Analysis of zz-www.sudokuoftheday.co.uk-20190207-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019
level: medium
position: 15............3....861......6.4...5...5..294..91...6....78...2.......4.5.3.62...7 initial
Autosolve
position: 15...6........3....861......6.4..758875362941491..8632..78...2.....3.4.5.3.62...7 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 2,4 => CTR => C1: 3,9 * DIS # H2: 7,9 => CTR => H2: 1,6,8 * PRF # A3: 7,9 => SOL * DIS # E3: 7,9 => CTR => E3: 4,5 * PRF # A3: 7,9 => SOL * DIS # C1: 4,9 => CTR => C1: 2,3 * PRF # F7: 1,9 => SOL * DIS # F8: 1,9 => CTR => F8: 7 * DIS # F9: 1,9 => CTR => F9: 4,5 * PRF # D2: 5,7 => SOL * DIS # E2: 5,7 => CTR => E2: 4,8,9 * DIS # A7: 5,9 => CTR => A7: 6 * DIS # F9: 5,9 => CTR => F9: 1,4 * DIS # F8: 1 => CTR => F8: 7,9 * DIS # D1: 7,9 => CTR => D1: 2 * DIS # H8: 1,8 => CTR => H8: 6,9 * DIS # G2: 1,8 => CTR => G2: 2,5 * CNT 17 HDP CHAINS / 44 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 2,4 => CTR => C1: 3,9 * DIS C1: 3,9 # C2: 9 => CTR => C2: 2,4 * DIS C1: 3,9 + C2: 2,4 # F8: 1,9 => CTR => F8: 7 * PRF C1: 3,9 + C2: 2,4 + F8: 7 => SOL * STA C1: 3,9 + C2: 2,4 + F8: 7 * CNT 4 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 15............3....861......6.4...5...5..294..91...6....78...2.......4.5.3.62...7 | initial |
| 15...6........3....861......6.4..758875362941491..8632..78...2.....3.4.5.3.62...7 | autosolve |
| 153296874924783516786145293362419758875362941491578632647851329218937465539624187 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) B2: 2,4 H3: 7,9 A4: 2,3 C4: 2,3 E4: 1,9 F4: 1,9 D6: 5,7 E6: 5,7 B7: 1,4 B8: 1,2 A9: 5,9 D8: 7,9 G7: 1,3 G9: 1,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G2,H2: 1.. / G2 = 1 => 0 pairs (X) / H2 = 1 => 17 pairs (_) E4,F4: 1.. / E4 = 1 => 13 pairs (_) / F4 = 1 => 0 pairs (X) B7,B8: 1.. / B7 = 1 => 20 pairs (_) / B8 = 1 => 0 pairs (*) E4,E7: 1.. / E4 = 1 => 13 pairs (_) / E7 = 1 => 0 pairs (X) D1,D2: 2.. / D1 = 2 => 21 pairs (_) / D2 = 2 => 0 pairs (X) A4,C4: 2.. / A4 = 2 => 0 pairs (X) / C4 = 2 => 17 pairs (_) A3,G3: 2.. / A3 = 2 => 0 pairs (X) / G3 = 2 => 17 pairs (_) B2,B8: 2.. / B2 = 2 => 0 pairs (*) / B8 = 2 => 0 pairs (X) C1,A3: 3.. / C1 = 3 => 17 pairs (_) / A3 = 3 => 0 pairs (X) A4,C4: 3.. / A4 = 3 => 17 pairs (_) / C4 = 3 => 0 pairs (X) G7,I7: 3.. / G7 = 3 => 16 pairs (_) / I7 = 3 => 0 pairs (X) A3,A4: 3.. / A3 = 3 => 0 pairs (X) / A4 = 3 => 17 pairs (_) C1,C4: 3.. / C1 = 3 => 17 pairs (_) / C4 = 3 => 0 pairs (X) B7,C9: 4.. / B7 = 4 => 0 pairs (*) / C9 = 4 => 0 pairs (X) C9,F9: 4.. / C9 = 4 => 20 pairs (_) / F9 = 4 => 0 pairs (*) B2,B7: 4.. / B2 = 4 => 20 pairs (_) / B7 = 4 => 0 pairs (*) G2,G3: 5.. / G2 = 5 => 17 pairs (_) / G3 = 5 => 0 pairs (X) D6,E6: 5.. / D6 = 5 => 16 pairs (_) / E6 = 5 => 0 pairs (X) A7,A9: 5.. / A7 = 5 => 0 pairs (X) / A9 = 5 => 