Analysis of zz-www.sudokuoftheday.co.uk-20190329-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: .37.......5....7....9.....1.7..852.....3.4....6...738...64.85.7....2......45...29 initial
Autosolve
position: .37.......5....7...49.....1.7..852.....3.4.7..6.2.738...64.85.7....2......45...29 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I2: 2,8 => CTR => I2: 3 * DIS # G1: 6,8 => CTR => G1: 4,9 * DIS # G8: 6,8 => CTR => G8: 1,4 * DIS # A4: 1,3 => CTR => A4: 4,9 * DIS # C8: 1,3 => CTR => C8: 5,8 * DIS # C5: 1,5 => CTR => C5: 2,8 * DIS # C8: 3,8 => CTR => C8: 1,5 * DIS # E5: 1,9 => CTR => E5: 6 * DIS # A6: 1,9 => CTR => A6: 4,5 * DIS # E1: 1,9 => CTR => E1: 4,5,6 * DIS # A4: 1,9 => CTR => A4: 3,4 * DIS # E5: 1,9 => CTR => E5: 6 * DIS # A6: 1,9 => CTR => A6: 4,5 * DIS # A8: 1,8 => CTR => A8: 3,5,7,9 * DIS # C8: 1,8 => CTR => C8: 3,5 * DIS # A9: 1,8 => CTR => A9: 3,7 * DIS # B5: 1,8 => CTR => B5: 2,9 * PRF # H8: 1,3 => SOL * DIS # A7: 1,3 => CTR => A7: 2,9 * DIS # A8: 3,8 => CTR => A8: 1,5,7,9 * DIS # C8: 3,8 => CTR => C8: 1,5 * DIS # I2: 2 => CTR => I2: 3,8 * CNT 22 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:
* DIS # I2: 2,8 => CTR => I2: 3 * DIS I2: 3 # G1: 6,8 => CTR => G1: 4,9 * DIS I2: 3 + G1: 4,9 # C8: 1,3 => CTR => C8: 5 * DIS I2: 3 + G1: 4,9 + C8: 5 # A2: 2,8 => CTR => A2: 1,6 * DIS I2: 3 + G1: 4,9 + C8: 5 + A2: 1,6 # F3: 2,6 => CTR => F3: 3 * PRF I2: 3 + G1: 4,9 + C8: 5 + A2: 1,6 + F3: 3 => SOL * STA I2: 3 + G1: 4,9 + C8: 5 + A2: 1,6 + F3: 3 * CNT 6 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .37.......5....7....9.....1.7..852.....3.4....6...738...64.85.7....2......45...29 | initial |
| .37.......5....7...49.....1.7..852.....3.4.7..6.2.738...64.85.7....2......45...29 | autosolve |
| 137846952658912743249753861473185296892364175561297384926438517715629438384571629 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) I1: 2,8 G3: 6,8 C4: 1,3 C6: 1,5 E6: 1,9 H4: 1,9 I4: 4,6 G5: 1,9 I5: 5,6 I6: 4,5 B9: 1,8 H7: 1,3 I8: 3,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H4,G5: 1.. / H4 = 1 => 0 pairs (X) / G5 = 1 => 26 pairs (_) I1,I2: 2.. / I1 = 2 => 13 pairs (_) / I2 = 2 => 0 pairs (X) A7,B7: 2.. / A7 = 2 => 21 pairs (_) / B7 = 2 => 13 pairs (_) A3,F3: 2.. / A3 = 2 => 15 pairs (_) / F3 = 2 => 25 pairs (_) B5,B7: 2.. / B5 = 2 => 21 pairs (_) / B7 = 2 => 13 pairs (_) C2,C5: 2.. / C2 = 2 => 23 pairs (_) / C5 = 2 => 14 pairs (_) A4,C4: 