1,6 # 17 pairs I1: 2,5 # 13 pairs * PAIR E9: 1,4 COL E E4: 1,4,2,3,5 # reduction candidate for 1,4 E4: 1,4 # 17 pairs E4: 2,3,5 # 15 pairs * PAIR F9: 1,4 COL F F4: 1,4,5,6,8 # reduction candidate for 1,4 F4: 1,4 # 16 pairs F4: 5,6,8 # 15 pairs * PAIR I8: 2,6 COL I I1: 2,6,1,5 # reduction candidate for 2,6 I1: 2,6 => CTR * 468157932537.2948191243865784521...9693874125.21.95..8359762814174583296286941573 I1: 1,5 # 16 pairs I2: 2,6,1 # reduction candidate for 2,6 I2: 2,6 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060805-absurd-base-pr-000.dot * REASONING * DIS # A4: 7 => CTR => A4: 4,8 * DIS # I1: 2,6 => CTR => I1: 1,5 * DIS # B5: 3,4 => CTR => B5: 9 * DIS # E4: 3,4 => CTR => E4: 1,2,5 * DIS # H4: 2,5 => CTR => H4: 4,6 * DIS # I1: 2,6 => CTR => I1: 1,5 * CNT 6 HDP CHAINS / 35 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B1,B4,C1,D6,E9,F9,G3,G4,G6,G8,H2,I5,I8) * .....793.5.7...4...1.4....7........96...7.1...21.....8359762814174583.9.2869..573 * PAIR A1: 4,8 COL A A4: 4,8,7 # reduction candidate for 4,8 A4: 7 => CTR * 462857931597.2.4868134962577456183296382791459213..768359762814174583.9.2869..573 * PAIR RESTART * PAIR C1: 2,8 BLK 1 C3: 2,8,3 # reduction candidate for 2,8 C3: 3 => CTR * 842157936567.394.191342...7.3....76969.37.1..7216..3.8359762814174583.9.2869..573 * PAIR C1: 2,8 ROW 1 D1: 2,8,1 # reduction candidate for 2,8 D1: 2,8 # 17 pairs D1: 1 # 16 pairs * PAIR H2: 2,8 BLK 3 H3: 2,8,5 # reduction candidate for 2,8 H3: 2,8 => SOLVED * 468127935537896421912435687843251769695378142721649358359762814174583296286914573 * DURATION: 0:00:06.419545 START: 01:35:50.296572 END: 01:35:56.716117 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060805-absurd-base-pr-001.dot * REASONING * DIS # A4: 7 => CTR => A4: 4,8 * DIS A4: 4,8 # C3: 3 => CTR => C3: 2,8 * PRF A4: 4,8 + C3: 2,8 # H3: 2,8 => SOL * STA A4: 4,8 + C3: 2,8 + H3: 2,8 * CNT 3 HDP CHAINS / 7 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060805, absurd
Solution
position: 468127935537896421912435687843251769695378142721649358359762814174583296286914573 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 # A4: 4,8 => UNS * DIS # A4: 7 => CTR => A4: 4,8 * INC # C3: 2,8 => UNS * INC # C3: 3 => UNS * INC # D1: 2,8 => UNS * INC # D1: 1,6 => UNS * INC # F3: 8,9 => UNS * INC # F3: 5,6 => UNS * INC # H3: 2,8 => UNS * INC # H3: 5 => UNS * INC # D2: 2,8 => UNS * INC # D2: 1,3,6 => UNS * DIS # I1: 2,6 => CTR => I1: 1,5 * INC # I1: 1,5 => UNS * INC # I2: 2,6 => UNS * DIS # B5: 3,4 => CTR => B5: 9 * INC # B5: 9 => UNS * DIS # E4: 3,4 => CTR => E4: 1,2,5 * INC # E4: 1,2,5 => UNS * INC # D4: 3,6 => UNS * INC # D4: 1,2,8 => UNS * INC # D2: 3,6 => UNS * INC # D2: 1,2,8 => UNS * DIS # H4: 2,5 => CTR => H4: 4,6 * INC # H4: 4,6 => UNS * INC # H5: 2,5 => UNS * INC # I1: 2,5 => UNS * INC # I1: 1,6 => UNS * INC # E4: 1,4 => UNS * INC # E4: 2,3,5 => UNS * INC # F4: 1,4 => UNS * INC # F4: 5,6,8 => UNS * DIS # I1: 2,6 => CTR => I1: 1,5 * INC # I1: 1,5 => UNS * INC # I2: 2,6 => UNS * CNT 35 HDP CHAINS / 35 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A4: 4,8 => UNS * DIS # A4: 7 => CTR => A4: 4,8 * INC A4: 4,8 # C3: 2,8 => UNS * DIS A4: 4,8 # C3: 3 => CTR => C3: 2,8 * INC A4: 4,8 + C3: 2,8 # D1: 2,8 => UNS * INC A4: 4,8 + C3: 2,8 # D1: 1 => UNS * PRF A4: 4,8 + C3: 2,8 # H3: 2,8 => SOL * STA A4: 4,8 + C3: 2,8 + H3: 2,8 * CNT 7 HDP CHAINS / 7 HYP OPENED