14 pairs (_) A9,F9: 5.. / A9 = 5 => 14 pairs (_) / F9 = 5 => 0 pairs (X) D2,D6: 5.. / D2 = 5 => 0 pairs (X) / D6 = 5 => 16 pairs (_) H2,I2: 6.. / H2 = 6 => 0 pairs (X) / I2 = 6 => 16 pairs (_) A7,A8: 6.. / A7 = 6 => 16 pairs (_) / A8 = 6 => 0 pairs (X) I7,H8: 6.. / I7 = 6 => 0 pairs (X) / H8 = 6 => 16 pairs (_) A7,I7: 6.. / A7 = 6 => 16 pairs (_) / I7 = 6 => 0 pairs (X) A8,H8: 6.. / A8 = 6 => 0 pairs (X) / H8 = 6 => 16 pairs (_) H2,H8: 6.. / H2 = 6 => 0 pairs (X) / H8 = 6 => 16 pairs (_) I2,I7: 6.. / I2 = 6 => 16 pairs (_) / I7 = 6 => 0 pairs (X) A2,A3: 7.. / A2 = 7 => 14 pairs (_) / A3 = 7 => 0 pairs (*) D6,E6: 7.. / D6 = 7 => 0 pairs (X) / E6 = 7 => 16 pairs (_) D8,F8: 7.. / D8 = 7 => 0 pairs (X) / F8 = 7 => 19 pairs (_) F3,F8: 7.. / F3 = 7 => 0 pairs (X) / F8 = 7 => 19 pairs (_) E1,E2: 8.. / E1 = 8 => 0 pairs (X) / E2 = 8 => 14 pairs (_) C8,C9: 8.. / C8 = 8 => 15 pairs (_) / C9 = 8 => 0 pairs (X) C8,H8: 8.. / C8 = 8 => 15 pairs (_) / H8 = 8 => 0 pairs (X) E4,F4: 9.. / E4 = 9 => 0 pairs (X) / F4 = 9 => 13 pairs (_) * DURATION: 0:00:39.028178 START: 03:33:22.135998 END: 03:34:01.164176 2019-05-01 * CP COUNT: (36) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A9,B2,B7,B8,C4,D6,D8,E4,E6,F4,G7,G9,H3) * 15...6........3....861......6.4..758875362941491..8632..78...2.....3.4.5.3.62...7 * PAIR B2: 2,4 BLK 1 C1: 2,4,3,9 # reduction candidate for 2,4 C1: 2,4 => CTR * 15.9.68737.92835163861.729426341975887536294149157863261789..2.9..73146553.62.187 C1: 3,9 # 16 pairs C2: 2,4,9 # reduction candidate for 2,4 C2: 2,4 # 20 pairs * PAIR H3: 7,9 BLK 3 H1: 7,9,8 # reduction candidate for 7,9 H1: 7,9 # 22 pairs H2: 7,9,1,6,8 # reduction candidate for 7,9 H2: 7,9 => CTR * 15...628....2.31.6.861..5...6.4..758875362941491..86326.78..329....3.46553.62.817 H2: 1,6,8 # 14 pairs * PAIR H3: 7,9 ROW 3 A3: 7,9,2,3 # reduction candidate for 7,9 A3: 7,9 => SOLVED * 153296874924783516786145293362419758875362941491578632647851329218937465539624187 A3: 2,3 # 18 pairs E3: 7,9,4,5 # reduction candidate for 7,9 E3: 7,9 => CTR * 15...628.7..2.316..8619.57..6.419758875362941491..86329.78..3266..93741553.621897 E3: 4,5 # 15 pairs F3: 7,9,4,5 # reduction candidate for 7,9 F3: 7,9 # 26 pairs * PAIR A4: 2,3 COL A A3: 2,3,7,9 # reduction candidate for 2,3 A3: 7,9 => SOLVED * 153296874924783516786145293362419758875362941491578632647851329218937465539624187 A3: 2,3 # 18 pairs * PAIR C4: 2,3 COL C C1: 2,3,4,9 # reduction candidate for 2,3 C1: 4,9 => CTR * 15.2.68737..9835163861.729426341975887536294149157863261789..2.9..73146553.62.187 C1: 2,3 # 18 pairs * PAIR E4: 1,9 COL E E7: 1,9,4,5 # reduction candidate for 1,9 E7: 1,9 # 26 pairs E7: 4,5 # 19 pairs * PAIR F4: 1,9 COL F F7: 1,9,4,5 # reduction candidate for 1,9 F7: 1,9 => SOLVED * 153296874924783516786145293362419758875362941491578632647851329218937465539624187 F7: 4,5 # 