Analysis of zz-www.sudokuoftheday.co.uk-20060801-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: .5.....8.2......3...7...6.167...9..4.43...2.85.1....6.8...97.15.....1...1.5.84..6 initial
Autosolve
position: .5.....8.21....53...7...6.167...9154943...2785.1....6.8...97.157....18..1.5.847.6 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C2: 6,9 => SOL * DIS # C2: 8 => CTR => C2: 6,9 * DIS # D1: 6,9 => CTR => D1: 1,2,7 * DIS # C2: 6 => CTR => C2: 8,9 * DIS # D3: 2,5 => CTR => D3: 8,9 * PRF # D2: 6,8 => SOL * PRF # C2: 9 => SOL * DIS # D3: 2,5 => CTR => D3: 8,9 * PRF # F3: 2,5 => SOL * DIS # H3: 2 => CTR => H3: 4,9 * DIS # I1: 7,9 => CTR => I1: 2 * DIS # D4: 3 => CTR => D4: 2,8 * PRF # D4: 2,3 => SOL * DIS # D4: 8 => CTR => D4: 2,3 * DIS # E8: 5,6 => CTR => E8: 2,3 * DIS # D5: 5,6 => CTR => D5: 1 * DIS # E2: 6 => CTR => E2: 4,7 * DIS # D4: 3 => CTR => D4: 2,8 * PRF # F3: 2,8 => SOL * DIS # I8: 2 => CTR => I8: 3,9 * PRF # C8: 2,4 => SOL * DIS # C8: 9 => CTR => C8: 2,4 * DIS # D7: 2,3 => CTR => D7: 6 * DIS # D8: 2,3 => CTR => D8: 5,6 * PRF # B9: 9 => SOL * PRF # D4: 2,3 => SOL * DIS # D4: 8 => CTR => D4: 2,3 * PRF # H8: 2,9 => SOL * PRF # H3: 4 => SOL * CNT 29 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:
* PRF # C2: 6,9 => SOL * STA C2: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .5.....8.2......3...7...6.167...9..4.43...2.85.1....6.8...97.15.....1...1.5.84..6 | initial |
| .5.....8.21....53...7...6.167...9154943...2785.1....6.8...97.157....18..1.5.847.6 | autosolve |
| 456713982219846537387952641678239154943165278521478369832697415764521893195384726 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (21) A1: 3,4 C1: 6,9 A3: 3,4 B3: 8,9 F2: 6,8 E3: 2,5 G1: 4,9 I2: 7,9 C4: 2,8 B6: 2,8 E4: 2,3 F5: 5,6 D6: 4,7 E6: 4,7 F6: 2,8 G6: 3,9 I6: 3,9 C7: 2,4 D9: 2,3 G7: 3,4 H9: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,E1: 1.. / D1 = 1 => 0 pairs (X) / E1 = 1 => 23 pairs (_) D5,E5: 1.. / D5 = 1 => 23 pairs (_) / E5 = 1 => 0 pairs (X) D1,D5: 1.. / D1 = 1 => 0 pairs (X) / D5 = 1 => 23 pairs (_) E1,E5: 1.. / E1 = 1 => 23 pairs (_) / E5 = 1 => 0 pairs (X) I1,H3: 2.. / I1 = 2 => 26 pairs (_) / H3 = 2 => 0 pairs (X) C4,B6: 2.. / C4 = 2 => 0 pairs (X) / B6 = 2 => 0 pairs (_) B6,F6: 2.. / B6 = 2 => 0 pairs (*) / F6 = 2 => 0 pairs (X) I1,I8: 2.. / I1 = 2 => 26 pairs (_) / I8 = 2 => 0 pairs (X) A1,A3: 3.. / A1 = 3 => 25 pairs (_) / A3 = 3 => 0 pairs (*) F1,F3: 3.. / F1 = 3 => 0 pairs (*) / F3 = 3 => 0 pairs (X) D4,E4: 3.. / D4 = 3 => 0 pairs (X) / E4 = 3 => 21 pairs (_) G6,I6: 3.. / G6 = 3 => 0 pairs (*) / I6 = 3 => 0 pairs (X) G7,I8: 3.. / G7 = 3 => 25 pairs (_) / I8 = 3 => 0 pairs (*) A1,F1: 3.. / A1 = 3 => 25 pairs (_) / F1 = 3 => 0 pairs (*) A3,F3: 3.. / A3 = 3 => 0 pairs (*) / F3 = 3 => 0 pairs (X) B9,D9: 3.. / B9 = 3 => 27 