3.. / A4 = 3 => 0 pairs (X) / C4 = 3 => 12 pairs (_) C4,C8: 3.. / C4 = 3 => 12 pairs (_) / C8 = 3 => 0 pairs (X) I2,I8: 3.. / I2 = 3 => 16 pairs (_) / I8 = 3 => 0 pairs (X) E1,E2: 4.. / E1 = 4 => 22 pairs (_) / E2 = 4 => 13 pairs (_) A4,A6: 4.. / A4 = 4 => 10 pairs (_) / A6 = 4 => 0 pairs (X) I4,I6: 4.. / I4 = 4 => 0 pairs (X) / I6 = 4 => 10 pairs (_) G8,H8: 4.. / G8 = 4 => 15 pairs (_) / H8 = 4 => 0 pairs (X) E2,H2: 4.. / E2 = 4 => 13 pairs (_) / H2 = 4 => 22 pairs (_) A4,I4: 4.. / A4 = 4 => 10 pairs (_) / I4 = 4 => 0 pairs (X) A6,I6: 4.. / A6 = 4 => 0 pairs (X) / I6 = 4 => 10 pairs (_) G1,G8: 4.. / G1 = 4 => 0 pairs (X) / G8 = 4 => 15 pairs (_) E1,E3: 5.. / E1 = 5 => 13 pairs (_) / E3 = 5 => 29 pairs (_) H1,H3: 5.. / H1 = 5 => 29 pairs (_) / H3 = 5 => 13 pairs (_) I5,I6: 5.. / I5 = 5 => 10 pairs (_) / I6 = 5 => 0 pairs (X) A8,C8: 5.. / A8 = 5 => 0 pairs (X) / C8 = 5 => 23 pairs (_) E1,H1: 5.. / E1 = 5 => 13 pairs (_) / H1 = 5 => 29 pairs (_) E3,H3: 5.. / E3 = 5 => 29 pairs (_) / H3 = 5 => 13 pairs (_) D4,E5: 6.. / D4 = 6 => 0 pairs (X) / E5 = 6 => 10 pairs (_) I4,I5: 6.. / I4 = 6 => 10 pairs (_) / I5 = 6 => 0 pairs (X) D4,I4: 6.. / D4 = 6 => 0 pairs (X) / I4 = 6 => 10 pairs (_) E5,I5: 6.. / E5 = 6 => 10 pairs (_) / I5 = 6 => 0 pairs (X) D3,E3: 7.. / D3 = 7 => 22 pairs (_) / E3 = 7 => 14 pairs (_) A8,A9: 7.. / A8 = 7 => 22 pairs (_) / A9 = 7 => 14 pairs (_) D8,E9: 7.. / D8 = 7 => 14 pairs (_) / E9 = 7 => 22 pairs (_) A8,D8: 7.. / A8 = 7 => 22 pairs (_) / D8 = 7 => 14 pairs (_) A9,E9: 7.. / A9 = 7 => 14 pairs (_) / E9 = 7 => 22 pairs (_) D3,D8: 7.. / D3 = 7 => 22 pairs (_) / D8 = 7 => 14 pairs (_) E3,E9: 7.. / E3 = 7 => 14 pairs (_) / E9 = 7 => 22 pairs (_) H4,G5: 9.. / H4 = 9 => 26 pairs (_) / G5 = 9 => 0 pairs (X) A6,E6: 9.. / A6 = 9 => 0 pairs (X) / E6 = 9 => 23 pairs (_) G1,G5: 9.. / G1 = 9 => 26 pairs (_) / G5 = 9 => 0 pairs (X) * DURATION: 0:00:36.466702 START: 04:53:31.218727 END: 04:54:07.685429 2019-05-01 * CP COUNT: (37) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,C4,C6,E6,G3,G5,H4,H7,I1,I4,I5,I6,I8) * .37.......5....7...49.....1.7..852.....3.4.7..6.2.738...64.85.7....2......45...29 * PAIR I1: 2,8 BLK 3 I2: 2,8,3 # reduction candidate for 2,8 I2: 2,8 => CTR * .37.4195.15296374.849752631.73.8529...83.417..6129738...6438517785.29463314576829 I2: 3 # 16 pairs * PAIR I1: 2,8 ROW 1 A1: 2,8,1,6 # reduction candidate for 2,8 A1: 2,8 # 14 pairs A1: 1,6 # 14 