Analysis of zz-www.sudokuoftheday.co.uk-20190406-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019
level: medium
position: .8......4......6.2.39.658..3....8..6...5..19...7......1..4.2......8.3..7....5.... initial
Autosolve
position: .8....954..19846324392658713..1.87.6...5..19..17......1..4.2......8.3..7....5.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B7: 6,9 => CTR => B7: 5,7 * DIS # E1: 1 => CTR => E1: 3,7 * DIS # E1: 1,7 => CTR => E1: 3 * DIS # F9: 1,7 => CTR => F9: 6,9 * DIS # F9: 6,7 => CTR => F9: 1,9 * PRF # A6: 2,8 => SOL * DIS # F9: 1,7 => CTR => F9: 6,9 * DIS # C4: 2,4 => CTR => C4: 5 * DIS # H9: 2,4 => CTR => H9: 1,8 * DIS # I6: 3,8 => CTR => I6: 5 * DIS # I7: 3,8 => CTR => I7: 5,9 * DIS # B7: 7,9 => CTR => B7: 5,6 * DIS # F9: 6,7 => CTR => F9: 1,9 * DIS # F9: 6,7 => CTR => F9: 1,9 * DIS # I7: 3,5 => CTR => I7: 8,9 * CNT 15 HDP CHAINS / 49 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B7: 6,9 => CTR => B7: 5,7 * DIS B7: 5,7 # E1: 1 => CTR => E1: 3,7 * DIS B7: 5,7 + E1: 3,7 # F9: 6,7 => CTR => F9: 9 * PRF B7: 5,7 + E1: 3,7 + F9: 9 # E4: 2,4 => SOL * STA B7: 5,7 + E1: 3,7 + F9: 9 + E4: 2,4 * CNT 4 HDP CHAINS / 12 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .8......4......6.2.39.658..3....8..6...5..19...7......1..4.2......8.3..7....5.... | initial |
| .8....954..19846324392658713..1.87.6...5..19..17......1..4.2......8.3..7....5.... | autosolve |
| 682731954571984632439265871395148726864527193217396485158472369926813547743659218 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) A1: 2,6 C1: 2,6 A2: 5,7 B2: 5,7 D1: 3,7 F1: 1,7 F5: 6,7 D6: 3,6 F6: 6,9 H4: 2,4 I5: 3,8 E7: 7,9 E8: 1,9 D9: 6,7 G7: 3,5 H7: 6,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,F1: 1.. / E1 = 1 => 0 pairs (X) / F1 = 1 => 15 pairs (_) E8,F9: 1.. / E8 = 1 => 15 pairs (_) / F9 = 1 => 0 pairs (X) H8,H9: 1.. / H8 = 1 => 0 pairs (X) / H9 = 1 => 15 pairs (_) E8,H8: 1.. / E8 = 1 => 15 pairs (_) / H8 = 1 => 0 pairs (X) F9,H9: 1.. / F9 = 1 => 0 pairs (X) / H9 = 1 => 15 pairs (_) E1,E8: 1.. / E1 = 1 => 0 pairs (X) / E8 = 1 => 15 pairs (_) F1,F9: 1.. / F1 = 1 => 15 pairs (_) / F9 = 1 => 0 pairs (X) A1,C1: 2.. / A1 = 2 => 15 pairs (_) / C1 = 2 => 15 pairs (_) D1,E1: 3.. / D1 = 3 => 0 pairs (X) / E1 = 3 => 13 pairs (_) C7,C9: 3.. / C7 = 3 => 18 pairs (_) / C9 = 3 => 18 pairs (_) E5,I5: 3.. / E5 = 3 => 0 pairs (X) / I5 = 3 => 17 pairs (_) D1,D6: 3.. / D1 = 3 => 0 pairs (X) / D6 = 3 => 13 pairs (_) A2,B2: 5.. / A2 = 5 => 9 pairs (_) / B2 = 5 => 15 pairs (_) B4,C4: 5.. / B4 = 5 => 0 pairs (X) / C4 = 5 => 16 pairs (_) G6,I6: 5.. / G6 = 5 => 0 pairs (X) / I6 = 5 => 16 pairs (_) A2,A8: 5.. / A2 = 5 => 9 pairs (_) / A8 = 5 => 15 pairs (_) I6,I7: 5.. / I6 = 5 => 16 pairs (_) / I7 = 5 => 0 pairs (X) A1,C1: 6.. / A1 = 6 => 15 pairs (_) / C1 = 6 => 15 pairs (_) D9,F9: 6.. / D9 = 6 => 13 pairs (_) / F9 = 6 => 0 pairs (X) H7,H8: 6.. / H7 = 6 => 15 pairs (_) / H8 = 6 => 21 pairs (_) D6,D9: 6.. / D6 = 6 => 0 pairs (X) / D9 = 6 => 13 