Analysis of zz-www.sudokuoftheday.co.uk-20190125-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019
level: medium
position: ..........5..8..1...9...43...39......8.6.25..6......87.1.8.9.5.2.5.4.3.....3...6. initial
Autosolve
position: .3..9.8...5..83.1.8.9...43.5.39.8....8.6.25.36...3..8731.8.9.5.2.5.4.3.8..83...6. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 4,7 => CTR => A1: 1 * DIS # C2: 4,7 => CTR => C2: 2,6 * DIS # A5: 4,7 => CTR => A5: 1,9 * DIS # F3: 5,6 => CTR => F3: 1,7 * PRF # I3: 5,6 => SOL * DIS # I3: 2 => CTR => I3: 5,6 * PRF # G2: 2,7 => SOL * DIS # G2: 6,9 => CTR => G2: 2,7 * DIS # G6: 1 => CTR => G6: 2,9 * DIS # G6: 1,2 => CTR => G6: 9 * DIS # A5: 1,7 => CTR => A5: 4,9 * DIS # F1: 4,5 => CTR => F1: 6,7 * DIS # B4: 7 => CTR => B4: 2,4 * DIS # A5: 1,7 => CTR => A5: 4,9 * PRF # F8: 1,7 => SOL * DIS # F8: 6 => CTR => F8: 1,7 * PRF # D3: 2,5 => SOL * DIS # F1: 5,7 => CTR => F1: 4,6 * DIS # F3: 5,7 => CTR => F3: 1,6 * DIS # G9: 2,7 => CTR => G9: 1,9 * PRF # G2: 2,7 => SOL * DIS # G2: 6,9 => CTR => G2: 2,7 * PRF # I9: 2,4 => SOL * DIS # G9: 7,9 => CTR => G9: 1,2 * DIS # B8: 7,9 => CTR => B8: 6 * PRF # B8: 6 => SOL * CNT 26 HDP CHAINS / 54 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 4,7 => CTR => A1: 1 * DIS A1: 1 # C2: 4,7 => CTR => C2: 2,6 * PRF A1: 1 + C2: 2,6 # C1: 2,6 => SOL * STA A1: 1 + C2: 2,6 + C1: 2,6 * CNT 3 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..........5..8..1...9...43...39......8.6.25..6......87.1.8.9.5.2.5.4.3.....3...6. | initial |
| .3..9.8...5..83.1.8.9...43.5.39.8....8.6.25.36...3..8731.8.9.5.2.5.4.3.8..83...6. | autosolve |
| 132496875456783219879251436543978621987612543621534987314869752265147398798325164 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) A2: 4,7 E3: 5,6 H1: 2,7 B6: 2,9 C6: 1,2 E4: 1,7 E5: 1,7 D6: 4,5 F6: 4,5 H4: 2,4 H5: 4,9 E7: 2,6 D8: 1,7 E9: 2,5 F9: 5,7 G7: 2,7 I7: 2,4 H8: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,C1: 1.. / A1 = 1 => 18 pairs (_) / C1 = 1 => 0 pairs (X) D3,F3: 1.. / D3 = 1 => 0 pairs (X) / F3 = 1 => 18 pairs (_) E4,E5: 1.. / E4 = 1 => 0 pairs (X) / E5 = 1 => 21 pairs (_) D8,F8: 1.. / D8 = 1 => 18 pairs (_) / F8 = 1 => 0 pairs (X) G9,I9: 1.. / G9 = 1 => 19 pairs (_) / I9 = 1 => 23 pairs (_) C6,G6: 1.. / C6 = 1 => 21 pairs (_) / G6 = 1 => 0 pairs (X) A1,A5: 1.. / A1 = 1 => 18 pairs (_) / A5 = 1 => 0 pairs (X) D3,D8: 1.. / D3 = 1 => 0 pairs (X) / D8 = 1 => 18 pairs (_) F3,F8: 1.. / F3 = 1 => 18 pairs (_) / F8 = 1 => 0 pairs (X) I4,I9: 1.. / I4 = 1 => 19 pairs (_) / I9 = 1 => 23 pairs (_) E7,E9: 2.. / E7 = 2 => 0 pairs (X) / E9 = 2 => 0 pairs (_) H1,H4: 2.. / H1 = 2 => 0 pairs (X) / H4 = 2 => 17 pairs (_) D6,F6: 4.. / D6 = 4 => 0 pairs (X) / F6 = 4 => 16 pairs (_) H4,H5: 4.. / H4 = 4 => 0 pairs (X) / H5 = 4 => 17 pairs (_) I7,I9: 4.. / I7 = 4 => 18 pairs (_) / I9 = 4 => 0 pairs (*) B4,H4: 4.. / B4 = 4 => 17 pairs (_) / H4 = 4 => 0 pairs (X) C7,I7: 4.. / C7 = 4 => 0 pairs (*) / I7 = 4 => 0 pairs (X) B4,B9: 4.. / B4 = 4 => 17 pairs (_) / B9 = 4 => 0 pairs (X) F1,F6: 4.. / F1 = 4 => 0 pairs (X) / F6 = 4 => 16 pairs (_) I1,I3: 5.. / I1 = 5 => 19 pairs (_) / I3 = 5 => 0 pairs (X) D6,F6: 5.. / D6 = 5 => 16 pairs (_) / F6 = 5 => 0 pairs (X) E9,F9: 5.. / E9 = 5 => 0 pairs (X) / F9 = 5 => 0 pairs (_) E3,E9: 5.. / E3 = 5 => 0 pairs (*) / E9 = 5 => 0 pairs (X) G4,I4: 6.. / G4 = 6 => 19 pairs (_) / I4 = 6 => 0 pairs (X) C7,B8: 6.. / C7 = 6 => 0 pairs (X) / B8 = 6 => 0 pairs (_) E7,F8: 6.. / E7 = 6 => 0 pairs (*) / F8 = 6 => 0 pairs (X) C7,E7: 6.. / C7 = 6 => 0 pairs (X) / E7 = 6 => 0 pairs (_) B8,F8: 6.. / B8 = 6 => 0 pairs (*) / F8 = 6 => 0 pairs (X) B3,B8: 6.. / B3 = 6 => 0 pairs (X) / B8 = 6 => 0 pairs (_) E3,E7: 6.. / E3 = 6 => 0 pairs (X) / E7 = 6 => 0 pairs (_) G2,G4: 6.. / G2 = 6 => 0 pairs (X) / G4 = 6 => 19 pairs (_) H1,G2: 7.. / H1 = 7 => 17 pairs (_) / G2 = 7 => 0 pairs (X) E4,E5: 7.. / E4 = 7 => 21 pairs (_) / E5 = 7 => 0 pairs (X) B4,E4: 7.. / B4 = 7 => 0 pairs (X) / E4 = 7 => 21 pairs (_) C7,G7: 7.. / C7 = 7 => 0 pairs (X) / G7 = 7 => 17 pairs (_) H1,H8: 7.. / H1 = 7 => 17 pairs (_) / H8 = 7 => 0 pairs (X) G2,I2: 9.. / G2 = 9 => 0 pairs (X) / I2 = 9 => 18 pairs (_) A5,B6: 9.. / A5 = 9 => 17 pairs (_) / B6 = 9 => 0 pairs (X) H5,G6: 9.. / H5 = 9 => 0 pairs (X) / G6 = 9 => 17 pairs (_) A5,H5: 9.. / A5 = 9 => 17 pairs (_) / H5 = 9 => 0 pairs (X) B6,G6: 9.. / B6 = 9 => 0 pairs (X) / G6 = 9 => 17 pairs (_) B8,H8: 9.. / B8 = 9 => 0 pairs (X) / H8 = 9 => 17 pairs (_) A5,A9: 9.. / A5 = 9 => 17 pairs (_) / A9 = 9 => 0 pairs (X) H5,H8: 9.. / H5 = 9 => 0 pairs (X) / H8 = 9 => 17 pairs (_) I2,I9: 9.. / I2 = 9 => 18 pairs (_) / I9 = 9 => 0 pairs (X) * DURATION: 0:00:53.213436 START: 03:11:58.455463 END: 03:12:51.668899 2019-05-01 * CP COUNT: (45) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B6,C6,D6,D8,E3,E4,E5,E7,E9,F6,F9,G7,H1,H4,H5,H8,I7) * .3..9.8...5..83.1.8.9...43.5.39.8....8.6.25.36...3..8731.8.9.5.2.5.4.3.8..83...6. * PAIR A2: 4,7 BLK 1 A1: 4,7,1 # reduction candidate for 4,7 A1: 4,7 => CTR * .31.9.8...5..83.1.8.9...43.5.39.8...18.672593692.3.18731.8.9.5.2.5.4.3789.83.726. A1: 1 # 18 pairs C1: 4,7,1,2,6 # reduction candidate for 4,7 C1: 4,7 # 24 pairs C2: 4,7,2,6 # reduction candidate for 4,7 C2: 4,7 => CTR * 13..9.87..542836198.9...43.543978126987612543621.3.987316829754275146398498357261 C2: 2,6 # 19 pairs * PAIR A2: 4,7 ROW 2 D2: 4,7,2 # reduction candidate for 4,7 D2: 2 # 20 pairs D2: 4,7 # 19 pairs * PAIR A2: 4,7 COL A A5: 4,7,1,9 # reduction candidate for 4,7 A5: 4,7 => CTR * 13..9.8...5..83.1.8.9...43.5.39.8....8.6.259369..3..8731.8.9.5.2.5.4.3789.83.7.6. A5: 1,9 # 22 pairs A9: 4,7,9 # reduction candidate for 4,7 A9: 4,7 # 17 pairs * PAIR E3: 5,6 BLK 2 F1: 5,6,4,7 # reduction candidate for 5,6 F1: 5,6 # 18 pairs F3: 5,6,1,7 # reduction candidate for 5,6 F3: 5,6 => CTR * .3..9782..5.2837198.91..43.5.39.8....8.6.25.36...3..8731.8.9.5.2.5741398..83.5.6. F3: 1,7 # 19 pairs * PAIR E3: 5,6 ROW 3 I3: 5,6,2 # reduction candidate for 5,6 I3: 5,6 => SOLVED * 132496875456783219879251436543978621987612543621534987314869752265147398798325164 I3: 2 => CTR * 13..9.875.5..836198.9...432543978126987612543621.3.987316829754275146398498357261 * PAIR H1: 2,7 BLK 3 G2: 2,7,6,9 # reduction candidate for 2,7 G2: 2,7 => SOLVED * 132496875456783219879251436543978621987612543621534987314869752265147398798325164 G2: 6,9 => CTR * 136.9.87..5..836198.9...43.543978126987612543621.3.98731.8297542.5.46398498357261 * PAIR H1: 2,7 ROW 1 C1: 2,7,1,4,6 # reduction candidate for 2,7 C1: 2,7 # 23 pairs D1: 2,7,4,5 # reduction candidate for 2,7 D1: 2,7 # 21 pairs * PAIR B6: 2,9 ROW 6 G6: 2,9,1 # reduction candidate for 2,9 G6: 1 => CTR * .3..9.8...5..83.1.8.9...43.5.39.8....8.6.2593692.3.18731.8.9.5.2.5.4.3789.83.726. G6: 2,9 # 21 pairs * PAIR C6: 1,2 ROW 6 G6: 1,2,9 # reduction candidate for 1,2 G6: 1,2 => CTR * .3..9.8...5..83.1.8.9...43.5.39.8....8.6.259369..3..8731.8.9.5.2.5.4.3789.83.7.6. G6: 9 # 17 pairs * PAIR C6: 1,2 COL C C1: 1,2,4,6,7 # reduction candidate for 1,2 C1: 1,2 # 20 pairs C1: 4,6,7 # 18 pairs * PAIR E5: 1,7 ROW 5 A5: 1,7,4,9 # reduction candidate for 1,7 A5: 1,7 => CTR * .3..9.8...5..83.1.8.9...43.5.39.8....8.6.259369..3..8731.8.9.5.2.5.4.3789.83.7.6. A5: 4,9 # 20 pairs C5: 1,7,4 # reduction candidate for 1,7 C5: 1,7 # 20 pairs * PAIR D6: 4,5 COL D D1: 4,5,2,7 # reduction candidate for 4,5 D1: 4,5 # 21 pairs D1: 2,7 # 21 pairs * PAIR F6: 4,5 COL F F1: 4,5,6,7 # reduction candidate for 4,5 F1: 4,5 => CTR * .3..9.8...5..83.1.8.9...43.5.39.8....8.6.25.36...3..8731.869.5.265.4.398..8325.6. F1: 6,7 # 18 pairs * PAIR H4: 2,4 ROW 4 B4: 2,4,7 # reduction candidate for 2,4 B4: 7 => CTR * .3..9.8...5..83.1.8.9...43.573918.4..8.672593692.3.18731.8.9.5.265.4.3789483.726. B4: 2,4 # 21 pairs * PAIR H5: 4,9 ROW 5 A5: 4,9,1,7 # reduction candidate for 4,9 A5: 1,7 => CTR * .3..9.8...5..83.1.8.9...43.5.39.8....8.6.259369..3..8731.8.9.5.2.5.4.3789.83.7.6. A5: 4,9 # 20 pairs * PAIR D8: 1,7 BLK 8 F8: 1,7,6 # reduction candidate for 1,7 F8: 1,7 => SOLVED * 132496875456783219879251436543978621987612543621534987314869752265147398798325164 F8: 6 => CTR * .3..9.8...5..83.1.8697514325.39.8....8.6.25.36...3..8731.8.9.5.2.51463.8..83.7.6. * PAIR D8: 1,7 COL D D3: 1,7,2,5 # reduction candidate for 1,7 D3: 2,5 => SOLVED * 132496875456783219879251436543978621987612543621534987314869752265147398798325164 D3: 1,7 # 20 pairs * PAIR F9: 5,7 COL F F1: 5,7,4,6 # reduction candidate for 5,7 F1: 5,7 => CTR * .3..97825.5..83.1.8.9...43.5.39.8....8.6.25.36..534.8731.869.5.265.4.398..8325.6. F1: 4,6 # 19 pairs F3: 5,7,1,6 # reduction candidate for 5,7 F3: 5,7 => CTR * .3..9687..5..83.198.915743.5.39.8.2.98.6.254362153498731.869.5.265741398..83.5.6. F3: 1,6 # 19 pairs * PAIR G7: 2,7 BLK 9 G9: 2,7,1,9 # reduction candidate for 2,7 G9: 2,7 => CTR * .3..9.87..5..83.198.9...43.543978126987612543621.3.987316829754275146398498357261 G9: 1,9 # 19 pairs * PAIR G7: 2,7 COL G G2: 2,7,6,9 # reduction candidate for 2,7 G2: 2,7 => SOLVED * 132496875456783219879251436543978621987612543621534987314869752265147398798325164 G2: 6,9 => CTR * 136.9.87..5..836198.9...43.543978126987612543621.3.98731.8297542.5.46398498357261 * PAIR I7: 2,4 BLK 9 I9: 2,4,1,9 # reduction candidate for 2,4 I9: 2,4 => SOLVED * 132496875456783219879251436543978621987612543621534987314869752265147398798325164 I9: 1,9 # 22 pairs * PAIR H8: 7,9 BLK 9 G9: 7,9,1,2 # reduction candidate for 7,9 G9: 7,9 => CTR * .3..9.875.5..836198.9.5643.5.39.8....8.6.25.36..534.8731.869254265.4.398..8325761 G9: 1,2 # 19 pairs * PAIR H8: 7,9 ROW 8 B8: 7,9,6 # reduction candidate for 7,9 B8: 7,9 => CTR * .3..9.8...5..83.1.869.5.4325.39.8.2..8.6.2543621534987316829.5.2.5.4.3.8..83...6. B8: 6 => SOLVED * 132496875456783219879251436543978621987612543621534987314869752265147398798325164 * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190125-absurd-base-pr-000.dot * REASONING * DIS # A1: 4,7 => CTR => A1: 1 * DIS # C2: 4,7 => CTR => C2: 2,6 * DIS # A5: 4,7 => CTR => A5: 1,9 * DIS # F3: 5,6 => CTR => F3: 1,7 * PRF # I3: 5,6 => SOL * DIS # I3: 2 => CTR => I3: 5,6 * PRF # G2: 2,7 => SOL * DIS # G2: 6,9 => CTR => G2: 2,7 * DIS # G6: 1 => CTR => G6: 2,9 * DIS # G6: 1,2 => CTR => G6: 9 * DIS # A5: 1,7 => CTR => A5: 4,9 * DIS # F1: 4,5 => CTR => F1: 6,7 * DIS # B4: 7 => CTR => B4: 2,4 * DIS # A5: 1,7 => CTR => A5: 4,9 * PRF # F8: 1,7 => SOL * DIS # F8: 6 => CTR => F8: 1,7 * PRF # D3: 2,5 => SOL * DIS # F1: 5,7 => CTR => F1: 4,6 * DIS # F3: 5,7 => CTR => F3: 1,6 * DIS # G9: 2,7 => CTR => G9: 1,9 * PRF # G2: 2,7 => SOL * DIS # G2: 6,9 => CTR => G2: 2,7 * PRF # I9: 2,4 => SOL * DIS # G9: 7,9 => CTR => G9: 1,2 * DIS # B8: 7,9 => CTR => B8: 6 * PRF # B8: 6 => SOL * CNT 26 HDP CHAINS / 54 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B6,C6,D6,D8,E3,E4,E5,E7,E9,F6,F9,G7,H1,H4,H5,H8,I7) * .3..9.8...5..83.1.8.9...43.5.39.8....8.6.25.36...3..8731.8.9.5.2.5.4.3.8..83...6. * PAIR A2: 4,7 BLK 1 A1: 4,7,1 # reduction candidate for 4,7 A1: 4,7 => CTR * .31.9.8...5..83.1.8.9...43.5.39.8...18.672593692.3.18731.8.9.5.2.5.4.3789.83.726. C1: 4,7,2,6 # reduction candidate for 4,7 C1: 4,7 # 24 pairs C2: 4,7,2,6 # reduction candidate for 4,7 C2: 4,7 => CTR * 13..9.87..542836198.9...43.543978126987612543621.3.987316829754275146398498357261 * RESTART * PAIR A2: 4,7 BLK 1 C1: 4,7,2,6 # reduction candidate for 4,7 C1: 2,6 => SOLVED * 132496875456783219879251436543978621987612543621534987314869752265147398798325164 * DURATION: 0:00:04.582852 START: 03:13:26.888108 END: 03:13:31.470960 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190125-absurd-base-pr-001.dot * REASONING * DIS # A1: 4,7 => CTR => A1: 1 * DIS A1: 1 # C2: 4,7 => CTR => C2: 2,6 * PRF A1: 1 + C2: 2,6 # C1: 2,6 => SOL * STA A1: 1 + C2: 2,6 + C1: 2,6 * CNT 3 HDP CHAINS / 5 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190125, absurd
Solution
position: 132496875456783219879251436543978621987612543621534987314869752265147398798325164 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 # A1: 4,7 => CTR => A1: 1 * INC # A1: 1 => UNS * INC # C1: 4,7 => UNS * DIS # C2: 4,7 => CTR => C2: 2,6 * INC # C2: 2,6 => UNS * INC # D2: 4,7 => UNS * INC # D2: 2 => UNS * DIS # A5: 4,7 => CTR => A5: 1,9 * INC # A5: 1,9 => UNS * INC # A9: 4,7 => UNS * INC # F1: 5,6 => UNS * DIS # F3: 5,6 => CTR => F3: 1,7 * INC # F3: 1,7 => UNS * PRF # I3: 5,6 => SOL * DIS # I3: 2 => CTR => I3: 5,6 * PRF # G2: 2,7 => SOL * DIS # G2: 6,9 => CTR => G2: 2,7 * INC # C1: 2,7 => UNS * INC # D1: 2,7 => UNS * INC # G6: 2,9 => UNS * DIS # G6: 1 => CTR => G6: 2,9 * DIS # G6: 1,2 => CTR => G6: 9 * INC # G6: 9 => UNS * INC # C1: 1,2 => UNS * INC # C1: 4,6,7 => UNS * DIS # A5: 1,7 => CTR => A5: 4,9 * INC # A5: 4,9 => UNS * INC # C5: 1,7 => UNS * INC # D1: 4,5 => UNS * INC # D1: 2,7 => UNS * DIS # F1: 4,5 => CTR => F1: 6,7 * INC # F1: 6,7 => UNS * INC # B4: 2,4 => UNS * DIS # B4: 7 => CTR => B4: 2,4 * INC # A5: 4,9 => UNS * DIS # A5: 1,7 => CTR => A5: 4,9 * PRF # F8: 1,7 => SOL * DIS # F8: 6 => CTR => F8: 1,7 * INC # D3: 1,7 => UNS * PRF # D3: 2,5 => SOL * DIS # F1: 5,7 => CTR => F1: 4,6 * INC # F1: 4,6 => UNS * DIS # F3: 5,7 => CTR => F3: 1,6 * INC # F3: 1,6 => UNS * DIS # G9: 2,7 => CTR => G9: 1,9 * INC # G9: 1,9 => UNS * PRF # G2: 2,7 => SOL * DIS # G2: 6,9 => CTR => G2: 2,7 * PRF # I9: 2,4 => SOL * INC # I9: 1,9 => UNS * DIS # G9: 7,9 => CTR => G9: 1,2 * INC # G9: 1,2 => UNS * DIS # B8: 7,9 => CTR => B8: 6 * PRF # B8: 6 => SOL * CNT 54 HDP CHAINS / 54 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 4,7 => CTR => A1: 1 * INC A1: 1 # C1: 4,7 => UNS * DIS A1: 1 # C2: 4,7 => CTR => C2: 2,6 * INC A1: 1 + C2: 2,6 # C1: 4,7 => UNS * PRF A1: 1 + C2: 2,6 # C1: 2,6 => SOL * STA A1: 1 + C2: 2,6 + C1: 2,6 * CNT 5 HDP CHAINS / 5 HYP OPENED