pairs * PAIR G3: 6,8 BLK 3 G1: 6,8,4,9 # reduction candidate for 6,8 G1: 6,8 => CTR * .37.59.42.5..4.793.49....51.73985216...364975965217384..6498537591.2.468.845..129 G1: 4,9 # 14 pairs * PAIR G3: 6,8 ROW 3 A3: 6,8,2 # reduction candidate for 6,8 A3: 6,8 # 25 pairs D3: 6,8,7 # reduction candidate for 6,8 D3: 6,8 # 14 pairs * PAIR G3: 6,8 COL G G8: 6,8,1,4 # reduction candidate for 6,8 G8: 6,8 => CTR * .37...4.2.5..4.7.3.49...8.1.73985216...364975965217384..6498537591.2.648.845..129 G8: 1,4 # 14 pairs G9: 6,8,1 # reduction candidate for 6,8 G9: 6,8 # 16 pairs * PAIR C4: 1,3 BLK 4 A4: 1,3,4,9 # reduction candidate for 1,3 A4: 1,3 => CTR * .37.......5....7...49.....1.7.685294...314.7646.297385..64.85.7....2......45...29 A4: 4,9 # 13 pairs * PAIR C4: 1,3 COL C C8: 1,3,5,8 # reduction candidate for 1,3 C8: 1,3 => CTR * .37.5.....58.4.7..249.73.51473.852.68.2364.75.652.7384326498517591726...784531629 C8: 5,8 # 13 pairs * PAIR C6: 1,5 BLK 4 A5: 1,5,2,8,9 # reduction candidate for 1,5 A5: 1,5 # 19 pairs C5: 1,5,2,8 # reduction candidate for 1,5 C5: 1,5 => CTR * .37.....2.52...7.8.49..26.1.73.852...8.3.4.7..6.2.738..264.85175987214637145..829 C5: 2,8 # 14 pairs A6: 1,5,4,9 # reduction candidate for 1,5 A6: 1,5 # 18 pairs * PAIR C6: 1,5 COL C C8: 1,5,3,8 # reduction candidate for 1,5 C8: 3,8 => CTR * .37.5.....5..4.7..249.73.51473.852.6..2364.75.652.7384326498517598721..3714536829 C8: 1,5 # 16 pairs * PAIR E6: 1,9 BLK 5 D4: 1,9,6 # reduction candidate for 1,9 D4: 1,9 # 10 pairs E5: 1,9,6 # reduction candidate for 1,9 E5: 1,9 => CTR * .37.......5....7...49.....1.7.6852.4...314976461297385..6438517....2......45...29 E5: 6 # 10 pairs * PAIR E6: 1,9 ROW 6 A6: 1,9,4,5 # reduction candidate for 1,9 A6: 1,9 => CTR * .37.......5....7...49.7..51473.852.6...364.75.652.738432649851759.72....7.45...29 A6: 4,5 # 23 pairs * PAIR E6: 1,9 COL E E1: 1,9,4,5,6 # reduction candidate for 1,9 E1: 1,9 => CTR * .37...45..5..4.79..4975..61.7..8521....364975.6.217384..64385.7....2..4...457..29 E1: 4,5,6 # 13 pairs E2: 1,9,3,4,6 # reduction candidate for 1,9 E2: 1,9 # 20 pairs E7: 1,9,3 # reduction candidate for 1,9 E7: 1,9 # 14 pairs * PAIR H4: 1,9 ROW 4 A4: 1,9,3,4 # reduction candidate for 1,9 A4: 1,9 => CTR * .37.......5....7...49.....1.736852.4...314976461297385..6438517....2......45...29 A4: 3,4 # 14 pairs D4: 1,9,6 # reduction candidate for 1,9 D4: 1,9 # 10 pairs * PAIR G5: 1,9 ROW 5 A5: 1,9,2,5,8 # reduction candidate for 1,9 A5: 1,9 # 15 pairs B5: 1,9,2,8 # reduction candidate for 1,9 B5: 1,9 # 18 pairs E5: 1,9,6 # reduction candidate for 1,9 E5: 1,9 => CTR * .37.......5....7...49.....1.7.6852.4...314976461297385..6438517....2......45...29 E5: 6 # 10 pairs * PAIR I6: 4,5 ROW 6 A6: 4,5,1,9 # reduction candidate for 4,5 A6: 1,9 => CTR * .37.......5....7...49.7..51473.852.6...364.75.652.738432649851759.72....7.45...29 A6: 4,5 # 23 pairs * PAIR B9: 1,8 BLK 7 A8: 1,8,3,5,7,9 # reduction candidate for 1,8 A8: 1,8 => CTR * .37.......5....7...49.7..51.73.852.....3.4.7..6129738.3.64.85.7..572....7.45...29 A8: 3,5,7,9 # 13 pairs B8: 1,8,9 # reduction candidate for 1,8 B8: 1,8 # 20 pairs C8: 1,8,3,5 # reduction candidate for 1,8 C8: 1,8 => CTR * .37.5.....5..4.7...49.73.51.739852.....3.4.7..6.2.738.32649851759.72....7.45...29 C8: 3,5 # 16 pairs A9: 1,8,3,7 # reduction candidate for 1,8 A9: 1,8 => CTR * .37.......5....7...497..8.1.73.852.....3.4.7..6129738.3.64.85.77.5.2......4573629 A9: 3,7 # 14 pairs * PAIR B9: 1,8 ROW 9 G9: 1,8,6 # reduction candidate for 1,8 G9: 6 # 19 pairs G9: 1,8 # 18 pairs * PAIR B9: 1,8 COL B B5: 1,8,2,9 # reduction candidate for 1,8 B5: 1,8 => CTR * .37.......5....7...49.....1.7.985216...36497596521738412649853759.72...878453..29 B5: 2,9 # 18 pairs * PAIR H7: 1,3 BLK 9 H8: 1,3,4,6 # reduction candidate for 1,3 H8: 1,3 => SOLVED * 137846952658912743249753861473185296892364175561297384926438517715629438384571629 H8: 4,6 # 14 pairs * PAIR H7: 1,3 ROW 7 A7: 1,3,2,9 # reduction candidate for 1,3 A7: 1,3 => CTR * .37.......5....7...49.....1.7.985216...36497596521738412649853759.72...878453..29 A7: 2,9 # 19 pairs E7: 1,3,9 # reduction candidate for 1,3 E7: 1,3 # 22 pairs * PAIR I8: 3,8 ROW 8 A8: 3,8,1,5,7,9 # reduction candidate for 3,8 A8: 3,8 => CTR * .37.5.....5..4.7..249.73.51.73.852....2364175561297384.264185373.5729.187.4536.29 A8: 1,5,7,9 # 13 pairs C8: 3,8,1,5 # reduction candidate for 3,8 C8: 3,8 => CTR * .37.5.....5..4.7..249.73.51473.852.6..2364.75.652.7384326498517598721..3714536829 C8: 1,5 # 16 pairs * PAIR I8: 3,8 COL I I2: 3,8,2 # reduction candidate for 3,8 I2: 2 => CTR * .37...9.8.58...7.2249...6.1.73.8529...23.417..6.2.738.926438517.85.2.463314576829 I2: 3,8 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190329-absurd-base-pr-000.dot * REASONING * DIS # I2: 2,8 => CTR => I2: 3 * DIS # G1: 6,8 => CTR => G1: 4,9 * DIS # G8: 