pairs (_) A2,B2: 7.. / A2 = 7 => 15 pairs (_) / B2 = 7 => 9 pairs (_) E5,F5: 7.. / E5 = 7 => 0 pairs (X) / F5 = 7 => 15 pairs (_) B7,E7: 7.. / B7 = 7 => 0 pairs (X) / E7 = 7 => 9 pairs (_) A2,A9: 7.. / A2 = 7 => 15 pairs (_) / A9 = 7 => 9 pairs (_) D1,D9: 7.. / D1 = 7 => 13 pairs (_) / D9 = 7 => 0 pairs (X) B4,A6: 9.. / B4 = 9 => 21 pairs (_) / A6 = 9 => 12 pairs (_) I7,I9: 9.. / I7 = 9 => 9 pairs (_) / I9 = 9 => 0 pairs (X) B4,E4: 9.. / B4 = 9 => 21 pairs (_) / E4 = 9 => 12 pairs (_) F6,F9: 9.. / F6 = 9 => 20 pairs (_) / F9 = 9 => 9 pairs (_) * DURATION: 0:00:31.168476 START: 05:06:26.795725 END: 05:06:57.964201 2019-05-01 * CP COUNT: (30) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,B2,C1,D1,D6,D9,E7,E8,F1,F5,F6,G7,H4,H7,I5) * .8....954..19846324392658713..1.87.6...5..19..17......1..4.2......8.3..7....5.... * PAIR A1: 2,6 COL A A5: 2,6,8 # reduction candidate for 2,6 A5: 2,6 # 19 pairs A6: 2,6,8,9 # reduction candidate for 2,6 A6: 2,6 # 24 pairs A8: 2,6,5,9 # reduction candidate for 2,6 A8: 2,6 # 12 pairs * PAIR C1: 2,6 COL C C5: 2,6,4,8 # reduction candidate for 2,6 C5: 2,6 # 21 pairs C8: 2,6,4,5 # reduction candidate for 2,6 C8: 2,6 # 19 pairs * PAIR B2: 5,7 COL B B7: 5,7,6,9 # reduction candidate for 5,7 B7: 6,9 => CTR * .8.731954..19846324392658713..1.87.6...5.7193.173.6.851.8472......813..7...659.18 B7: 5,7 # 17 pairs * PAIR D1: 3,7 BLK 2 E1: 3,7,1 # reduction candidate for 3,7 E1: 1 => CTR * .8.317954..19846324392658713..1.87.6...57619..17......1..4.2......8.3..7....5.... E1: 3,7 # 15 pairs * PAIR F1: 1,7 BLK 2 E1: 1,7,3 # reduction candidate for 1,7 E1: 1,7 => CTR * .8.3.19547519846324392658713951.87.6...5.719..176.9...17.492......8.3..7...756.1. E1: 3 # 13 pairs * PAIR F1: 1,7 COL F F9: 1,7,6,9 # reduction candidate for 1,7 F9: 1,7 => CTR * 2867319547519846324392658713951.87.68..5.61936173.9...1..4.2......813..7...657.1. F9: 6,9 # 15 pairs * PAIR F5: 6,7 COL F F9: 6,7,1,9 # reduction candidate for 6,7 F9: 6,7 => CTR * .8...19545719846324392658713951.87.6...5..19..17..9...1..492...9..813..77.865..19 F9: 1,9 # 9 pairs * PAIR F6: 6,9 ROW 6 A6: 6,9,2,8 # reduction candidate for 6,9 A6: 2,8 => SOLVED * 682731954571984632439265871395148726864527193217396485158472369926813547743659218 A6: 6,9 # 15 pairs * PAIR F6: 6,9 COL F F9: 6,9,1,7 # reduction candidate for 6,9 F9: 1,7 => CTR * 2867319547519846324392658713951.87.68..5.61936173.9...1..4.2......813..7...657.1. F9: 6,9 # 15 pairs * PAIR H4: 2,4 BLK 6 G6: 2,4,3,5 # reduction candidate for 2,4 G6: 2,4 # 17 pairs H6: 2,4,8 # reduction candidate for 2,4 H6: 2,4 # 23 pairs * PAIR H4: 2,4 ROW 4 B4: 2,4,5,9 # reduction candidate for 2,4 B4: 2,4 # 12 pairs C4: 2,4,5 # reduction candidate for 2,4 C4: 2,4 => CTR * .8.73195457198463243926587135.1987.6...5.71939173.6...16.472.8..9.813..7...659.1. C4: 5 # 16 pairs E4: 2,4,9 # reduction candidate for 2,4 E4: 2,4 # 21 pairs * PAIR H4: 2,4 COL H H8: 2,4,1,6 # reduction candidate for 2,4 H8: 2,4 # 20 pairs H9: 2,4,1,8 # reduction