Analysis of zz-www.sudokuoftheday.co.uk-20190226-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: ...87...6......2.....3.184...7.....11..238..759.6...82....4..6......5..98.....1.. initial
Autosolve
position: ...87.916.18...273...3.1845287...6311..238597593617482....4..68....85.298.....154 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 3,4 => CTR => B1: 2,5 * DIS # A8: 3,4 => CTR => A8: 6,7 * DIS # C1: 2,4 => CTR => C1: 5 * PRF # B8: 3,7 => SOL * PRF # C8: 4,6 => SOL * DIS # C8: 1 => CTR => C8: 4,6 * DIS # E2: 6 => CTR => E2: 5,9 * DIS # F2: 4,9 => CTR => F2: 6 * DIS # C7: 2,9 => CTR => C7: 1,5 * DIS # C3: 6 => CTR => C3: 2,9 * DIS # F9: 6 => CTR => F9: 2,3 * DIS # B7: 2,3 => CTR => B7: 5,7 * PRF # D7: 1,7 => SOL * DIS # D7: 9 => CTR => D7: 1,7 * PRF # D7: 7,9 => SOL * DIS # D7: 1 => CTR => D7: 7,9 * DIS # F9: 2,6 => CTR => F9: 3 * DIS # E3: 9 => CTR => E3: 2,6 * DIS # A7: 3,7 => CTR => A7: 9 * PRF # A7: 9 => SOL * DIS # B7: 3,7 => CTR => B7: 2,5 * DIS # A8: 3,7 => CTR => A8: 4,6 * PRF # B8: 3,7 => SOL * CNT 23 HDP CHAINS / 39 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B1: 3,4 => CTR => B1: 2,5 * DIS B1: 2,5 # C1: 2,4 => CTR => C1: 5 * DIS B1: 2,5 + C1: 5 # B8: 4,6 => CTR => B8: 3,7 * PRF B1: 2,5 + C1: 5 + B8: 3,7 => SOL * STA B1: 2,5 + C1: 5 + B8: 3,7 * CNT 4 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...87...6......2.....3.184...7.....11..238..759.6...82....4..6......5..98.....1.. | initial |
| ...87.916.18...273...3.1845287...6311..238597593617482....4..68....85.298.....154 | autosolve |
| 325874916418596273769321845287459631146238597593617482951742368634185729872963154 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) A1: 3,4 F1: 2,4 D2: 4,5 B5: 4,6 C5: 4,6 D4: 4,5 E4: 5,9 F4: 4,9 C9: 2,9 F7: 2,3 D8: 1,7 D9: 7,9 E9: 2,6 G7: 3,7 G8: 3,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C7,C8: 1.. / C7 = 1 => 0 pairs (*) / C8 = 1 => 0 pairs (X) D7,D8: 1.. / D7 = 1 => 0 pairs (X) / D8 = 1 => 0 pairs (_) C7,D7: 1.. / C7 = 1 => 0 pairs (*) / D7 = 1 => 0 pairs (X) C8,D8: 1.. / C8 = 1 => 0 pairs (X) / D8 = 1 => 0 pairs (_) F1,E3: 2.. / F1 = 2 => 0 pairs (X) / E3 = 2 => 15 pairs (_) E3,E9: 2.. / E3 = 2 => 15 pairs (_) / E9 = 2 => 0 pairs (X) A1,B1: 3.. / A1 = 3 => 15 pairs (_) / B1 = 3 => 0 pairs (X) F7,F9: 3.. / F7 = 3 => 0 pairs (X) / F9 = 3 => 18 pairs (_) G7,G8: 3.. / G7 = 3 => 0 pairs (*) / G8 = 3 => 0 pairs (X) B9,F9: 3.. / B9 = 3 => 0 pairs (X) / F9 = 3 => 18 pairs (_) B5,C5: 4.. / B5 = 4 => 17 pairs (_) / C5 = 4 => 16 pairs (_) D4,F4: 4.. / D4 = 4 => 13 pairs (_) / F4 = 4 => 0 pairs (X) D2,D4: 4.. / D2 = 4 => 0 pairs (X) / D4 = 4 => 13 pairs (_) B1,C1: 5.. / B1 = 5 => 0 pairs (X) / C1 = 5 => 15 pairs (_) D2,E2: 5.. / D2 = 5 => 13 pairs (_) / E2 = 5 => 0 pairs (X) D4,E4: 5.. / D4 = 5 => 0 pairs (X) / E4 = 5 => 13 pairs (_) B7,C7: 5.. / B7 = 5 => 15 pairs (_) / C7 = 5 => 0 pairs (X) B1,B7: 5.. / B1 = 5 => 0 pairs (X) / B7 = 5 => 15 pairs (_) C1,C7: 5.. / C1 = 5 => 15 pairs (_) / C7 = 5 => 0 pairs (X) D2,D4: 5.. / D2 = 5 => 13 pairs (_) / D4 = 5 => 0 pairs (X) E2,E4: 5.. / E2 = 5 => 0 pairs (X) / E4 = 5 => 13 pairs (_) B5,C5: 6.. / B5 = 6 => 16 pairs (_) / C5 = 6 => 17 pairs (_) E9,F9: 6.. / E9 = 6 => 15 pairs (_) / F9 = 6 => 0 pairs (X) F2,F9: 6.. / F2 = 6 => 15 pairs (_) / F9 = 6 => 0 pairs (X) A3,B3: 7.. / A3 = 7 => 17 pairs (_) / B3 = 7 => 0 pairs (X) G7,G8: 7.. / G7 = 7 => 15 pairs (_) / G8 = 7 => 0 pairs (*) B9,D9: 7.. / B9 = 7 => 0 pairs (*) / D9 = 7 => 0 pairs (X) E4,F4: 9.. / E4 = 9 => 0 pairs (X) / F4 = 9 => 13 pairs (_) D7,D9: 9.. / D7 = 9 => 0 pairs (X) / D9 = 9 => 0 pairs (_) C9,D9: 9.. / C9 = 9 => 0 pairs (X) / D9 = 9 => 0 pairs (_) F2,F4: 9.. / F2 = 9 => 0 pairs (X) / F4 = 9 => 13 pairs (_) * DURATION: 0:00:55.357638 START: 04:02:09.142617 END: 04:03:04.500255 2019-05-01 * CP COUNT: (31) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B5,C5,C9,D2,D4,D8,D9,E4,E9,F1,F4,F7,G7,G8) * ...87.916.18...273...3.1845287...6311..238597593617482....4..68....85.298.....154 * PAIR A1: 3,4 BLK 1 B1: 3,4,2,5 # reduction candidate for 3,4 B1: 3,4 => CTR * ..5872916.18...273...3.1845287...6311..238597593617482.52143768..17853298.....154 B1: 2,5 # 16 pairs * PAIR A1: 3,4 COL A A8: 3,4,6,7 # reduction candidate for 3,4 A8: 3,4 => CTR * ...872916.18...273...3.1845287...6311..238597593617482.25143768..17853298.....154 A8: 6,7 # 17 pairs * PAIR F1: 2,4 ROW 1 B1: 2,4,3,5 # reduction candidate for 2,4 B1: 2,4 # 16 pairs C1: 2,4,5 # reduction candidate for 2,4 C1: 2,4 => CTR * 35.87.916.18..62737.9321845287..96311.62385975936174829.514..68..178532987.9.3154 C1: 5 # 15 pairs * PAIR B5: 4,6 COL B B8: 4,6,3,7 # reduction candidate for 4,6 B8: 3,7 => SOLVED * 325874916418596273769321845287459631146238597593617482951742368634185729872963154 B8: 4,6 # 17 pairs * PAIR C5: 4,6 COL C C8: 4,6,1 # reduction candidate for 4,6 C8: 4,6 => SOLVED * 325874916418596273769321845287459631146238597593617482951742368634185729872963154 C8: 1 => CTR * .2587491641859627376.3.1845287..96311..238597593617482...142768641785329872963154 * PAIR E4: 5,9 COL E E2: 5,9,6 # reduction candidate for 5,9 E2: 6 => CTR * ...872916918564273...3918452874596311..238597593617482....43768....85.298...26154 E2: 5,9 # 18 pairs * PAIR F4: 4,9 COL F F2: 4,9,6 # reduction candidate for 4,9 F2: 4,9 => CTR * ...87.916.18...273...3.1845287...6311..238597593617482....43768....8532983.726154 F2: 6 # 15 pairs * PAIR C9: 2,9 BLK 7 C7: 2,9,1,5 # reduction candidate for 2,9 C7: 2,9 => CTR * .35872916.18...273...3.1845287...6311..238597593617482.5.14..68..178532987.9.3154 C7: 1,5 # 16 pairs * PAIR C9: 2,9 COL C C3: 2,9,6 # reduction candidate for 2,9 