Analysis of zz-www.sudokuoftheday.co.uk-20190422-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: ..84..7..7......2..5..18.6.4.2....3....93......1..2....6..8917.......6......7...8 initial
Autosolve
position: ..842.7..7...9.82.25.718.6.4.2....3....93......1..2....6..8917.......6......7...8 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B4: 7,8 => CTR => B4: 9 * DIS # B8: 7,8 => CTR => B8: 1,2,3,4,9 * DIS # E6: 5,6 => CTR => E6: 4 * DIS # I4: 5,6 => CTR => I4: 1,7,9 * DIS # D4: 1 => CTR => D4: 5,8 * DIS # A6: 5,8 => CTR => A6: 3,6,9 * DIS # I4: 5,9 => CTR => I4: 1,6,7 * DIS # H6: 5,9 => CTR => H6: 4,8 * DIS # I6: 5,9 => CTR => I6: 4,6,7 * DIS # G9: 5,9 => CTR => G9: 2,3,4 * DIS # C7: 3,5 => CTR => C7: 4 * PRF # C7: 4 => SOL * DIS # A8: 3,5 => CTR => A8: 1,8,9 * DIS # C8: 3,5 => CTR => C8: 4,7,9 * DIS # A9: 3,5 => CTR => A9: 1,9 * PRF # C9: 3,5 => SOL * DIS # D7: 3,5 => CTR => D7: 2 * PRF # I7: 3,5 => SOL * DIS # C8: 4,5 => CTR => C8: 3,7,9 * DIS # I8: 4,5 => CTR => I8: 2,3,9 * DIS # E6: 6 => CTR => E6: 4,5 * CNT 21 HDP CHAINS / 48 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B4: 7,8 => CTR => B4: 9 * DIS B4: 9 # B8: 7,8 => CTR => B8: 1,2,3,4 * PRF B4: 9 + B8: 1,2,3,4 # B9: 1,4 => SOL * STA B4: 9 + B8: 1,2,3,4 + B9: 1,4 * CNT 3 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..84..7..7......2..5..18.6.4.2....3....93......1..2....6..8917.......6......7...8 | initial |
| ..842.7..7...9.82.25.718.6.4.2....3....93......1..2....6..8917.......6......7...8 | autosolve |
| 138426795746395821259718364492861537685937412371542986564289173827153649913674258 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) B5: 7,8 E4: 5,6 D6: 5,8 G4: 5,9 A7: 3,5 E8: 4,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,I2: 1.. / B2 = 1 => 0 pairs (X) / I2 = 1 => 0 pairs (_) H1,H5: 1.. / H1 = 1 => 0 pairs (X) / H5 = 1 => 0 pairs (_) G5,I5: 2.. / G5 = 2 => 6 pairs (_) / I5 = 2 => 0 pairs (*) B8,B9: 2.. / B8 = 2 => 11 pairs (_) / B9 = 2 => 6 pairs (_) D7,I7: 2.. / D7 = 2 => 6 pairs (_) / I7 = 2 => 0 pairs (X) G5,G9: 2.. / G5 = 2 => 6 pairs (_) / G9 = 2 => 0 pairs (*) A6,B6: 3.. / A6 = 3 => 16 pairs (_) / B6 = 3 => 8 pairs (_) G3,G9: 3.. / G3 = 3 => 0 pairs (*) / G9 = 3 => 0 pairs (X) F5,E6: 4.. / F5 = 4 => 0 pairs (X) / E6 = 4 => 16 pairs (_) C7,I7: 4.. / C7 = 4 => 0 pairs (*) / I7 = 4 => 0 pairs (X) E6,E8: 4.. / E6 = 4 => 16 pairs (_) / E8 = 4 => 0 pairs (X) A1,C2: 6.. / A1 = 6 => 0 pairs (X) / C2 = 6 => 11 pairs (_) E4,E6: 6.. / E4 = 6 => 16 pairs (_) / E6 = 6 => 0 pairs (X) D9,F9: 6.. / D9 = 6 => 7 pairs (_) / F9 = 6 => 0 pairs (X) A1,F1: 6.. / A1 = 6 => 0 pairs (X) / F1 = 6 => 11 pairs (_) E4,I4: 6.. / E4 = 6 => 16 pairs (_) / I4 = 6 => 0 pairs (X) C2,C5: 6.. / C2 = 6 => 11 pairs (_) / C5 = 6 => 0 pairs (X) D2,D9: 6.. / D2 = 6 => 0 pairs (X) / D9 = 6 => 7 pairs (_) F4,F5: 7.. / F4 = 7 => 7 