pairs (_) / D9 = 3 => 24 pairs (_) E4,E8: 3.. / E4 = 3 => 21 pairs (_) / E8 = 3 => 0 pairs (X) G6,G7: 3.. / G6 = 3 => 0 pairs (*) / G7 = 3 => 0 pairs (X) I6,I8: 3.. / I6 = 3 => 25 pairs (_) / I8 = 3 => 0 pairs (*) A1,A3: 4.. / A1 = 4 => 0 pairs (*) / A3 = 4 => 0 pairs (X) D2,E2: 4.. / D2 = 4 => 20 pairs (_) / E2 = 4 => 19 pairs (_) G1,H3: 4.. / G1 = 4 => 25 pairs (_) / H3 = 4 => 0 pairs (*) D6,E6: 4.. / D6 = 4 => 19 pairs (_) / E6 = 4 => 20 pairs (_) C7,C8: 4.. / C7 = 4 => 25 pairs (_) / C8 = 4 => 0 pairs (*) G7,H8: 4.. / G7 = 4 => 0 pairs (*) / H8 = 4 => 0 pairs (X) A1,G1: 4.. / A1 = 4 => 0 pairs (*) / G1 = 4 => 0 pairs (X) A3,H3: 4.. / A3 = 4 => 25 pairs (_) / H3 = 4 => 0 pairs (*) C7,G7: 4.. / C7 = 4 => 25 pairs (_) / G7 = 4 => 0 pairs (*) C8,H8: 4.. / C8 = 4 => 0 pairs (*) / H8 = 4 => 0 pairs (X) D2,D6: 4.. / D2 = 4 => 20 pairs (_) / D6 = 4 => 19 pairs (_) E2,E6: 4.. / E2 = 4 => 19 pairs (_) / E6 = 4 => 20 pairs (_) G1,G7: 4.. / G1 = 4 => 25 pairs (_) / G7 = 4 => 0 pairs (*) H3,H8: 4.. / H3 = 4 => 0 pairs (*) / H8 = 4 => 0 pairs (X) D8,E8: 5.. / D8 = 5 => 22 pairs (_) / E8 = 5 => 0 pairs (X) F3,F5: 5.. / F3 = 5 => 0 pairs (X) / F5 = 5 => 24 pairs (_) C1,C2: 6.. / C1 = 6 => 22 pairs (_) / C2 = 6 => 0 pairs (X) B7,B8: 6.. / B7 = 6 => 0 pairs (X) / B8 = 6 => 25 pairs (_) B7,D7: 6.. / B7 = 6 => 0 pairs (X) / D7 = 6 => 25 pairs (_) I1,I2: 7.. / I1 = 7 => 0 pairs (X) / I2 = 7 => 24 pairs (_) D6,E6: 7.. / D6 = 7 => 20 pairs (_) / E6 = 7 => 19 pairs (_) C2,B3: 8.. / C2 = 8 => 0 pairs (X) / B3 = 8 => 0 pairs (_) C4,B6: 8.. / C4 = 8 => 0 pairs (*) / B6 = 8 => 0 pairs (X) D4,F6: 8.. / D4 = 8 => 0 pairs (X) / F6 = 8 => 0 pairs (_) C4,D4: 8.. / C4 = 8 => 0 pairs (*) / D4 = 8 => 0 pairs (X) B6,F6: 8.. / B6 = 8 => 0 pairs (X) / F6 = 8 => 0 pairs (_) B3,B6: 8.. / B3 = 8 => 0 pairs (*) / B6 = 8 => 0 pairs (X) C2,C4: 8.. / C2 = 8 => 0 pairs (X) / C4 = 8 => 0 pairs (_) G6,I6: 9.. / G6 = 9 => 25 pairs (_) / I6 = 9 => 0 pairs (*) B9,H9: 9.. / B9 = 9 => 0 pairs (*) / H9 = 9 => 0 pairs (X) G1,G6: 9.. / G1 = 9 => 0 pairs (*) / G6 = 9 => 0 pairs (X) * DURATION: 0:01:05.917351 START: 01:27:58.459991 END: 01:29:04.377342 2019-05-01 * CP COUNT: (50) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B3,B6,C1,C4,C7,D6,D9,E3,E4,E6,F2,F5,F6,G1,G6,G7,H9,I2,I6) * .5.....8.21....53...7...6.167...9154943...2785.1....6.8...97.157....18..1.5.847.6 * PAIR C1: 6,9 BLK 1 C2: 6,9,8 # reduction candidate for 6,9 C2: 6,9 => SOLVED * 456713982219846537387952641678239154943165278521478369832697415764521893195384726 C2: 8 => CTR * .56..348.218..653..97...6.1672839154943..5278581..2.6.8.4.973157.9..18421.5.84796 * PAIR C1: 6,9 ROW 1 D1: 6,9,1,2,7 # reduction candidate for 6,9 D1: 6,9 => CTR * .5..1248721....5394.7.5362167..29154943165278521..896386..973157....18421.5.84796 D1: 1,2,7 # 