15 pairs F8: 1,9,7 # reduction candidate for 1,9 F8: 1,9 => CTR * 15...6.7.7....3..6.861.7.9..6.4..7588753629414915786326.78.532992873146553.62...7 F8: 7 # 19 pairs F9: 1,9,4,5 # reduction candidate for 1,9 F9: 1,9 => CTR * 15...62...4.2.31..2861..573362419758875362941491578632.178.5326628937415534621897 F9: 4,5 # 17 pairs * PAIR D6: 5,7 COL D D2: 5,7,2,9 # reduction candidate for 5,7 D2: 5,7 => SOLVED * 153296874924783516786145293362419758875362941491578632647851329218937465539624187 D2: 2,9 # 17 pairs * PAIR E6: 5,7 COL E E2: 5,7,4,8,9 # reduction candidate for 5,7 E2: 5,7 => CTR * 153.862.4...253..62861..5.33624..7588753629414915786326.78.5329928731465534629..7 E2: 4,8,9 # 14 pairs E3: 5,7,4,9 # reduction candidate for 5,7 E3: 5,7 # 15 pairs * PAIR B7: 1,4 ROW 7 E7: 1,4,5,9 # reduction candidate for 1,4 E7: 1,4 # 18 pairs F7: 1,4,5,9 # reduction candidate for 1,4 F7: 1,4 # 18 pairs * PAIR A9: 5,9 BLK 7 A7: 5,9,6 # reduction candidate for 5,9 A7: 5,9 => CTR * 15...628....2.316..861..5...6.4..758875362941491..8632..78..3266...3.4.5.3.62.8.7 A7: 6 # 16 pairs * PAIR A9: 5,9 ROW 9 F9: 5,9,1,4 # reduction candidate for 5,9 F9: 5,9 => CTR * 15...6....4...3....861.7.9..6.419758875362941491.78632.178.4329.28.314.5.3462...7 F9: 1,4 # 15 pairs * PAIR D8: 7,9 BLK 8 F8: 7,9,1 # reduction candidate for 7,9 F8: 1 => CTR * 15...6........3....861.7.9..6.4..758875362941491.78632..78...29...731465.3.629..7 F8: 7,9 # 20 pairs * PAIR D8: 7,9 COL D D1: 7,9,2 # reduction candidate for 7,9 D1: 7,9 => CTR * 15...6....492.3..6.861......6.4..7588753629414915786326178..329928731465534629..7 D1: 2 # 21 pairs D2: 7,9,2,5 # reduction candidate for 7,9 D2: 7,9 # 18 pairs * PAIR G9: 1,8 BLK 9 H8: 1,8,6,9 # reduction candidate for 1,8 H8: 1,8 => CTR * 15...628.7..2.316..861..57..6.4..758875362941491..8632..78..3266...3741553.621897 H8: 6,9 # 16 pairs H9: 1,8,9 # reduction candidate for 1,8 H9: 1,8 # 19 pairs * PAIR G9: 1,8 COL G G2: 1,8,2,5 # reduction candidate for 1,8 G2: 1,8 => CTR * 153.862.4749253..62861..5.33624..7588753629414915786326178.5329928731465534629..7 G2: 2,5 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190207-absurd-base-pr-000.dot * REASONING * DIS # C1: 2,4 => CTR => C1: 3,9 * DIS # H2: 7,9 => CTR => H2: 1,6,8 * PRF # A3: 7,9 => SOL * DIS # E3: 7,9 => CTR => E3: 4,5 * PRF # A3: 7,9 => SOL * DIS # C1: 4,9 => CTR => C1: 2,3 * PRF # F7: 1,9 => SOL * DIS # F8: 1,9 => CTR => F8: 7 * DIS # F9: 1,9 => CTR => F9: 4,5 * PRF # D2: 5,7 => SOL * DIS # E2: 5,7 => CTR => E2: 4,8,9 * DIS # A7: 5,9 => CTR => A7: 6 * DIS # F9: 5,9 => CTR => F9: 1,4 * DIS # F8: 1 => CTR => F8: 7,9 * DIS # D1: 7,9 => CTR => D1: 2 * DIS # H8: 1,8 => CTR => H8: 6,9 * DIS # G2: 1,8 => CTR => G2: 2,5 * CNT 17 HDP CHAINS / 44 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A9,B2,B7,B8,C4,D6,D8,E4,E6,F4,G7,G9,H3) * 