Analysis of zz-www.sudokuoftheday.co.uk-20190322-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019
level: medium
position: 9.8....32...2.5.87.2..8.....3...17..8.1.67.....6.....43.5....16.8.6...2....5..... initial
Autosolve
position: 9.81...32...2.5.87.2..8..41.3...17688.1.672.3..6...1.43.5....16.8.6...25...5...79 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E2: 9 => CTR => E2: 3,4 * DIS # B1: 5,6 => CTR => B1: 4,7 * DIS # G3: 9 => CTR => G3: 5,6 * DIS # B1: 5,6 => CTR => B1: 4,7 * DIS # B1: 4,6 => CTR => B1: 5,7 * DIS # G3: 5 => CTR => G3: 6,9 * DIS # G3: 9 => CTR => G3: 5,6 * DIS # B1: 5,6 => CTR => B1: 4,7 * DIS # G3: 5 => CTR => G3: 6,9 * DIS # C4: 2 => CTR => C4: 4,9 * DIS # E6: 3 => CTR => E6: 2,5 * DIS # A4: 4 => CTR => A4: 2,5 * DIS # B5: 5 => CTR => B5: 4,9 * DIS # F6: 2 => CTR => F6: 3,8 * DIS # B5: 5,9 => CTR => B5: 4 * DIS # B6: 7 => CTR => B6: 5,9 * DIS # C4: 2,4 => CTR => C4: 9 * DIS # G9: 3 => CTR => G9: 4,8 * DIS # F7: 4,8 => CTR => F7: 2,9 * DIS # G9: 3,4 => CTR => G9: 8 * DIS # E8: 3,4 => CTR => E8: 1,7,9 * CNT 21 HDP CHAINS / 47 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E2: 9 => CTR => E2: 3,4 * DIS E2: 3,4 # C4: 2 => CTR => C4: 4,9 * DIS E2: 3,4 + C4: 4,9 # B5: 5 => CTR => B5: 4,9 * DIS E2: 3,4 + C4: 4,9 + B5: 4,9 # F7: 4,8 => CTR => F7: 2 * PRF E2: 3,4 + C4: 4,9 + B5: 4,9 + F7: 2 => SOL * STA E2: 3,4 + C4: 4,9 + B5: 4,9 + F7: 2 * CNT 5 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 9.8....32...2.5.87.2..8.....3...17..8.1.67.....6.....43.5....16.8.6...2....5..... | initial |
| 9.81...32...2.5.87.2..8..41.3...17688.1.672.3..6...1.43.5....16.8.6...25...5...79 | autosolve |
| 978146532614235987523789641239451768841967253756328194395872416187694325462513879 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) C2: 3,4 A3: 5,6 C3: 3,7 E1: 4,7 F1: 4,6 D3: 3,7 F3: 6,9 G1: 5,6 G2: 6,9 D4: 4,9 E4: 2,5 D5: 4,9 D6: 3,8 H5: 5,9 H6: 5,9 C9: 2,4 D7: 7,8 G7: 4,8 G8: 3,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,B2: 1.. / A2 = 1 => 0 pairs (X) / B2 = 1 => 21 pairs (_) E8,E9: 1.. / E8 = 1 => 25 pairs (_) / E9 = 1 => 26 pairs (_) A8,E8: 1.. / A8 = 1 => 26 pairs (_) / E8 = 1 => 25 pairs (_) B2,B9: 1.. / B2 = 1 => 21 pairs (_) / B9 = 1 => 0 pairs (X) A9,C9: 2.. / A9 = 2 => 0 pairs (X) / C9 = 2 => 20 pairs (_) E7,F7: 2.. / E7 = 2 => 0 pairs (X) / F7 = 2 => 21 pairs (_) C4,C9: 2.. / C4 = 2 => 0 pairs (X) / C9 = 2 => 20 pairs (_) F6,F7: 2.. / F6 = 2 => 0 pairs (X) / F7 = 2 => 21 pairs (_) C2,C3: 3.. / C2 = 3 => 0 pairs (X) / C3 = 3 => 0 pairs (_) E2,D3: 3.. / E2 = 3 => 0 pairs (*) / D3 = 3 => 0 pairs (X) G8,G9: 3.. / G8 = 3 => 22 pairs (_) / G9 = 3 => 0 pairs (X) C2,E2: 3.. / C2 = 3 => 0 pairs (X) / E2 = 3 => 0 pairs (_) C3,D3: 3.. / C3 = 3 => 0 pairs (*) / D3 = 3 => 0 pairs (X) D3,D6: 3.. / D3 = 3 => 0 pairs (X) / D6 = 3 => 0 pairs (_) D4,D5: 4.. / D4 = 4 => 21 pairs (_) / D5 = 4 => 0 pairs (X) B5,D5: 4.. / B5 = 4 => 21 pairs (_) / D5 = 4 => 0 pairs (X) B1,A3: 5.. / B1 = 5 => 0 pairs (X) / A3 = 5 => 23 pairs (_) G1,G3: 5.. / G1 = 5 => 23 pairs (_) / G3 = 5 => 0 pairs (X) E4,E6: 5.. / E4 = 5 => 21 pairs (_) / E6 = 5 => 0 pairs (X) H5,H6: 5.. / H5 = 5 => 19 pairs (_) / H6 = 5 => 0 pairs (X) B1,G1: 5.. / B1 = 5 => 0 pairs (X) / G1 = 5 => 23 pairs (_) A3,G3: 5.. / A3 = 5 => 23 pairs (_) / G3 = 5 => 0 pairs (X) A4,E4: 5.. / A4 = 5 => 0 pairs (X) / E4 = 5 => 21 pairs (_) B5,H5: 5.. / B5 = 5 => 0 pairs (X) / H5 = 5 => 19 pairs (_) F1,F3: 6.. / F1 = 6 => 26 pairs (_) / F3 = 6 => 0 pairs (X) A9,B9: 6.. / A9 = 6 => 24 pairs (_) / B9 = 6 => 20 pairs (_) B1,C3: 7.. / B1 = 7 => 0 pairs (*) / C3 = 7 => 0 pairs (X) E1,D3: 7.. / E1 = 7 => 0 pairs (X) / D3 = 7 => 0 pairs (_) A6,B6: 7.. / A6 = 7 => 23 pairs (_) / B6 = 7 => 0 pairs (X) B1,E1: 7.. / B1 = 7 => 0 pairs (*) / E1 = 7 => 0 pairs (X) C3,D3: 7.. / C3 = 7 => 0 pairs (X) / D3 = 7 => 0 pairs (_) A6,A8: 7.. / A6 = 7 => 23 pairs (_) / A8 = 7 => 0 pairs (X) C3,C8: 7.. / C3 = 7 => 0 pairs (X) / C8 = 7 => 0 pairs (_) D3,D7: 7.. / D3 = 7 => 0 pairs (*) / D7 = 7 => 0 pairs (X) D6,F6: 8.. / D6 = 8 => 0 pairs (X) / F6 = 8 => 0 pairs (_) G7,G9: 8.. / G7 = 8 => 0 pairs (X) / G9 = 8 => 22 pairs (_) F9,G9: 8.. / F9 = 8 => 0 pairs (X) / G9 = 8 => 22 pairs (_) D6,D7: 8.. / D6 = 8 => 0 pairs (X) / D7 = 8 => 0 pairs (_) E2,F3: 9.. / E2 = 9 => 0 pairs (X) / F3 = 9 => 26 pairs (_) G2,G3: 9.. / G2 = 9 => 26 pairs (_) / G3 = 9 => 0 pairs (X) D4,D5: 9.. / D4 = 9 => 0 pairs (X) / D5 = 9 => 21 pairs (_) H5,H6: 9.. / H5 = 9 => 0 pairs (X) / H6 = 9 => 19 pairs (_) B7,C8: 9.. / B7 = 9 => 21 pairs (_) / C8 = 9 => 0 pairs (X) E2,G2: 9.. / E2 = 9 => 0 pairs (X) / G2 = 9 => 26 pairs (_) F3,G3: 9.. / F3 = 9 => 26 pairs (_) / G3 = 9 => 0 pairs (X) C4,D4: 9.. / C4 = 9 => 21 pairs (_) / D4 = 9 => 0 pairs (X) B6,H6: 9.. / B6 = 9 => 0 pairs (X) / H6 = 9 => 19 pairs (_) C4,C8: 9.. / C4 = 9 => 21 pairs (_) / C8 = 9 => 0 pairs (X) * DURATION: 0:00:58.034000 START: 04:42:28.895077 END: 04:43:26.929077 2019-05-01 * CP COUNT: (48) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,C2,C3,C9,D3,D4,D5,D6,D7,E1,E4,F1,F3,G1,G2,G7,G8,H5,H6) * 9.81...32...2.5.87.2..8..41.3...17688.1.672.3..6...1.43.5....16.8.6...25...5...79 * PAIR C2: 3,4 ROW 2 E2: 3,4,9 # reduction candidate for 3,4 E2: 9 => CTR * 968174532143295687527386941439..17688.1.672.3..68..1.43.57...1678.61..256125...79 E2: 3,4 # 26 pairs * PAIR A3: 5,6 BLK 1 B1: 5,6,4,7 # reduction candidate for 5,6 B1: 5,6 => CTR * 9.8174532..3295687527386941.3..517688.1.672.327683.1.43.57...1678.61..25...5...79 B1: 4,7 # 26 pairs * PAIR A3: 5,6 ROW 3 G3: 5,6,9 # reduction candidate for 5,6 G3: 9 => CTR * 968174532...29568752738694123..517688.1.672.37.68..1.4375....16.8.6...256.25...79 G3: 5,6 # 26 pairs * PAIR E1: 4,7 ROW 1 B1: 4,7,5,6 # reduction candidate for 4,7 B1: 5,6 => CTR * 9.8174532..3295687527386941.3..517688.1.672.327683.1.43.57...1678.61..25...5...79 B1: 4,7 # 26 pairs * PAIR E1: 4,7 COL E E7: 4,7,2,9 # reduction candidate for 4,7 E7: 4,7 # 25 pairs E8: 4,7,1,3,9 # reduction candidate for 4,7 E8: 4,7 # 31 pairs * PAIR F1: 4,6 ROW 1 B1: 4,6,5,7 # reduction candidate for 4,6 B1: 4,6 => CTR * 9.817.532..32.5.8752738..41.3..517688.1.672.327683.1.43.57...1678.61..25...5...79 B1: 5,7 # 23 pairs * PAIR F3: 6,9 ROW 3 G3: 6,9,5 # reduction candidate for 6,9 G3: 5 => CTR * 95817..32...2.5987.2..89541.3...17688.1.672.3..6...1.43.5....16.8.6...25...5...79 G3: 6,9 # 23 pairs * PAIR G1: 5,6 BLK 3 G3: 5,6,9 # reduction candidate for 5,6 G3: 9 => CTR * 968174532...29568752738694123..517688.1.672.37.68..1.4375....16.8.6...256.25...79 G3: 5,6 # 26 pairs * PAIR G1: 5,6 ROW 1 B1: 5,6,4,7 # reduction candidate for 5,6 B1: 5,6 => CTR * 9.8174532..3295687527386941.3..517688.1.672.327683.1.43.57...1678.61..25...5...79 B1: 4,7 # 26 pairs * PAIR G2: 6,9 BLK 3 G3: 6,9,5 # reduction candidate for 6,9 G3: 5 => CTR * 95817..32...2.5987.2..89541.3...17688.1.672.3..6...1.43.5....16.8.6...25...5...79 G3: 6,9 # 23 pairs * PAIR D4: 4,9 ROW 4 C4: 4,9,2 # reduction candidate for 4,9 C4: 2 => CTR * 9.81...32.132.5.87.2738..414329517688.14672.3..68..1.4375....16.896...2526451..79 C4: 4,9 # 20 pairs * PAIR E4: 2,5 BLK 5 E6: 2,5,3 # reduction candidate for 2,5 E6: 3 => CTR * 9.8174.32..3295687.27386941.3..517688.1.672.35.68321.43.572..1678.61..25...54..79 E6: 2,5 # 21 pairs * PAIR E4: 2,5 ROW 4 A4: 2,5,4 # reduction candidate for 2,5 A4: 4 => CTR * 9.81...32...2.5.87.2738..414329517688.14672.3..68..1.43.57...1678961..252..5...79 A4: 2,5 # 20 pairs * PAIR D5: 4,9 ROW 5 B5: 4,9,5 # reduction candidate for 4,9 B5: 5 => CTR * 9.81..532...2.5.8752738..41.3.9517688514672937968..154375....16.896...25...5...79 B5: 4,9 # 19 pairs * PAIR D6: 3,8 BLK 5 F6: 3,8,2 # reduction candidate for 3,8 F6: 2 => CTR * 9.8174.32..3295687.27386941.3..517688.1.672535768321943.572..1678.61..25...54..79 F6: 3,8 # 21 pairs * PAIR H5: 5,9 ROW 5 B5: 5,9,4 # reduction candidate for 5,9 B5: 5,9 => CTR * 9.8174.32413295687.27386941.349.1768891467253.768..194345729816789613425..25.8.79 B5: 4 # 21 pairs * PAIR H6: 5,9 ROW 6 B6: 5,9,7 # reduction candidate for 5,9 B6: 7 => CTR * 958174632..3295.87.2738..41.3...17688.1.67253.768..1943.57...1678.61..25...5...79 B6: 5,9 # 23 pairs * PAIR C9: 2,4 BLK 7 A9: 2,4,1,6 # reduction candidate for 2,4 A9: 2,4 # 26 pairs A9: 1,6 # 21 pairs * PAIR C9: 2,4 COL C C4: 2,4,9 # reduction candidate for 2,4 C4: 2,4 => CTR * 9.8174.32413295687.27386941.349.1768891467253.768..194345729816789613425..25.8.79 C4: 9 # 21 pairs * PAIR G7: 4,8 BLK 9 G9: 4,8,3 # reduction candidate for 4,8 G9: 3 => CTR * 9.8174.32..3295687.27386941.349.1768891467253.768321943457..816789613425...548379 G9: 4,8 # 22 pairs * PAIR G7: 4,8 ROW 7 F7: 4,8,2,9 # reduction candidate for 4,8 F7: 4,8 => CTR * 958174632..32.5.87.2738..41.39451768841967253.7683219439572..16784619325..2543879 F7: 2,9 # 20 pairs * PAIR G8: 3,4 BLK 9 G9: 3,4,8 # reduction candidate for 3,4 G9: 3,4 => CTR * 958174632..3295.87.2738..41.3...17688.1.67253.768..1943.57..81678.61..25...5.8.79 G9: 8 # 22 pairs * PAIR G8: 3,4 ROW 8 E8: 3,4,1,7,9 # reduction candidate for 3,4 E8: 3,4 => CTR * 978146.32...2.5.87.2..8..41.3...17688.1.672.3..6...1.43.5....161876.9.25...51..79 E8: 1,7,9 # 19 pairs F8: 3,4,9 # reduction candidate for 3,4 F8: 3,4 # 22 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190322-absurd-base-pr-000.dot * REASONING * DIS # E2: 9 => CTR => E2: 3,4 * DIS # B1: 5,6 => CTR => B1: 4,7 * DIS # G3: 9 => CTR => G3: 5,6 * DIS # B1: 5,6 => CTR => B1: 4,7 * DIS # B1: 4,6 => CTR => B1: 5,7 * DIS # G3: 5 => CTR => G3: 6,9 * DIS # G3: 9 => CTR => G3: 5,6 * DIS # B1: 5,6 => CTR => B1: 4,7 * DIS # G3: 5 => CTR => G3: 6,9 * DIS # C4: 2 => CTR => C4: 4,9 * DIS # E6: 3 => CTR => E6: 2,5 * DIS # A4: 4 => CTR => A4: 2,5 * DIS # B5: 5 => CTR => B5: 4,9 * DIS # F6: 2 => CTR => F6: 3,8 * DIS # B5: 5,9 => CTR => B5: 4 * DIS # B6: 7 => CTR => B6: 5,9 * DIS # C4: 2,4 => CTR => C4: 9 * DIS # G9: 3 => CTR => G9: 4,8 * DIS # F7: 4,8 => CTR => F7: 2,9 * DIS # G9: 3,4 => CTR => G9: 8 * DIS # E8: 3,4 => CTR => E8: 1,7,9 * CNT 21 HDP CHAINS / 47 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,C2,C3,C9,D3,D4,D5,D6,D7,E1,E4,F1,F3,G1,G2,G7,G8,H5,H6) * 9.81...32...2.5.87.2..8..41.3...17688.1.672.3..6...1.43.5....16.8.6...25...5...79 * PAIR C2: 3,4 ROW 2 E2: 3,4,9 # reduction candidate for 3,4 E2: 9 => CTR * 968174532143295687527386941439..17688.1.672.3..68..1.43.57...1678.61..256125...79 * PAIR RESTART * PAIR D4: 4,9 ROW 4 C4: 4,9,2 # reduction candidate for 4,9 C4: 2 => CTR * 9.81.653261.2.598752..89641.329517688.14672.37.6...1.43.5....1618967..2526451..79 * PAIR RESTART * PAIR D5: 4,9 ROW 5 B5: 4,9,5 # reduction candidate for 4,9 B5: 5 => CTR * 948176532613245987527389641234951768851467293796832154375....1618.6...2546251..79 * PAIR RESTART * PAIR G7: 