candidate for 2,4 H9: 2,4 => CTR * .8..17954..19846324392658713..1.87.6...5761936173.....1..4.2......8.3.17....51... H9: 1,8 # 17 pairs * PAIR I5: 3,8 BLK 6 I6: 3,8,5 # reduction candidate for 3,8 I6: 3,8 => CTR * .8...19545719846324392658713951.87.6...5..19..17..95..16.4.23.59..813..7..3.5..19 I6: 5 # 16 pairs * PAIR I5: 3,8 COL I I7: 3,8,5,9 # reduction candidate for 3,8 I7: 3,8 => CTR * .8...19545719846324392658713951.87.6...5..19..17..9..51..4.2...9..813..7....5..19 I7: 5,9 # 17 pairs I9: 3,8,9 # reduction candidate for 3,8 I9: 3,8 # 9 pairs * PAIR E7: 7,9 BLK 8 F9: 7,9,1,6 # reduction candidate for 7,9 F9: 1,6 # 21 pairs F9: 7,9 # 13 pairs * PAIR E7: 7,9 ROW 7 B7: 7,9,5,6 # reduction candidate for 7,9 B7: 7,9 => CTR * .8...19545719846324392658713..1.87.6...5..19..17..9...1..4.2...9..813..7....5..19 B7: 5,6 # 9 pairs * PAIR E8: 1,9 BLK 8 F9: 1,9,6,7 # reduction candidate for 1,9 F9: 6,7 => CTR * .8...19545719846324392658713951.87.6...5..19..17..9...1..492...9..813..77.865..19 F9: 1,9 # 9 pairs * PAIR D9: 6,7 BLK 8 F9: 6,7,1,9 # reduction candidate for 6,7 F9: 6,7 => CTR * .8...19545719846324392658713951.87.6...5..19..17..9...1..492...9..813..77.865..19 F9: 1,9 # 9 pairs * PAIR G7: 3,5 BLK 9 I7: 3,5,8,9 # reduction candidate for 3,5 I7: 3,5 => CTR * .8...19545719846324392658713951.87.6...5..19..17..9...1..4.2...9..813..7....5..19 I7: 8,9 # 17 pairs * PAIR G7: 3,5 ROW 7 C7: 3,5,6,8 # reduction candidate for 3,5 C7: 6,8 # 19 pairs C7: 3,5 # 19 pairs * PAIR G7: 3,5 COL G G6: 3,5,2,4 # reduction candidate for 3,5 G6: 3,5 # 23 pairs G6: 2,4 # 17 pairs * PAIR H7: 6,8 ROW 7 C7: 6,8,3,5 # reduction candidate for 6,8 C7: 6,8 # 19 pairs C7: 3,5 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190406-absurd-base-pr-000.dot * REASONING * DIS # B7: 6,9 => CTR => B7: 5,7 * DIS # E1: 1 => CTR => E1: 3,7 * DIS # E1: 1,7 => CTR => E1: 3 * DIS # F9: 1,7 => CTR => F9: 6,9 * DIS # F9: 6,7 => CTR => F9: 1,9 * PRF # A6: 2,8 => SOL * DIS # F9: 1,7 => CTR => F9: 6,9 * DIS # C4: 2,4 => CTR => C4: 5 * DIS # H9: 2,4 => CTR => H9: 1,8 * DIS # I6: 3,8 => CTR => I6: 5 * DIS # I7: 3,8 => CTR => I7: 5,9 * DIS # B7: 7,9 => CTR => B7: 5,6 * DIS # F9: 6,7 => CTR => F9: 1,9 * DIS # F9: 6,7 => CTR => F9: 1,9 * DIS # I7: 3,5 => CTR => I7: 8,9 * CNT 15 HDP CHAINS / 49 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,B2,C1,D1,D6,D9,E7,E8,F1,F5,F6,G7,H4,H7,I5) * .8....954..19846324392658713..1.87.6...5..19..17......1..4.2......8.3..7....5.... * PAIR A1: 2,6 COL A A5: 2,6,8 # reduction candidate for 2,6 A5: 2,6 # 19 pairs A6: 2,6,8,9 # reduction candidate for 2,6 A6: 2,6 # 24 pairs A8: 2,6,5,9 # reduction candidate for 2,6 A8: 2,6 # 12 pairs * PAIR C1: 2,6 COL C C5: 2,6,4,8 # reduction candidate for 2,6 C5: 2,6 # 21 pairs C8: 2,6,4,5 # reduction candidate for 2,6 C8: 2,6 # 19 pairs * PAIR B2: 5,7 COL B B7: 5,7,6,9 # reduction candidate for 5,7 B7: 6,9 => CTR * .8.731954..19846324392658713..1.87.6...5.7193.173.6.851.8472......813..7...659.18 * PAIR RESTART * PAIR D1: 3,7 BLK 2 E1: 3,7,1 # reduction candidate for 3,7 E1: 1 => CTR * .8.317954..19846324392658713.51.87.6...57619..17......1..4.2......8.3..7....5.... * PAIR F5: 6,7 COL F F9: 6,7,9 # reduction candidate for 6,7 F9: 6,7 => CTR * .8...1954..19846324392658713.51.87.6...5..19..17..9...1..492...9..8135.7....5..19 * PAIR RESTART * PAIR H4: 2,4 ROW 4 B4: 2,4,9 # reduction candidate for 2,4 B4: 2,4 # 12 pairs E4: 2,4,9 # reduction candidate for 2,4 E4: 2,4 => SOLVED * 682731954571984632439265871395148726864527193217396485158472369926813547743659218 * DURATION: 0:00:09.391068 START: 05:07:26.972125 END: 05:07:36.363193 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190406-absurd-base-pr-001.dot * REASONING * DIS # B7: 6,9 => CTR => B7: 5,7 * DIS B7: 5,7 # E1: 1 => CTR => E1: 3,7 * DIS B7: 5,7 + E1: 3,7 # F9: 6,7 => CTR => F9: 9 * PRF B7: 5,7 + E1: 3,7 + F9: 9 # E4: 2,4 => SOL * STA B7: 5,7 + E1: 3,7 + F9: 9 + E4: 2,4 * CNT 4 HDP CHAINS / 12 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190406, absurd
Solution
position: 682731954571984632439265871395148726864527193217396485158472369926813547743659218 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 # A5: 2,6 => UNS * INC # A6: 2,6 => UNS * INC # A8: 2,6 => UNS * INC # C5: 2,6 => UNS * INC # C8: 2,6 => UNS * INC # B7: 5,7 => UNS * DIS # B7: 6,9 => CTR => B7: 5,7 * INC # E1: 3,7 => UNS * DIS # E1: 1 => CTR => E1: 3,7 * DIS # E1: 1,7 => CTR => E1: 3 * INC # E1: 3 => UNS * DIS # F9: 1,7 => CTR => F9: 6,9 * INC # F9: 6,9 => UNS * DIS # F9: 6,7 => CTR => F9: 1,9 * INC # F9: 1,9 => UNS * INC # A6: 6,9 => UNS * PRF # A6: 2,8 => SOL * INC # F9: 6,9 => UNS * DIS # F9: 1,7 => CTR => F9: 6,9 * INC # G6: 2,4 => UNS * INC # H6: 2,4 => UNS * INC # B4: 2,4 => UNS * DIS # C4: 2,4 => CTR => C4: 5 * INC # C4: 5 => UNS * INC # E4: 2,4 => UNS * INC # H8: 2,4 => UNS * DIS # H9: 2,4 => CTR => H9: 1,8 * INC # H9: 1,8 => UNS * DIS # I6: 3,8 => CTR => I6: 5 * INC # I6: 5 => UNS * DIS # I7: 3,8 => CTR => I7: 5,9 * INC # I7: 5,9 => UNS * INC # I9: 3,8 => UNS * INC # F9: 7,9 => UNS * INC # F9: 1,6 => UNS * DIS # B7: 7,9 => CTR => B7: 5,6 * INC # B7: 5,6 => UNS * INC # F9: 1,9 => UNS * DIS # F9: 6,7 => CTR => F9: 1,9 * DIS # F9: 6,7 => CTR => F9: 1,9 * INC # F9: 1,9 => UNS * DIS # I7: 3,5 => CTR => I7: 8,9 * INC # I7: 8,9 => UNS * INC # C7: 3,5 => UNS * INC # C7: 6,8 => UNS * INC # G6: 3,5 => UNS * INC # G6: 2,4 => UNS * INC # C7: 6,8 => UNS * INC # C7: 3,5 => UNS * CNT 49 HDP CHAINS / 49 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A5: 2,6 => UNS * INC # A6: 2,6 => UNS * INC # A8: 2,6 => UNS * INC # C5: 2,6 => UNS * INC # C8: 2,6 => UNS * INC # B7: 5,7 => UNS * DIS # B7: 6,9 => CTR => B7: 5,7 * INC B7: 5,7 # E1: 3,7 => UNS * DIS B7: 5,7 # E1: 1 => CTR => E1: 3,7 * DIS B7: 5,7 + E1: 3,7 # F9: 6,7 => CTR => F9: 9 * INC B7: 5,7 + E1: 3,7 + F9: 9 # B4: 2,4 => UNS * PRF B7: 5,7 + E1: 3,7 + F9: 9 # E4: 2,4 => SOL * STA B7: 5,7 + E1: 3,7 + F9: 9 + E4: 2,4 * CNT 12 HDP CHAINS / 12 HYP OPENED