pairs (_) / F5 = 7 => 15 pairs (_) B8,C8: 7.. / B8 = 7 => 0 pairs (X) / C8 = 7 => 7 pairs (_) B6,I6: 7.. / B6 = 7 => 18 pairs (_) / I6 = 7 => 6 pairs (_) C5,C8: 7.. / C5 = 7 => 0 pairs (X) / C8 = 7 => 7 pairs (_) D4,D6: 8.. / D4 = 8 => 16 pairs (_) / D6 = 8 => 0 pairs (X) H5,H6: 8.. / H5 = 8 => 0 pairs (X) / H6 = 8 => 16 pairs (_) A8,B8: 8.. / A8 = 8 => 7 pairs (_) / B8 = 8 => 0 pairs (X) B4,D4: 8.. / B4 = 8 => 0 pairs (X) / D4 = 8 => 16 pairs (_) * DURATION: 0:00:26.747614 START: 05:31:08.347226 END: 05:31:35.094840 2019-05-01 * CP COUNT: (26) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B5,D6,E4,E8,G4) * ..842.7..7...9.82.25.718.6.4.2....3....93......1..2....6..8917.......6......7...8 * PAIR B5: 7,8 BLK 4 B4: 7,8,9 # reduction candidate for 7,8 B4: 7,8 => CTR * ..842.71.71..9.82.25.718.6.482157936.7.934281..1862..7.6..8917.8.7.416..14.276..8 B4: 9 # 16 pairs B6: 7,8,3,9 # reduction candidate for 7,8 B6: 7,8 # 18 pairs * PAIR B5: 7,8 COL B B8: 7,8,1,2,3,4,9 # reduction candidate for 7,8 B8: 7,8 => CTR * .1842.7..74..9.82125.718.6.4.28.1.3....937214.31542987.64.8917...7.5.6...2..7...8 B8: 1,2,3,4,9 # 10 pairs * PAIR E4: 5,6 BLK 5 E6: 5,6,4 # reduction candidate for 5,6 E6: 5,6 => CTR * ..842.71.71..9.82.25.718.6.4821.7.36.7.934281..1862..7.6..8917.8.7.416..14.276..8 E6: 4 # 16 pairs * PAIR E4: 5,6 ROW 4 I4: 5,6,1,7,9 # reduction candidate for 5,6 I4: 5,6 => CTR * ..842.71.71..9.82.25.718.6.482157936.7.934281..1862..7.6..8917.8.7.416..14.276..8 I4: 1,7,9 # 16 pairs * PAIR D6: 5,8 BLK 5 D4: 5,8,1 # reduction candidate for 5,8 D4: 1 => CTR * ..842.71.71..9.82.25.718.6.4821.7.36.7.93.281..1862..7.6..8917.8.7.416..14.276..8 D4: 5,8 # 16 pairs * PAIR D6: 5,8 ROW 6 A6: 5,8,3,6,9 # reduction candidate for 5,8 A6: 5,8 => CTR * ..842.7..7...9.82.25.718.6.4928.7531...931..6.315.2..7.6..8917.......6......7...8 A6: 3,6,9 # 7 pairs H6: 5,8,4,9 # reduction candidate for 5,8 H6: 5,8 # 10 pairs * PAIR G4: 5,9 BLK 6 I4: 5,9,1,6,7 # reduction candidate for 5,9 I4: 5,9 => CTR * ..842.7..7...9.82.25.718.6.4.2.6..3....93......1..2....6..8917.......6......7...8 I4: 1,6,7 # 6 pairs G6: 5,9,4 # reduction candidate for 5,9 G6: 5,9 # 10 pairs H6: 5,9,4,8 # reduction candidate for 5,9 H6: 5,9 => CTR * ..842.71.71..9.82.25.718.6.4.2..7.3..7.93..8...1..2..7.6..8917...7...6......7...8 H6: 4,8 # 7 pairs I6: 5,9,4,6,7 # reduction candidate for 5,9 I6: 5,9 => CTR * ..842.7..7...9.82.25.718.6.4.2....3..8.93....371.62.8.56..8917.8.7.4.6......7...8 I6: 4,6,7 # 6 pairs * PAIR G4: 5,9 COL G G9: 5,9,2,3,4 # reduction candidate for 5,9 G9: 5,9 => CTR * ..842.7..74..9.8212597183644.28...3....93421...1..248..64.8917.....4.6......7..48 G9: 2,3,4 # 6 pairs * PAIR A7: 3,5 BLK 7 C7: 3,5,4 # reduction candidate for 3,5 C7: 3,5 => CTR * 69842.71.714.9682.2537184694.2.6.93...693.24.931.42....65289174.47.5.692.29.74358 C7: 4 => SOLVED * 138426795746395821259718364492861537685937412371542986564289173827153649913674258 A8: 3,5,1,8,9 # reduction candidate for 3,5 A8: 3,5 => CTR * ..842.7..74..9.82125.718.6.4.28.1.3..7.93.21...15.2.87.6..8917..8715.6.2129.7...8 A8: 1,8,9 # 6 pairs C8: 3,5,4,7,9 # reduction candidate for 3,5 C8: 3,5 => CTR * ..842.7..746.9.82125.718.6.4.2..7.3..8793.21...1..2.87.6..8917.87....6..12967...8 C8: 4,7,9 # 6 pairs A9: 3,5,1,9 # reduction candidate for 3,5 A9: 3,5 => CTR * ..842.7..746.9.821253718.6.4.28.1.3...5937.1..31542987.64.8917...7.5.6....967.3.8 A9: 1,9 # 7 pairs C9: 3,5,4,9 # reduction candidate for 3,5 C9: 3,5 => SOLVED * 138426795746395821259718364492861537685937412371542986564289173827153649913674258 C9: 4,9 # 7 pairs * PAIR A7: 3,5 ROW 7 D7: 3,5,2 # reduction candidate for 3,5 D7: 3,5 => CTR * ..842.7..74..9.82125.718.6.4.28.1.3....937214..154298.564389172..7.54693....76.48 D7: 2 # 6 pairs I7: 3,5,2,4 # reduction candidate for 3,5 I7: 3,5 => SOLVED * 138426795746395821259718364492861537685937412371542986564289173827153649913674258 I7: 2,4 # 7 pairs * PAIR A7: 3,5 COL A A6: 3,5,6,8,9 # reduction candidate for 3,5 A6: 3,5 # 10 pairs A6: 6,8,9 # 9 pairs * PAIR E8: 4,5 BLK 8 F8: 4,5,1,3 # reduction candidate for 4,5 F8: 4,5 # 12 pairs F9: 4,5,1,3,6 # reduction candidate for 4,5 F9: 4,5 # 10 pairs * PAIR E8: 4,5 ROW 8 C8: 4,5,3,7,9 # reduction candidate for 4,5 C8: 4,5 => CTR * ..842.7..746.9.82125.718.6.4.2..7.3..8793.21...1..2.87.6..8917.87....6..12967...8 C8: 3,7,9 # 6 pairs H8: 4,5,9 # reduction candidate for 4,5 H8: 4,5 # 8 pairs I8: 4,5,2,3,9 # reduction candidate for 4,5 I8: 4,5 => CTR * ..842.75.74..9.82125.718.6.4.28.1.3....93..1...1..2.8..64.8917.......69.....7..48 I8: 2,3,9 # 6 pairs * PAIR E8: 4,5 COL E E6: 4,5,6 # reduction candidate for 4,5 E6: 6 => CTR * ..842.71.71..9.82.25.718.6.482157936.7.934281..1862..7.6..8917.8.7.416..14.276..8 E6: 4,5 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190422-absurd-base-pr-000.dot * REASONING * DIS # B4: 7,8 => CTR => B4: 9 * DIS # B8: 7,8 => CTR => B8: 1,2,3,4,9 * DIS # E6: 5,6 => CTR => E6: 4 * DIS # I4: 5,6 => CTR => I4: 1,7,9 * DIS # D4: 1 => CTR => D4: 5,8 * DIS # A6: 5,8 => CTR => A6: 3,6,9 * DIS # I4: 5,9 => CTR => I4: 1,6,7 * DIS # H6: 5,9 => CTR => H6: 4,8 * DIS # I6: 5,9 => CTR => I6: 4,6,7 * DIS # G9: 5,9 => CTR => G9: 2,3,4 * DIS # C7: 3,5 => CTR => C7: 4 * PRF # C7: 4 => SOL * DIS # A8: 3,5 => CTR => A8: 1,8,9 * DIS # C8: 3,5 => CTR => C8: 4,7,9 * DIS # A9: 3,5 => CTR => A9: 1,9 * PRF # C9: 3,5 => SOL * DIS # D7: 3,5 => CTR => D7: 2 * PRF # I7: 3,5 => SOL * DIS # C8: 4,5 => CTR => C8: 3,7,9 * DIS # I8: 4,5 => CTR => I8: 2,3,9 * DIS # E6: 6 => CTR => E6: 4,5 * CNT 21 HDP CHAINS / 48 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B5,D6,E4,E8,G4) * ..842.7..7...9.82.25.718.6.4.2....3....93......1..2....6..8917.......6......7...8 * PAIR B5: 7,8 BLK 4 B4: 7,8,9 # reduction candidate for 7,8 B4: 7,8 => CTR * ..842.71.71..9.82.25.718.6.482157936.7.934281..1862..7.6..8917.8.7.416..14.276..8 * RESTART * PAIR B5: 7,8 COL B B8: 7,8,1,2,3,4 # reduction candidate for 7,8 B8: 7,8 => CTR * ..842.7..74..9.82125.718.6.492861537...937214.71542986.64.8917..8..5.6...2..7...8 * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A1,A9,B2,B8,C3,C7,F4,F5,F8,F9,G3,G5,H1,H5,H8,I2,I4,I7) * .384267.57.639582.25.718.6.49286.53.68593....37154298656.28917.8.715.6.....67..58 * PAIR B2: 1,4 COL B B9: 1,4,2 # reduction candidate for 1,4 B9: 1,4 => SOLVED * 138426795746395821259718364492861537685937412371542986564289173827153649913674258 * DURATION: 0:00:03.898761 START: 05:31:58.866610 END: 05:32:02.765371 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190422-absurd-base-pr-001.dot * REASONING * DIS # B4: 7,8 => CTR => B4: 9 * DIS B4: 9 # B8: 7,8 => CTR => B8: 1,2,3,4 * PRF B4: 9 + B8: 1,2,3,4 # B9: 1,4 => SOL * STA B4: 9 + B8: 1,2,3,4 + B9: 1,4 * CNT 3 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190422, absurd
Solution
position: 138426795746395821259718364492861537685937412371542986564289173827153649913674258 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 # B4: 7,8 => CTR => B4: 9 * INC # B4: 9 => UNS * INC # B6: 7,8 => UNS * DIS # B8: 7,8 => CTR => B8: 1,2,3,4,9 * INC # B8: 1,2,3,4,9 => UNS * DIS # E6: 5,6 => CTR => E6: 4 * INC # E6: 4 => UNS * DIS # I4: 5,6 => CTR => I4: 1,7,9 * INC # I4: 1,7,9 => UNS * INC # D4: 5,8 => UNS * DIS # D4: 1 => CTR => D4: 5,8 * DIS # A6: 5,8 => CTR => A6: 3,6,9 * INC # A6: 3,6,9 => UNS * INC # H6: 5,8 => UNS * DIS # I4: 5,9 => CTR => I4: 1,6,7 * INC # I4: 1,6,7 => UNS * INC # G6: 5,9 => UNS * DIS # H6: 5,9 => CTR => H6: 4,8 * INC # H6: 4,8 => UNS * DIS # I6: 5,9 => CTR => I6: 4,6,7 * INC # I6: 4,6,7 => UNS * DIS # G9: 5,9 => CTR => G9: 2,3,4 * INC # G9: 2,3,4 => UNS * DIS # C7: 3,5 => CTR => C7: 4 * PRF # C7: 4 => SOL * DIS # A8: 3,5 => CTR => A8: 1,8,9 * INC # A8: 1,8,9 => UNS * DIS # C8: 3,5 => CTR => C8: 4,7,9 * INC # C8: 4,7,9 => UNS * DIS # A9: 3,5 => CTR => A9: 1,9 * INC # A9: 1,9 => UNS * PRF # C9: 3,5 => SOL * INC # C9: 4,9 => UNS * DIS # D7: 3,5 => CTR => D7: 2 * INC # D7: 2 => UNS * PRF # I7: 3,5 => SOL * INC # I7: 2,4 => UNS * INC # A6: 3,5 => UNS * INC # A6: 6,8,9 => UNS * INC # F8: 4,5 => UNS * INC # F9: 4,5 => UNS * DIS # C8: 4,5 => CTR => C8: 3,7,9 * INC # C8: 3,7,9 => UNS * INC # H8: 4,5 => UNS * DIS # I8: 4,5 => CTR => I8: 2,3,9 * INC # I8: 2,3,9 => UNS * INC # E6: 4,5 => UNS * DIS # E6: 6 => CTR => E6: 4,5 * CNT 48 HDP CHAINS / 48 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B4: 7,8 => CTR => B4: 9 * DIS B4: 9 # B8: 7,8 => CTR => B8: 1,2,3,4 * PRF B4: 9 + B8: 1,2,3,4 # B9: 1,4 => SOL * STA B4: 9 + B8: 1,2,3,4 + B9: 1,4 * CNT 3 HDP CHAINS / 3 HYP OPENED