21 pairs * PAIR B3: 8,9 BLK 1 C2: 8,9,6 # reduction candidate for 8,9 C2: 6 => CTR * .5.....8.216..853..87...6.1678..9154943...278521....6.8...97.157....18..1.5.847.6 C2: 8,9 # 22 pairs * PAIR B3: 8,9 ROW 3 D3: 8,9,2,5 # reduction candidate for 8,9 D3: 2,5 => CTR * .5.71..82218946537.97..86416728391549431.5278581.72.6.8...97.157....18..1.5.847.6 D3: 8,9 # 24 pairs * PAIR F2: 6,8 BLK 2 D2: 6,8,4,7,9 # reduction candidate for 6,8 D2: 6,8 => SOLVED * 456713982219846537387952641678239154943165278521478369832697415764521893195384726 D2: 4,7,9 # 21 pairs * PAIR F2: 6,8 ROW 2 C2: 6,8,9 # reduction candidate for 6,8 C2: 9 => SOLVED * 456713982219846537387952641678239154943165278521478369832697415764521893195384726 C2: 6,8 # 23 pairs * PAIR E3: 2,5 BLK 2 D3: 2,5,8,9 # reduction candidate for 2,5 D3: 2,5 => CTR * .5.71..82218946537.97..86416728391549431.5278581.72.6.8...97.157....18..1.5.847.6 D3: 8,9 # 24 pairs F3: 2,5,3,8 # reduction candidate for 2,5 F3: 2,5 => SOLVED * 456713982219846537387952641678239154943165278521478369832697415764521893195384726 F3: 3,8 # 25 pairs * PAIR E3: 2,5 COL E E8: 2,5,3,6 # reduction candidate for 2,5 E8: 3,6 # 27 pairs E8: 2,5 # 24 pairs * PAIR G1: 4,9 BLK 3 H3: 4,9,2 # reduction candidate for 4,9 H3: 2 => CTR * 35....48.21....53.4.7.53621672839154943..5278581..29638.4.973157.95618421.5384796 H3: 4,9 # 26 pairs * PAIR I2: 7,9 BLK 3 I1: 7,9,2 # reduction candidate for 7,9 I1: 7,9 => CTR * 356..248.218..653.497.5362167...9154943..52785.1...9638.4.973157.95.18421.5.84796 I1: 2 # 26 pairs * PAIR I2: 7,9 ROW 2 D2: 7,9,4,6,8 # reduction candidate for 7,9 D2: 7,9 # 21 pairs D2: 4,6,8 # 21 pairs * PAIR C4: 2,8 ROW 4 D4: 2,8,3 # reduction candidate for 2,8 D4: 3 => CTR * .5.....8.21....53...7...6.1678329154943...278521..8.6.8...97.157...318..135284796 D4: 2,8 # 21 pairs * PAIR E4: 2,3 BLK 5 D4: 2,3,8 # reduction candidate for 2,3 D4: 2,3 => SOLVED * 456713982219846537387952641678239154943165278521478369832697415764521893195384726 D4: 8 => CTR * .5.....8.218..653..97..86.1672839154943..5278581..2.6.8.4.973157.9..18421.5.84796 * PAIR E4: 2,3 COL E E8: 2,3,5,6 # reduction candidate for 2,3 E8: 5,6 => CTR * .56.2348.21....53...7...6.1672839154943...278581..2.6.8.4.973157.9..18421.5.84796 E8: 2,3 # 24 pairs * PAIR F5: 5,6 BLK 5 D5: 5,6,1 # reduction candidate for 5,6 D5: 5,6 => CTR * .5.1...8.21....53...79..6.167.839154943.1.278581....6.8...97.157....18..1.5.847.6 D5: 1 # 23 pairs E5: 5,6,1 # reduction candidate for 5,6 E5: 5,6 # 23 pairs * PAIR D6: 4,7 COL D D2: 4,7,6,8,9 # reduction candidate for 4,7 D2: 4,7 # 22 pairs D2: 6,8,9 # 20 pairs * PAIR E6: 4,7 COL E E2: 4,7,6 # reduction candidate for 4,7 E2: 6 => CTR * .5.....8.21.468537.87...6.1678..9154943..6278521....6.8...97.157....18..1.5.847.6 E2: 4,7 # 22 pairs * PAIR F6: 2,8 BLK 