6,8 => CTR => G8: 1,4 * DIS # A4: 1,3 => CTR => A4: 4,9 * DIS # C8: 1,3 => CTR => C8: 5,8 * DIS # C5: 1,5 => CTR => C5: 2,8 * DIS # C8: 3,8 => CTR => C8: 1,5 * DIS # E5: 1,9 => CTR => E5: 6 * DIS # A6: 1,9 => CTR => A6: 4,5 * DIS # E1: 1,9 => CTR => E1: 4,5,6 * DIS # A4: 1,9 => CTR => A4: 3,4 * DIS # E5: 1,9 => CTR => E5: 6 * DIS # A6: 1,9 => CTR => A6: 4,5 * DIS # A8: 1,8 => CTR => A8: 3,5,7,9 * DIS # C8: 1,8 => CTR => C8: 3,5 * DIS # A9: 1,8 => CTR => A9: 3,7 * DIS # B5: 1,8 => CTR => B5: 2,9 * PRF # H8: 1,3 => SOL * DIS # A7: 1,3 => CTR => A7: 2,9 * DIS # A8: 3,8 => CTR => A8: 1,5,7,9 * DIS # C8: 3,8 => CTR => C8: 1,5 * DIS # I2: 2 => CTR => I2: 3,8 * CNT 22 HDP CHAINS / 61 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,C4,C6,E6,G3,G5,H4,H7,I1,I4,I5,I6,I8) * .37.......5....7...49.....1.7..852.....3.4.7..6.2.738...64.85.7....2......45...29 * PAIR I1: 2,8 BLK 3 I2: 2,8,3 # reduction candidate for 2,8 I2: 2,8 => CTR * .37.4195.15296374.849752631.73.8529...83.417..6129738...6438517785.29463314576829 * PAIR G3: 6,8 BLK 3 G1: 6,8,4,9 # reduction candidate for 6,8 G1: 6,8 => CTR * .37.5..42.5..4.793.49....51.73.8521....3.497..6.2.738.216498537.95.2.468.845..129 * PAIR C4: 1,3 COL C C8: 1,3,5 # reduction candidate for 1,3 C8: 1,3 => CTR * .37.....2.5....7.3.49673851473985216.1.3649759652173843.64.85.75..72...87845...29 * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A3,A4,A6,A7,A8,A9,B5,B7,C2,C5,D3,D4,E5,E7,G1,G5,G8,G9,H3,H4,H7,H8,I4,I5,I6) * .37.....2.5....7.3.49...8.1.73.852.....3.4.7..6129738...64.85.7.15.2...8.845...29 * PAIR C2: 2,8 BLK 1 A2: 2,8,1,6 # reduction candidate for 2,8 A2: 2,8 => CTR * 13785...2.5..4.7.3649732851.73.852.....364175561297384..64185.7715.2...838457..29 * PAIR A3: 2,6 ROW 3 F3: 2,6,3 # reduction candidate for 2,6 F3: 2,6 => CTR * .37.....2.5....7.3.49.3.851.73.852.....3.4.7..6129738...6418537.15.2..48.8457.129 F3: 3 => SOLVED * 137846952658912743249753861473185296892364175561297384926438517715629438384571629 * DURATION: 0:00:08.456150 START: 04:54:39.832350 END: 04:54:48.288500 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190329-absurd-base-pr-001.dot * REASONING * DIS # I2: 2,8 => CTR => I2: 3 * DIS I2: 3 # G1: 6,8 => CTR => G1: 4,9 * DIS I2: 3 + G1: 4,9 # C8: 1,3 => CTR => C8: 5 * DIS I2: 3 + G1: 4,9 + C8: 5 # A2: 2,8 => CTR => A2: 1,6 * DIS I2: 3 + G1: 4,9 + C8: 5 + A2: 1,6 # F3: 2,6 => CTR => F3: 3 * PRF I2: 3 + G1: 4,9 + C8: 5 + A2: 1,6 + F3: 3 => SOL * STA I2: 3 + G1: 4,9 + C8: 5 + A2: 1,6 + F3: 3 * CNT 6 HDP CHAINS / 5 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190329, absurd