C3: 6 => CTR * ...87.916.18..6273726391845287...631164238597593617482....4..6864178532987.9.3154 C3: 2,9 # 18 pairs * PAIR F7: 2,3 BLK 8 F9: 2,3,6 # reduction candidate for 2,3 F9: 6 => CTR * ...87.916.18...273...3.1845287...6311..238597593617482....43768....8532983.726154 F9: 2,3 # 15 pairs * PAIR F7: 2,3 ROW 7 B7: 2,3,5,7 # reduction candidate for 2,3 B7: 2,3 => CTR * 35.87.916.18..62737.9321845287..96311.62385975936174829.514..68..178532987.9.3154 B7: 5,7 # 16 pairs * PAIR D8: 1,7 BLK 8 D7: 1,7,9 # reduction candidate for 1,7 D7: 1,7 => SOLVED * 325874916418596273769321845287459631146238597593617482951742368634185729872963154 D7: 9 => CTR * ..587.916.18...273..23.1845287...6311..238597593617482.51942.68...185.29829763154 * PAIR D9: 7,9 BLK 8 D7: 7,9,1 # reduction candidate for 7,9 D7: 7,9 => SOLVED * 325874916418596273769321845287459631146238597593617482951742368634185729872963154 D7: 1 => CTR * .2587491641859627376.3.1845287..96311..238597593617482...142768641785329872963154 * PAIR E9: 2,6 BLK 8 F9: 2,6,3 # reduction candidate for 2,6 F9: 2,6 => CTR * 3..87.916.18...273...3.1845287...6311..2385975936174829..143768....8532983.7..154 F9: 3 # 18 pairs * PAIR E9: 2,6 COL E E3: 2,6,9 # reduction candidate for 2,6 E3: 9 => CTR * ...872916.18...273...391845287.596311..238597593617482....43768....8532983.726154 E3: 2,6 # 18 pairs * PAIR G7: 3,7 ROW 7 A7: 3,7,9 # reduction candidate for 3,7 A7: 3,7 => CTR * .2587491641859627397.3.1845287...6311..238597593617482.5..42.68....85.298...63154 A7: 9 => SOLVED * 325874916418596273769321845287459631146238597593617482951742368634185729872963154 B7: 3,7,2,5 # reduction candidate for 3,7 B7: 3,7 => CTR * .5.87.916.18...273...3.1845287...6311..238597593617482..5142.68..1785329872963154 B7: 2,5 # 16 pairs * PAIR G8: 3,7 ROW 8 A8: 3,7,4,6 # reduction candidate for 3,7 A8: 3,7 => CTR * ..587.916.18...273...3.1845287...6311..238597593617482.51.42.68...185.298...63154 A8: 4,6 # 16 pairs B8: 3,7,4,6 # reduction candidate for 3,7 B8: 3,7 => SOLVED * 325874916418596273769321845287459631146238597593617482951742368634185729872963154 B8: 4,6 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190226-absurd-base-pr-000.dot * REASONING * DIS # B1: 3,4 => CTR => B1: 2,5 * DIS # A8: 3,4 => CTR => A8: 6,7 * DIS # C1: 2,4 => CTR => C1: 5 * PRF # B8: 3,7 => SOL * PRF # C8: 4,6 => SOL * DIS # C8: 1 => CTR => C8: 4,6 * DIS # E2: 6 => CTR => E2: 5,9 * DIS # F2: 4,9 => CTR => F2: 6 * DIS # C7: 2,9 => CTR => C7: 1,5 * DIS # C3: 6 => CTR => C3: 2,9 * DIS # F9: 6 => CTR => F9: 2,3 * DIS # B7: 2,3 => CTR => B7: 5,7 * PRF # D7: 1,7 => SOL * DIS # D7: 9 => CTR => D7: 1,7 * PRF # D7: 7,9 => SOL * DIS # D7: 1 => CTR => D7: 7,9 * DIS # F9: 2,6 => CTR => F9: 3 * DIS # E3: 9 => CTR => E3: 2,6 * DIS # A7: 3,7 => CTR => A7: 9 * PRF # A7: 9 => SOL * DIS # B7: 3,7 => CTR => B7: 2,5 * DIS # A8: 3,7 => CTR => A8: 4,6 * PRF # B8: 3,7 => SOL * CNT 23 HDP CHAINS / 39 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B5,C5,C9,D2,D4,D8,D9,E4,E9,F1,F4,F7,G7,G8) * ...87.916.18...273...3.1845287...6311..238597593617482....4..68....85.298.....154 * PAIR A1: 3,4 BLK 1 B1: 3,4,2,5 # reduction candidate for 3,4 B1: 3,4 => CTR * ..5872916.18...273...3.1845287...6311..238597593617482.52143768..17853298.....154 * PAIR F1: 2,4 ROW 1 C1: 2,4,5 # reduction candidate for 2,4 C1: 2,4 => CTR * 35.87.916.18..62737.9321845287..96311.62385975936174829.514..68..178532987.9.3154 * PAIR RESTART * PAIR B5: 4,6 COL B B8: 4,6,3,7 # reduction candidate for 4,6 B8: 4,6 => CTR * 325874916418596273.7.3218452874596311..238597593617482.52.4..68....8532983.762154 B8: 3,7 => SOLVED * 325874916418596273769321845287459631146238597593617482951742368634185729872963154 * DURATION: 0:00:06.680844 START: 04:03:40.474113 END: 04:03:47.154957 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190226-absurd-base-pr-001.dot * REASONING * DIS # B1: 3,4 => CTR => B1: 2,5 * DIS B1: 2,5 # C1: 2,4 => CTR => C1: 5 * DIS B1: 2,5 + C1: 5 # B8: 4,6 => CTR => B8: 3,7 * PRF B1: 2,5 + C1: 5 + B8: 3,7 => SOL * STA B1: 2,5 + C1: 5 + B8: 3,7 * CNT 4 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190226, absurd
Solution
position: 325874916418596273769321845287459631146238597593617482951742368634185729872963154 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 # B1: 3,4 => CTR => B1: 2,5 * INC # B1: 2,5 => UNS * DIS # A8: 3,4 => CTR => A8: 6,7 * INC # A8: 6,7 => UNS * INC # B1: 2,4 => UNS * DIS # C1: 2,4 => CTR => C1: 5 * INC # C1: 5 => UNS * INC # B8: 4,6 => UNS * PRF # B8: 3,7 => SOL * PRF # C8: 4,6 => SOL * DIS # C8: 1 => CTR => C8: 4,6 * INC # E2: 5,9 => UNS * DIS # E2: 6 => CTR => E2: 5,9 * DIS # F2: 4,9 => CTR => F2: 6 * INC # F2: 6 => UNS * DIS # C7: 2,9 => CTR => C7: 1,5 * INC # C7: 1,5 => UNS * INC # C3: 2,9 => UNS * DIS # C3: 6 => CTR => C3: 2,9 * INC # F9: 2,3 => UNS * DIS # F9: 6 => CTR => F9: 2,3 * DIS # B7: 2,3 => CTR => B7: 5,7 * INC # B7: 5,7 => UNS * PRF # D7: 1,7 => SOL * DIS # D7: 9 => CTR => D7: 1,7 * PRF # D7: 7,9 => SOL * DIS # D7: 1 => CTR => D7: 7,9 * DIS # F9: 2,6 => CTR => F9: 3 * INC # F9: 3 => UNS * INC # E3: 2,6 => UNS * DIS # E3: 9 => CTR => E3: 2,6 * DIS # A7: 3,7 => CTR => A7: 9 * PRF # A7: 9 => SOL * DIS # B7: 3,7 => CTR => B7: 2,5 * INC # B7: 2,5 => UNS * DIS # A8: 3,7 => CTR => A8: 4,6 * INC # A8: 4,6 => UNS * PRF # B8: 3,7 => SOL * INC # B8: 4,6 => UNS * CNT 39 HDP CHAINS / 39 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B1: 3,4 => CTR => B1: 2,5 * DIS B1: 2,5 # C1: 2,4 => CTR => C1: 5 * DIS B1: 2,5 + C1: 5 # B8: 4,6 => CTR => B8: 3,7 * PRF B1: 2,5 + C1: 5 + B8: 3,7 => SOL * STA B1: 2,5 + C1: 5 + B8: 3,7 * CNT 4 HDP CHAINS / 3 HYP OPENED