5 D4: 2,8,3 # reduction candidate for 2,8 D4: 3 => CTR * .5.....8.21....53...7...6.1678329154943...278521..8.6.8...97.157...318..135284796 D4: 2,8 # 21 pairs * PAIR F6: 2,8 COL F F3: 2,8,3,5 # reduction candidate for 2,8 F3: 2,8 => SOLVED * 456713982219846537387952641678239154943165278521478369832697415764521893195384726 F3: 3,5 # 22 pairs * PAIR I6: 3,9 COL I I8: 3,9,2 # reduction candidate for 3,9 I8: 2 => CTR * 356..248.218..653.497..362167...9154943..52785.1...9638.4.973157.9..18421.5.84796 I8: 3,9 # 26 pairs * PAIR C7: 2,4 BLK 7 C8: 2,4,9 # reduction candidate for 2,4 C8: 2,4 => SOLVED * 456713982219846537387952641678239154943165278521478369832697415764521893195384726 C8: 9 => CTR * .56...48.218..653.497..36216728.9154943...2785.1....6.8.4.973157.9..18421.5.84796 * PAIR D9: 2,3 BLK 8 D7: 2,3,6 # reduction candidate for 2,3 D7: 2,3 => CTR * .5.....8.218..653..97528641672839154943...278581..2.6.86..97.157....18..1.5.847.6 D7: 6 # 25 pairs D8: 2,3,5,6 # reduction candidate for 2,3 D8: 2,3 => CTR * .5.....8221....537..7.2.6.1672839154943...278581..2.6.824697315769.518..1.5.847.6 D8: 5,6 # 22 pairs E8: 2,3,5,6 # reduction candidate for 2,3 E8: 2,3 # 24 pairs * PAIR D9: 2,3 ROW 9 B9: 2,3,9 # reduction candidate for 2,3 B9: 9 => SOLVED * 456713982219846537387952641678239154943165278521478369832697415764521893195384726 B9: 2,3 # 26 pairs * PAIR D9: 2,3 COL D D4: 2,3,8 # reduction candidate for 2,3 D4: 2,3 => SOLVED * 456713982219846537387952641678239154943165278521478369832697415764521893195384726 D4: 8 => CTR * .5.....8.218..653..97..86.1672839154943..5278581..2.6.8.4.973157.9..18421.5.84796 * PAIR H9: 2,9 BLK 9 H8: 2,9,4 # reduction candidate for 2,9 H8: 2,9 => SOLVED * 456713982219846537387952641678239154943165278521478369832697415764521893195384726 H8: 4 # 25 pairs I8: 2,9,3 # reduction candidate for 2,9 I8: 2,9 # 25 pairs * PAIR H9: 2,9 ROW 9 B9: 2,9,3 # reduction candidate for 2,9 B9: 3 # 27 pairs B9: 2,9 # 24 pairs * PAIR H9: 2,9 COL H H3: 2,9,4 # reduction candidate for 2,9 H3: 4 => SOLVED * 456713982219846537387952641678239154943165278521478369832697415764521893195384726 H3: 2,9 # 25 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060801-absurd-base-pr-000.dot * REASONING * PRF # C2: 6,9 => SOL * DIS # C2: 8 => CTR => C2: 6,9 * DIS # D1: 6,9 => CTR => D1: 1,2,7 * DIS # C2: 6 => CTR => C2: 8,9 * DIS # D3: 2,5 => CTR => D3: 8,9 * PRF # D2: 6,8 => SOL * PRF # C2: 9 => SOL * DIS # D3: 2,5 => CTR => D3: 8,9 * PRF # F3: 2,5 => SOL * DIS # H3: 2 => CTR => H3: 4,9 * DIS # I1: 7,9 => CTR => I1: 2 * DIS # D4: 3 => CTR => D4: 2,8 * PRF # D4: 2,3 => SOL * DIS # D4: 8 => CTR => D4: 2,3 * DIS # E8: 5,6 => CTR => E8: 2,3 * DIS # D5: 5,6 => CTR => D5: 1 * DIS # E2: 6 => CTR => E2: 4,7 * DIS # D4: 3 => CTR => D4: 2,8 * PRF # F3: 2,8 => SOL * DIS # I8: 