4,8 ROW 7 F7: 4,8,2 # reduction candidate for 4,8 F7: 4,8 => CTR * 9.817653261.245987527.8964123..517688.1.67253756..21943.5.2..1618.69..2546251..79 F7: 2 => SOLVED * 978146532614235987523789641239451768841967253756328194395872416187694325462513879 * DURATION: 0:00:08.270892 START: 04:43:57.141558 END: 04:44:05.412450 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190322-absurd-base-pr-001.dot * REASONING * DIS # E2: 9 => CTR => E2: 3,4 * DIS E2: 3,4 # C4: 2 => CTR => C4: 4,9 * DIS E2: 3,4 + C4: 4,9 # B5: 5 => CTR => B5: 4,9 * DIS E2: 3,4 + C4: 4,9 + B5: 4,9 # F7: 4,8 => CTR => F7: 2 * PRF E2: 3,4 + C4: 4,9 + B5: 4,9 + F7: 2 => SOL * STA E2: 3,4 + C4: 4,9 + B5: 4,9 + F7: 2 * CNT 5 HDP CHAINS / 7 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190322, absurd
Solution
position: 978146532614235987523789641239451768841967253756328194395872416187694325462513879 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 # E2: 3,4 => UNS * DIS # E2: 9 => CTR => E2: 3,4 * DIS # B1: 5,6 => CTR => B1: 4,7 * INC # B1: 4,7 => UNS * INC # G3: 5,6 => UNS * DIS # G3: 9 => CTR => G3: 5,6 * INC # B1: 4,7 => UNS * DIS # B1: 5,6 => CTR => B1: 4,7 * INC # E7: 4,7 => UNS * INC # E8: 4,7 => UNS * DIS # B1: 4,6 => CTR => B1: 5,7 * INC # B1: 5,7 => UNS * INC # G3: 6,9 => UNS * DIS # G3: 5 => CTR => G3: 6,9 * INC # G3: 5,6 => UNS * DIS # G3: 9 => CTR => G3: 5,6 * DIS # B1: 5,6 => CTR => B1: 4,7 * INC # B1: 4,7 => UNS * INC # G3: 6,9 => UNS * DIS # G3: 5 => CTR => G3: 6,9 * INC # C4: 4,9 => UNS * DIS # C4: 2 => CTR => C4: 4,9 * INC # E6: 2,5 => UNS * DIS # E6: 3 => CTR => E6: 2,5 * INC # A4: 2,5 => UNS * DIS # A4: 4 => CTR => A4: 2,5 * INC # B5: 4,9 => UNS * DIS # B5: 5 => CTR => B5: 4,9 * INC # F6: 3,8 => UNS * DIS # F6: 2 => CTR => F6: 3,8 * DIS # B5: 5,9 => CTR => B5: 4 * INC # B5: 4 => UNS * INC # B6: 5,9 => UNS * DIS # B6: 7 => CTR => B6: 5,9 * INC # A9: 2,4 => UNS * INC # A9: 1,6 => UNS * DIS # C4: 2,4 => CTR => C4: 9 * INC # C4: 9 => UNS * INC # G9: 4,8 => UNS * DIS # G9: 3 => CTR => G9: 4,8 * DIS # F7: 4,8 => CTR => F7: 2,9 * INC # F7: 2,9 => UNS * DIS # G9: 3,4 => CTR => G9: 8 * INC # G9: 8 => UNS * DIS # E8: 3,4 => CTR => E8: 1,7,9 * INC # E8: 1,7,9 => UNS * INC # F8: 3,4 => UNS * CNT 47 HDP CHAINS / 47 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E2: 3,4 => UNS * DIS # E2: 9 => CTR => E2: 3,4 * INC E2: 3,4 # C4: 4,9 => UNS * DIS E2: 3,4 # C4: 2 => CTR => C4: 4,9 * INC E2: 3,4 + C4: 4,9 # B5: 4,9 => UNS * DIS E2: 3,4 + C4: 4,9 # B5: 5 => CTR => B5: 4,9 * DIS E2: 3,4 + C4: 4,9 + B5: 4,9 # F7: 4,8 => CTR => F7: 2 * PRF E2: 3,4 + C4: 4,9 + B5: 4,9 + F7: 2 => SOL * STA E2: 3,4 + C4: 4,9 + B5: 4,9 + F7: 2 * CNT 8 HDP CHAINS / 7 HYP OPENED