Solution
position: 137846952658912743249753861473185296892364175561297384926438517715629438384571629 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 # I2: 2,8 => CTR => I2: 3 * INC # I2: 3 => UNS * INC # A1: 2,8 => UNS * INC # A1: 1,6 => UNS * DIS # G1: 6,8 => CTR => G1: 4,9 * INC # G1: 4,9 => UNS * INC # A3: 6,8 => UNS * INC # D3: 6,8 => UNS * DIS # G8: 6,8 => CTR => G8: 1,4 * INC # G8: 1,4 => UNS * INC # G9: 6,8 => UNS * DIS # A4: 1,3 => CTR => A4: 4,9 * INC # A4: 4,9 => UNS * DIS # C8: 1,3 => CTR => C8: 5,8 * INC # C8: 5,8 => UNS * INC # A5: 1,5 => UNS * DIS # C5: 1,5 => CTR => C5: 2,8 * INC # C5: 2,8 => UNS * INC # A6: 1,5 => UNS * INC # C8: 1,5 => UNS * DIS # C8: 3,8 => CTR => C8: 1,5 * INC # D4: 1,9 => UNS * DIS # E5: 1,9 => CTR => E5: 6 * INC # E5: 6 => UNS * DIS # A6: 1,9 => CTR => A6: 4,5 * INC # A6: 4,5 => UNS * DIS # E1: 1,9 => CTR => E1: 4,5,6 * INC # E1: 4,5,6 => UNS * INC # E2: 1,9 => UNS * INC # E7: 1,9 => UNS * DIS # A4: 1,9 => CTR => A4: 3,4 * INC # A4: 3,4 => UNS * INC # D4: 1,9 => UNS * INC # A5: 1,9 => UNS * INC # B5: 1,9 => UNS * DIS # E5: 1,9 => CTR => E5: 6 * INC # E5: 6 => UNS * INC # A6: 4,5 => UNS * DIS # A6: 1,9 => CTR => A6: 4,5 * DIS # A8: 1,8 => CTR => A8: 3,5,7,9 * INC # A8: 3,5,7,9 => UNS * INC # B8: 1,8 => UNS * DIS # C8: 1,8 => CTR => C8: 3,5 * INC # C8: 3,5 => UNS * DIS # A9: 1,8 => CTR => A9: 3,7 * INC # A9: 3,7 => UNS * INC # G9: 1,8 => UNS * INC # G9: 6 => UNS * DIS # B5: 1,8 => CTR => B5: 2,9 * INC # B5: 2,9 => UNS * PRF # H8: 1,3 => SOL * INC # H8: 4,6 => UNS * DIS # A7: 1,3 => CTR => A7: 2,9 * INC # A7: 2,9 => UNS * INC # E7: 1,3 => UNS * DIS # A8: 3,8 => CTR => A8: 1,5,7,9 * INC # A8: 1,5,7,9 => UNS * DIS # C8: 3,8 => CTR => C8: 1,5 * INC # C8: 1,5 => UNS * INC # I2: 3,8 => UNS * DIS # I2: 2 => CTR => I2: 3,8 * CNT 61 HDP CHAINS / 61 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # I2: 2,8 => CTR => I2: 3 * DIS I2: 3 # G1: 6,8 => CTR => G1: 4,9 * DIS I2: 3 + G1: 4,9 # C8: 1,3 => CTR => C8: 5 * DIS I2: 3 + G1: 4,9 + C8: 5 # A2: 2,8 => CTR => A2: 1,6 * DIS I2: 3 + G1: 4,9 + C8: 5 + A2: 1,6 # F3: 2,6 => CTR => F3: 3 * PRF I2: 3 + G1: 4,9 + C8: 5 + A2: 1,6 + F3: 3 => SOL * STA I2: 3 + G1: 4,9 + C8: 5 + A2: 1,6 + F3: 3 * CNT 6 HDP CHAINS / 5 HYP OPENED