2 => CTR => I8: 3,9 * PRF # C8: 2,4 => SOL * DIS # C8: 9 => CTR => C8: 2,4 * DIS # D7: 2,3 => CTR => D7: 6 * DIS # D8: 2,3 => CTR => D8: 5,6 * PRF # B9: 9 => SOL * PRF # D4: 2,3 => SOL * DIS # D4: 8 => CTR => D4: 2,3 * PRF # H8: 2,9 => SOL * PRF # H3: 4 => SOL * CNT 29 HDP CHAINS / 61 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B3,B6,C1,C4,C7,D6,D9,E3,E4,E6,F2,F5,F6,G1,G6,G7,H9,I2,I6) * .5.....8.21....53...7...6.167...9154943...2785.1....6.8...97.157....18..1.5.847.6 * PAIR C1: 6,9 BLK 1 C2: 6,9,8 # reduction candidate for 6,9 C2: 6,9 => SOLVED * 456713982219846537387952641678239154943165278521478369832697415764521893195384726 * DURATION: 0:00:01.794071 START: 01:29:52.723580 END: 01:29:54.517651 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060801-absurd-base-pr-001.dot * REASONING * PRF # C2: 6,9 => SOL * STA C2: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060801, absurd
Solution
position: 456713982219846537387952641678239154943165278521478369832697415764521893195384726 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:
* PRF # C2: 6,9 => SOL * DIS # C2: 8 => CTR => C2: 6,9 * DIS # D1: 6,9 => CTR => D1: 1,2,7 * INC # D1: 1,2,7 => UNS * INC # C2: 8,9 => UNS * DIS # C2: 6 => CTR => C2: 8,9 * INC # D3: 8,9 => UNS * DIS # D3: 2,5 => CTR => D3: 8,9 * PRF # D2: 6,8 => SOL * INC # D2: 4,7,9 => UNS * INC # C2: 6,8 => UNS * PRF # C2: 9 => SOL * DIS # D3: 2,5 => CTR => D3: 8,9 * INC # D3: 8,9 => UNS * PRF # F3: 2,5 => SOL * INC # F3: 3,8 => UNS * INC # E8: 2,5 => UNS * INC # E8: 3,6 => UNS * INC # H3: 4,9 => UNS * DIS # H3: 2 => CTR => H3: 4,9 * DIS # I1: 7,9 => CTR => I1: 2 * INC # I1: 2 => UNS * INC # D2: 7,9 => UNS * INC # D2: 4,6,8 => UNS * INC # D4: 2,8 => UNS * DIS # D4: 3 => CTR => D4: 2,8 * PRF # D4: 2,3 => SOL * DIS # D4: 8 => CTR => D4: 2,3 * INC # E8: 2,3 => UNS * DIS # E8: 5,6 => CTR => E8: 2,3 * DIS # D5: 5,6 => CTR => D5: 1 * INC # D5: 1 => UNS * INC # E5: 5,6 => UNS * INC # D2: 4,7 => UNS * INC # D2: 6,8,9 => UNS * INC # E2: 4,7 => UNS * DIS # E2: 6 => CTR => E2: 4,7 * INC # D4: 2,8 => UNS * DIS # D4: 3 => CTR => D4: 2,8 * PRF # F3: 2,8 => SOL * INC # F3: 3,5 => UNS * INC # I8: 3,9 => UNS * DIS # I8: 2 => CTR => I8: 3,9 * PRF # C8: 2,4 => SOL * DIS # C8: 9 => CTR => C8: 2,4 * DIS # D7: 2,3 => CTR => D7: 6 * INC # D7: 6 => UNS * DIS # D8: 2,3 => CTR => D8: 5,6 * INC # D8: 5,6 => UNS * INC # E8: 2,3 => UNS * INC # B9: 2,3 => UNS * PRF # B9: 9 => SOL * PRF # D4: 2,3 => SOL * DIS # D4: 8 => CTR => D4: 2,3 * PRF # H8: 2,9 => SOL * INC # H8: 4 => UNS * INC # I8: 2,9 => UNS * INC # B9: 2,9 => UNS * INC # B9: 3 => UNS * INC # H3: 2,9 => UNS * PRF # H3: 4 => SOL * CNT 61 HDP CHAINS / 61 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C2: 6,9 => SOL * STA C2: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED