Analysis of zz-www.sudokuoftheday.co.uk-20190209-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: ..132.8.9......3.7.6..........1.4.......98....8..6..5.57......2.28.3.7.1....8.... initial
Autosolve
position: .5132.8.98.2.5.3.736.8....5..5174..8...598.7..8.263.54573....82.28.357.1...7825.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D2: 6 => CTR => D2: 4,9 * DIS # B9: 4,9 => CTR => B9: 1 * DIS # H3: 1,4 => CTR => H3: 2 * PRF # H3: 2 => SOL * DIS # H2: 4,6 => CTR => H2: 1 * PRF # H2: 1 => SOL * PRF # H3: 2,4 => SOL * DIS # H3: 1 => CTR => H3: 2,4 * PRF # H4: 3,9 => SOL * DIS # H4: 2 => CTR => H4: 3,9 * DIS # A5: 4,6 => CTR => A5: 1,2 * PRF # A6: 7,9 => SOL * DIS # A6: 1 => CTR => A6: 7,9 * DIS # A6: 1,9 => CTR => A6: 7 * PRF # A6: 7 => SOL * DIS # A9: 4,6 => CTR => A9: 1,9 * DIS # H9: 4,9 => CTR => H9: 3 * DIS # A8: 4,9 => CTR => A8: 6 * CNT 18 HDP CHAINS / 27 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D2: 6 => CTR => D2: 4,9 * DIS D2: 4,9 # B9: 4,9 => CTR => B9: 1 * DIS D2: 4,9 + B9: 1 # H3: 1,4 => CTR => H3: 2 * PRF D2: 4,9 + B9: 1 + H3: 2 => SOL * STA D2: 4,9 + B9: 1 + H3: 2 * CNT 4 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..132.8.9......3.7.6..........1.4.......98....8..6..5.57......2.28.3.7.1....8.... | initial |
| .5132.8.98.2.5.3.736.8....5..5174..8...598.7..8.263.54573....82.28.357.1...7825.. | autosolve |
| 451327869892456317367819425235174698146598273789263154573641982628935741914782536 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) A1: 4,7 B2: 4,9 C3: 7,9 F1: 6,7 E3: 1,4 F3: 7,9 H1: 4,6 G3: 2,4 B4: 3,9 C5: 4,6 C6: 7,9 I5: 3,6 G6: 1,9 C9: 4,6 E7: 1,4 H8: 4,9 I9: 3,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F2,E3: 1.. / F2 = 1 => 0 pairs (X) / E3 = 1 => 0 pairs (_) H2,H3: 1.. / H2 = 1 => 0 pairs (*) / H3 = 1 => 0 pairs (X) G5,G6: 1.. / G5 = 1 => 0 pairs (X) / G6 = 1 => 0 pairs (_) A9,B9: 1.. / A9 = 1 => 0 pairs (X) / B9 = 1 => 22 pairs (_) E7,F7: 1.. / E7 = 1 => 0 pairs (X) / F7 = 1 => 0 pairs (_) F2,H2: 1.. / F2 = 1 => 0 pairs (X) / H2 = 1 => 0 pairs (_) E3,H3: 1.. / E3 = 1 => 0 pairs (*) / H3 = 1 => 0 pairs (X) A6,G6: 1.. / A6 = 1 => 0 pairs (X) / G6 = 1 => 0 pairs (_) B5,B9: 1.. / B5 = 1 => 0 pairs (X) / B9 = 1 => 22 pairs (_) E3,E7: 1.. / E3 = 1 => 0 pairs (*) / E7 = 1 => 0 pairs (X) F2,F7: 1.. / F2 = 1 => 0 pairs (X) / F7 = 1 => 0 pairs (_) G3,H3: 2.. / G3 = 2 => 0 pairs (X) / H3 = 2 => 0 pairs (_) A4,A5: 2.. / A4 = 2 => 0 pairs (*) / A5 = 2 => 0 pairs (X) A5,G5: 2.. / A5 = 2 => 19 pairs (_) / G5 = 2 => 0 pairs (*) H3,H4: 2.. / H3 = 2 => 0 pairs (*) / H4 = 2 => 0 pairs (X) B4,B5: 3.. / B4 = 3 => 20 pairs (_) / B5 = 3 => 0 pairs (X) H4,I5: 3.. / H4 = 3 => 0 pairs (X) / I5 = 3 => 20 pairs (_) H9,I9: 3.. / H9 = 3 => 20 pairs (_) / I9 = 3 => 0 pairs (X) B4,H4: 3.. / B4 = 3 => 20 pairs (_) / H4 = 3 => 0 pairs (X) B5,I5: 3.. / B5 = 3 => 0 pairs (X) / I5 = 3 => 20 pairs (_) H4,H9: 3.. / H4 = 3 => 0 pairs (X) / H9 = 3 => 20 pairs (_) I5,I9: 3.. / I5 = 3 => 20 pairs (_) / I9 = 3 => 0 pairs (X) A1,B2: 4.. / A1 = 4 => 0 pairs (*) / B2 = 4 => 0 pairs (X) D2,E3: 4.. / D2 = 4 => 0 pairs (*) / E3 = 4 => 0 pairs (X) A1,H1: 4.. / A1 = 4 => 0 pairs (*) / H1 = 4 => 0 pairs (X) C5,C9: 4.. / C5 = 4 => 0 pairs (X) / C9 = 4 => 20 pairs (_) E3,E7: 4.. / E3 = 4 => 0 pairs (X) / E7 = 4 => 0 pairs (_) G3,G7: 4.. / G3 = 4 => 0 pairs (*) / G7 = 4 => 0 pairs (X) H1,H2: 6.. / H1 = 6 => 0 pairs (*) / H2 = 6 => 0 pairs (X) G7,I9: 6.. / G7 = 6 => 0 pairs (X) / I9 = 6 => 20 pairs (_) F1,H1: 6.. / F1 = 6 => 0 pairs (X) / H1 = 6 => 0 pairs (_) A4,G4: 6.. / A4 = 6 => 0 pairs (X) / G4 = 6 => 20 pairs (_) A8,D8: 6.. / A8 = 6 => 20 pairs (_) / D8 = 6 => 0 pairs (X) C5,C9: 6.. / C5 = 6 => 20 pairs (_) / C9 = 6 => 0 pairs (X) I5,I9: 6.. / I5 = 6 => 0 pairs (X) / I9 = 6 => 20 pairs (_) A1,C3: 7.. / A1 = 7 => 0 pairs (X) / C3 = 7 => 0 pairs (_) F1,F3: 7.. / F1 = 7 => 0 pairs (*) / F3 = 7 => 0 pairs (X) A6,C6: 7.. / A6 = 7 => 0 pairs (*) / C6 = 7 => 0 pairs (X) A1,F1: 7.. / A1 = 7 => 0 pairs (X) / F1 = 7 => 0 pairs (_) C3,F3: 7.. / C3 = 7 => 0 pairs (*) / F3 = 7 => 0 pairs (X) A1,A6: 7.. / A1 = 7 => 0 pairs (X) / A6 = 7 => 0 pairs (_) C3,C6: 7.. / C3 = 7 => 0 pairs (*) / C6 = 7 => 0 pairs (X) B2,C3: 9.. / B2 = 9 => 0 pairs (*) / C3 = 9 => 0 pairs (X) C3,F3: 9.. / C3 = 9 => 0 pairs (X) / F3 = 9 => 0 pairs (_) C3,C6: 9.. / C3 = 9 => 0 pairs (X) / C6 = 9 => 0 pairs (_) * DURATION: 0:00:59.263942 START: 03:35:58.544307 END: 03:36:57.808249 2019-05-01 * CP COUNT: (45) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B2,B4,C3,C5,C6,C9,E3,E7,F1,F3,G3,G6,H1,H8,I5,I9) * .5132.8.98.2.5.3.736.8....5..5174..8...598.7..8.263.54573....82.28.357.1...7825.. * PAIR B2: 4,9 ROW 2 D2: 4,9,6 # reduction candidate for 4,9 D2: 6 => CTR * 4513278698926513473678492159.5174.282..598.73.8.263.54573.16482628435791..4782536 D2: 4,9 # 21 pairs * PAIR B2: 4,9 COL B B9: 4,9,1 # reduction candidate for 4,9 B9: 4,9 => CTR * .5132.8.9842.5.3.736984...5.35174..8.16598273.8.263154573....82628.357.1194782536 B9: 1 # 22 pairs * PAIR E3: 1,4 ROW 3 H3: 1,4,2 # reduction candidate for 1,4 H3: 1,4 => CTR * .5132.8.98.2.5.3.736.84.215.35174.282.6598173187263954573.1.482628435791.14782536 H3: 2 => SOLVED * 451327869892456317367819425235174698146598273789263154573641982628935741914782536 * PAIR H1: 4,6 BLK 3 H2: 4,6,1 # reduction candidate for 4,6 H2: 4,6 => CTR * .5132.8.98.2.513.736.84.215.35174.282.6598173187263954573.1.482628435791.14782536 H2: 1 => SOLVED * 451327869892456317367819425235174698146598273789263154573641982628935741914782536 * PAIR G3: 2,4 BLK 3 H3: 2,4,1 # reduction candidate for 2,4 H3: 2,4 => SOLVED * 451327869892456317367819425235174698146598273789263154573641982628935741914782536 H3: 1 => CTR * .5132.8.98.2.513.736.84.215.35174.282.6598173187263954573.1.482628435791.14782536 * PAIR B4: 3,9 ROW 4 H4: 3,9,2 # reduction candidate for 3,9 H4: 3,9 => SOLVED * 451327869892456317367819425235174698146598273789263154573641982628935741914782536 H4: 2 => CTR * .5132.8.98.2.5.3.736.8..2.5.35174.282.6598173187263954573...482628435791.14782536 * PAIR C5: 4,6 BLK 4 A5: 4,6,1,2 # reduction candidate for 4,6 A5: 4,6 => CTR * 45132.8.98.2.5.3.736.8....52.51746.8...598273.8.263154573...982.28935741194782536 A5: 1,2 # 18 pairs * PAIR C6: 7,9 BLK 4 A6: 7,9,1 # reduction candidate for 7,9 A6: 7,9 => SOLVED * 451327869892456317367819425235174698146598273789263154573641982628935741914782536 A6: 1 => CTR * 751326849842951367369847215..5174.282.4598.7318.263.54573....82.28.357.1...7825.. * PAIR G6: 1,9 ROW 6 A6: 1,9,7 # reduction candidate for 1,9 A6: 1,9 => CTR * 751326849842951367369847215..5174.282.4598.73.87263.54573.19482.284357914..7825.. A6: 7 => SOLVED * 451327869892456317367819425235174698146598273789263154573641982628935741914782536 * PAIR C9: 4,6 BLK 7 A8: 4,6,9 # reduction candidate for 4,6 A8: 4,6 # 21 pairs A9: 4,6,1,9 # reduction candidate for 4,6 A9: 4,6 => CTR * 45132.8.98.2.5.3.736.8....5..5174.38.3.598.76.8.263.54573...682928635741.16782593 A9: 1,9 # 18 pairs * PAIR H8: 4,9 BLK 9 G7: 4,9,6 # reduction candidate for 4,9 G7: 4,9 # 20 pairs H9: 4,9,3 # reduction candidate for 4,9 H9: 4,9 => CTR * .5132.8.984295.3.7369847..5..5174.38.3.598.76.8.263.54573...682.286357.1.167825.3 H9: 3 # 20 pairs * PAIR H8: 4,9 ROW 8 A8: 4,9,6 # reduction candidate for 4,9 A8: 4,9 => CTR * .5132.8.98.2.5.3.736.8..4256.5174238234598176187263954573.41682.286357.1.167825.3 A8: 6 # 20 pairs D8: 4,9,6 # reduction candidate for 4,9 D8: 4,9 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190209-absurd-base-pr-000.dot * REASONING * DIS # D2: 6 => CTR => D2: 4,9 * DIS # B9: 4,9 => CTR => B9: 1 * DIS # H3: 1,4 => CTR => H3: 2 * PRF # H3: 2 => SOL * DIS # H2: 4,6 => CTR => H2: 1 * PRF # H2: 1 => SOL * PRF # H3: 2,4 => SOL * DIS # H3: 1 => CTR => H3: 2,4 * PRF # H4: 3,9 => SOL * DIS # H4: 2 => CTR => H4: 3,9 * DIS # A5: 4,6 => CTR => A5: 1,2 * PRF # A6: 7,9 => SOL * DIS # A6: 1 => CTR => A6: 7,9 * DIS # A6: 1,9 => CTR => A6: 7 * PRF # A6: 7 => SOL * DIS # A9: 4,6 => CTR => A9: 1,9 * DIS # H9: 4,9 => CTR => H9: 3 * DIS # A8: 4,9 => CTR => A8: 6 * CNT 18 HDP CHAINS / 27 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B2,B4,C3,C5,C6,C9,E3,E7,F1,F3,G3,G6,H1,H8,I5,I9) * .5132.8.98.2.5.3.736.8....5..5174..8...598.7..8.263.54573....82.28.357.1...7825.. * PAIR B2: 4,9 ROW 2 D2: 4,9,6 # reduction candidate for 4,9 D2: 6 => CTR * 4513278698926513473678492159.5174.282..598.73.8.263.54573.16482628435791..4782536 * PAIR B2: 4,9 COL B B9: 4,9,1 # reduction candidate for 4,9 B9: 4,9 => CTR * .5132.8.984295.3.736984...5.35174..8.16598273.8.2631545736...82628.357.1194782536 * PAIR RESTART * PAIR E3: 1,4 ROW 3 H3: 1,4,2 # reduction candidate for 1,4 H3: 1,4 => CTR * .5132.8.98.2.5.3.736.8..2.5..5174.282..598173187263954573...482.28435791914782536 H3: 2 => SOLVED * 451327869892456317367819425235174698146598273789263154573641982628935741914782536 * DURATION: 0:00:05.550967 START: 03:37:19.227696 END: 03:37:24.778663 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190209-absurd-base-pr-001.dot * REASONING * DIS # D2: 6 => CTR => D2: 4,9 * DIS D2: 4,9 # B9: 4,9 => CTR => B9: 1 * DIS D2: 4,9 + B9: 1 # H3: 1,4 => CTR => H3: 2 * PRF D2: 4,9 + B9: 1 + H3: 2 => SOL * STA D2: 4,9 + B9: 1 + H3: 2 * CNT 4 HDP CHAINS / 4 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190209, absurd
Solution
position: 451327869892456317367819425235174698146598273789263154573641982628935741914782536 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 # D2: 4,9 => UNS * DIS # D2: 6 => CTR => D2: 4,9 * DIS # B9: 4,9 => CTR => B9: 1 * INC # B9: 1 => UNS * DIS # H3: 1,4 => CTR => H3: 2 * PRF # H3: 2 => SOL * DIS # H2: 4,6 => CTR => H2: 1 * PRF # H2: 1 => SOL * PRF # H3: 2,4 => SOL * DIS # H3: 1 => CTR => H3: 2,4 * PRF # H4: 3,9 => SOL * DIS # H4: 2 => CTR => H4: 3,9 * DIS # A5: 4,6 => CTR => A5: 1,2 * INC # A5: 1,2 => UNS * PRF # A6: 7,9 => SOL * DIS # A6: 1 => CTR => A6: 7,9 * DIS # A6: 1,9 => CTR => A6: 7 * PRF # A6: 7 => SOL * INC # A8: 4,6 => UNS * DIS # A9: 4,6 => CTR => A9: 1,9 * INC # A9: 1,9 => UNS * INC # G7: 4,9 => UNS * DIS # H9: 4,9 => CTR => H9: 3 * INC # H9: 3 => UNS * DIS # A8: 4,9 => CTR => A8: 6 * INC # A8: 6 => UNS * INC # D8: 4,9 => UNS * CNT 27 HDP CHAINS / 27 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D2: 4,9 => UNS * DIS # D2: 6 => CTR => D2: 4,9 * DIS D2: 4,9 # B9: 4,9 => CTR => B9: 1 * DIS D2: 4,9 + B9: 1 # H3: 1,4 => CTR => H3: 2 * PRF D2: 4,9 + B9: 1 + H3: 2 => SOL * STA D2: 4,9 + B9: 1 + H3: 2 * CNT 5 HDP CHAINS / 4 HYP OPENED