15...6........3....861......6.4..758875362941491..8632..78...2.....3.4.5.3.62...7 * PAIR B2: 2,4 BLK 1 C1: 2,4,3,9 # reduction candidate for 2,4 C1: 2,4 => CTR * 15.9.68737.92835163861.729426341975887536294149157863261789..2.9..73146553.62.187 C2: 2,4,9 # reduction candidate for 2,4 C2: 2,4 # 20 pairs * RESTART * PAIR B2: 2,4 BLK 1 C2: 2,4,9 # reduction candidate for 2,4 C2: 9 => CTR * 15...6....49..3..6.861......6.4..758875362941491..86326178..329.28.3.465534629..7 * PAIR F4: 1,9 COL F F8: 1,9,7 # reduction candidate for 1,9 F8: 1,9 => CTR * 15.2.687.7.498351638615729426.4..7588753629414915786326.78.5329..873.46553.624187 F8: 7 => SOLVED * 153296874924783516786145293362419758875362941491578632647851329218937465539624187 * DURATION: 0:00:05.782330 START: 03:34:27.861962 END: 03:34:33.644292 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190207-absurd-base-pr-001.dot * REASONING * DIS # C1: 2,4 => CTR => C1: 3,9 * DIS C1: 3,9 # C2: 9 => CTR => C2: 2,4 * DIS C1: 3,9 + C2: 2,4 # F8: 1,9 => CTR => F8: 7 * PRF C1: 3,9 + C2: 2,4 + F8: 7 => SOL * STA C1: 3,9 + C2: 2,4 + F8: 7 * CNT 4 HDP CHAINS / 5 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190207, absurd
Solution
position: 153296874924783516786145293362419758875362941491578632647851329218937465539624187 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:
* DIS # C1: 2,4 => CTR => C1: 3,9 * INC # C1: 3,9 => UNS * INC # C2: 2,4 => UNS * INC # H1: 7,9 => UNS * DIS # H2: 7,9 => CTR => H2: 1,6,8 * INC # H2: 1,6,8 => UNS * PRF # A3: 7,9 => SOL * INC # A3: 2,3 => UNS * DIS # E3: 7,9 => CTR => E3: 4,5 * INC # E3: 4,5 => UNS * INC # F3: 7,9 => UNS * INC # A3: 2,3 => UNS * PRF # A3: 7,9 => SOL * INC # C1: 2,3 => UNS * DIS # C1: 4,9 => CTR => C1: 2,3 * INC # E7: 1,9 => UNS * INC # E7: 4,5 => UNS * PRF # F7: 1,9 => SOL * INC # F7: 4,5 => UNS * DIS # F8: 1,9 => CTR => F8: 7 * INC # F8: 7 => UNS * DIS # F9: 1,9 => CTR => F9: 4,5 * INC # F9: 4,5 => UNS * PRF # D2: 5,7 => SOL * INC # D2: 2,9 => UNS * DIS # E2: 5,7 => CTR => E2: 4,8,9 * INC # E2: 4,8,9 => UNS * INC # E3: 5,7 => UNS * INC # E7: 1,4 => UNS * INC # F7: 1,4 => UNS * DIS # A7: 5,9 => CTR => A7: 6 * INC # A7: 6 => UNS * DIS # F9: 5,9 => CTR => F9: 1,4 * INC # F9: 1,4 => UNS * INC # F8: 7,9 => UNS * DIS # F8: 1 => CTR => F8: 7,9 * DIS # D1: 7,9 => CTR => D1: 2 * INC # D1: 2 => UNS * INC # D2: 7,9 => UNS * DIS # H8: 1,8 => CTR => H8: 6,9 * INC # H8: 6,9 => UNS * INC # H9: 1,8 => UNS * DIS # G2: 1,8 => CTR => G2: 2,5 * INC # G2: 2,5 => UNS * CNT 44 HDP CHAINS / 44 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C1: 2,4 => CTR => C1: 3,9 * INC C1: 3,9 # C2: 2,4 => UNS * INC C1: 3,9 # C2: 2,4 => UNS * DIS C1: 3,9 # C2: 9 => CTR => C2: 2,4 * DIS C1: 3,9 + C2: 2,4 # F8: 1,9 => CTR => F8: 7 * PRF C1: 3,9 + C2: 2,4 + F8: 7 => SOL * STA C1: 3,9 + C2: 2,4 + F8: 7 * CNT 6 HDP CHAINS / 5 HYP OPENED