Analysis of zz-www.sudokuoftheday.co.uk-20190102-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: .651........4.6..14....2.9...738.56......7...89....1....6...97...........2.9..63. initial
Autosolve
position: .651.......24.6.514....2.962.738.56.65.2.7...893...127..6...97...9....1..2.9..63. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B3: 1,8 => CTR => B3: 3,7 * PRF # B3: 3,7 => SOL * DIS # G1: 4,8 => CTR => G1: 2,3,7 * DIS # I1: 4,8 => CTR => I1: 2,3 * DIS # E6: 5,6 => CTR => E6: 4 * DIS # D8: 5,6 => CTR => D8: 7,8 * DIS # E6: 6 => CTR => E6: 4,5 * PRF # I5: 4,9 => SOL * DIS # I5: 3,8 => CTR => I5: 4,9 * DIS # G5: 4,8 => CTR => G5: 3 * PRF # G5: 3 => SOL * DIS # I5: 4,8 => CTR => I5: 3,9 * PRF # D8: 5,8 => SOL * PRF # D3: 7 => SOL * CNT 14 HDP CHAINS / 34 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B3: 1,8 => CTR => B3: 3,7 * PRF B3: 3,7 => SOL * STA B3: 3,7 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .651........4.6..14....2.9...738.56......7...89....1....6...97...........2.9..63. | initial |
| .651.......24.6.514....2.962.738.56.65.2.7...893...127..6...97...9....1..2.9..63. | autosolve |
| 765198243982436751431752896217389564654217389893645127346521978579863412128974635 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) C3: 1,8 H1: 4,8 B4: 1,4 C5: 1,4 F4: 1,9 E5: 1,9 D6: 5,6 F6: 4,5 I4: 4,9 H5: 4,8 C9: 4,8 D7: 5,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B3,C3: 1.. / B3 = 1 => 0 pairs (X) / C3 = 1 => 0 pairs (_) B4,C5: 1.. / B4 = 1 => 0 pairs (*) / C5 = 1 => 0 pairs (X) F4,E5: 1.. / F4 = 1 => 0 pairs (X) / E5 = 1 => 0 pairs (_) A7,A9: 1.. / A7 = 1 => 13 pairs (_) / A9 = 1 => 0 pairs (*) B4,F4: 1.. / B4 = 1 => 0 pairs (*) / F4 = 1 => 0 pairs (X) C5,E5: 1.. / C5 = 1 => 0 pairs (X) / E5 = 1 => 0 pairs (_) B3,B4: 1.. / B3 = 1 => 0 pairs (X) / B4 = 1 => 0 pairs (_) C3,C5: 1.. / C3 = 1 => 0 pairs (*) / C5 = 1 => 0 pairs (X) G1,I1: 2.. / G1 = 2 => 13 pairs (_) / I1 = 2 => 0 pairs (X) E7,E8: 2.. / E7 = 2 => 12 pairs (_) / E8 = 2 => 0 pairs (X) E7,I7: 2.. / E7 = 2 => 12 pairs (_) / I7 = 2 => 0 pairs (X) G1,G8: 2.. / G1 = 2 => 13 pairs (_) / G8 = 2 => 0 pairs (X) G5,I5: 3.. / G5 = 3 => 0 pairs (*) / I5 = 3 => 0 pairs (X) I1,I5: 3.. / I1 = 3 => 0 pairs (*) / I5 = 3 => 0 pairs (X) B4,C5: 4.. / B4 = 4 => 0 pairs (X) / C5 = 4 => 0 pairs (_) E6,F6: 4.. / E6 = 4 => 11 pairs (_) / F6 = 4 => 0 pairs (X) B4,I4: 4.. / B4 = 4 => 0 pairs (X) / I4 = 4 => 0 pairs (_) C5,C9: 4.. / C5 = 4 => 0 pairs (*) / C9 = 4 => 0 pairs (X) H1,H5: 4.. / H1 = 4 => 11 pairs (_) / H5 = 4 => 0 pairs (X) D3,E3: 5.. / D3 = 5 => 0 pairs (X) / E3 = 5 => 14 pairs (_) D6,E6: 6.. / D6 = 6 => 13 pairs (_) / E6 = 6 => 0 pairs (X) D8,E8: 6.. / D8 = 6 => 0 pairs (X) / E8 = 6 => 13 pairs (_) D6,D8: 6.. / D6 = 6 => 13 pairs (_) / D8 = 6 => 0 pairs (X) E6,E8: 6.. / E6 = 6 => 0 pairs (X) / E8 = 6 => 13 pairs (_) A9,E9: 7.. / A9 = 7 => 18 pairs (_) / E9 = 7 => 0 pairs (*) D3,D8: 7.. / D3 = 7 => 0 pairs (*) / D8 = 7 => 0 pairs (X) F1,D3: 8.. / F1 = 8 => 0 pairs (*) / D3 = 8 => 0 pairs (X) B2,G2: 8.. / B2 = 8 => 0 pairs (*) / G2 = 8 => 0 pairs (X) C3,C9: 8.. / C3 = 8 => 0 pairs (X) / C9 = 8 => 0 pairs (_) H1,H5: 8.. / H1 = 8 => 0 pairs (X) / H5 = 8 => 11 pairs (_) A1,A2: 9.. / A1 = 9 => 0 pairs (X) / A2 = 9 => 14 pairs (_) F4,E5: 9.. / F4 = 9 => 0 pairs (*) / E5 = 9 => 0 pairs (X) I4,I5: 9.. / I4 = 9 => 0 pairs (X) / I5 = 9 => 0 pairs (_) A2,E2: 9.. / A2 = 9 => 14 pairs (_) / E2 = 9 => 0 pairs (X) F4,I4: 9.. / F4 = 9 => 0 pairs (*) / I4 = 9 => 0 pairs (X) E5,I5: 9.. / E5 = 9 => 0 pairs (X) / I5 = 9 => 0 pairs (_) F1,F4: 9.. / F1 = 9 => 0 pairs (X) / F4 = 9 => 0 pairs (_) * DURATION: 0:00:40.764803 START: 02:39:21.755640 END: 02:40:02.520443 2019-05-01 * CP COUNT: (37) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,C3,C5,C9,D6,D7,E5,F4,F6,H1,H5,I4) * .651.......24.6.514....2.962.738.56.65.2.7...893...127..6...97...9....1..2.9..63. * PAIR C3: 1,8 BLK 1 B3: 1,8,3,7 # reduction candidate for 1,8 B3: 1,8 => CTR * .651.8243..24.6851481.32796217389564654217389893...127.46...97...976.41..289..635 B3: 3,7 => SOLVED * 765198243982436751431752896217389564654217389893645127346521978579863412128974635 * PAIR H1: 4,8 BLK 3 G1: 4,8,2,3,7 # reduction candidate for 4,8 G1: 4,8 => CTR * .651.9..29.24.6.514..852.96247381569651297..3893...127..6.2.97...9...21..2.91.63. G1: 2,3,7 # 12 pairs I1: 4,8,2,3 # reduction candidate for 4,8 I1: 4,8 => CTR * .651.92..9.24.6.514..852.96247381569651297..3893...127..6...97...9....1..2.9..63. I1: 2,3 # 13 pairs * PAIR D6: 5,6 BLK 5 E6: 5,6,4 # reduction candidate for 5,6 E6: 5,6 => CTR * .651.8243..24.6.514.1..2.96217389564654217389893..4127.468..972..9.2.418.2894.635 E6: 4 # 11 pairs * PAIR D6: 5,6 COL D D8: 5,6,7,8 # reduction candidate for 5,6 D8: 5,6 => CTR * .651.8243..2436751431752896217389564654217389893...127.4682.97...9...41..289..635 D8: 7,8 # 14 pairs * PAIR F6: 4,5 BLK 5 E6: 4,5,6 # reduction candidate for 4,5 E6: 6 => CTR * .651.8243..2436751431752896217389564654217389893564127.4682.97...96..41..2894.635 E6: 4,5 # 13 pairs * PAIR F6: 4,5 COL F F7: 4,5,1,3,8 # reduction candidate for 4,5 F7: 4,5 # 15 pairs F8: 4,5,3,8 # reduction candidate for 4,5 F8: 4,5 # 14 pairs F9: 4,5,1,8 # reduction candidate for 4,5 F9: 4,5 # 20 pairs * PAIR I4: 4,9 BLK 6 I5: 4,9,3,8 # reduction candidate for 4,9 I5: 4,9 => SOLVED * 765198243982436751431752896217389564654217389893645127346521978579863412128974635 I5: 3,8 => CTR * .651.9...9.24.6.514..852.96247381569651297...893...127..6...97...9....1..2.9..63. * PAIR H5: 4,8 BLK 6 G5: 4,8,3 # reduction candidate for 4,8 G5: 4,8 => CTR * .651.9...9.24.6.514..852.96247381569651297..3893...127..6...97...9....1..2.9..63. G5: 3 => SOLVED * 765198243982436751431752896217389564654217389893645127346521978579863412128974635 I5: 4,8,3,9 # reduction candidate for 4,8 I5: 4,8 => CTR * .65179..3..24.6.514....2.962.738.56965.2973..893...127..6...97...9....1..2.9..63. I5: 3,9 # 13 pairs * PAIR C9: 4,8 BLK 7 B7: 4,8,3 # reduction candidate for 4,8 B7: 4,8 # 14 pairs B8: 4,8,3,7 # reduction candidate for 4,8 B8: 4,8 # 18 pairs * PAIR C9: 4,8 ROW 9 F9: 4,8,1,5 # reduction candidate for 4,8 F9: 4,8 # 19 pairs I9: 4,8,5 # reduction candidate for 4,8 I9: 4,8 # 17 pairs * PAIR D7: 5,8 BLK 8 F7: 5,8,1,3,4 # reduction candidate for 5,8 F7: 5,8 # 19 pairs D8: 5,8,6,7 # reduction candidate for 5,8 D8: 5,8 => SOLVED * 765198243982436751431752896217389564654217389893645127346521978579863412128974635 D8: 6,7 # 13 pairs F8: 5,8,3,4 # reduction candidate for 5,8 F8: 5,8 # 15 pairs F9: 5,8,1,4 # reduction candidate for 5,8 F9: 5,8 # 21 pairs * PAIR D7: 5,8 ROW 7 I7: 5,8,2,4 # reduction candidate for 5,8 I7: 5,8 # 15 pairs I7: 2,4 # 13 pairs * PAIR D7: 5,8 COL D D3: 5,8,7 # reduction candidate for 5,8 D3: 7 => SOLVED * 765198243982436751431752896217389564654217389893645127346521978579863412128974635 D3: 5,8 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190102-absurd-base-pr-000.dot * REASONING * DIS # B3: 1,8 => CTR => B3: 3,7 * PRF # B3: 3,7 => SOL * DIS # G1: 4,8 => CTR => G1: 2,3,7 * DIS # I1: 4,8 => CTR => I1: 2,3 * DIS # E6: 5,6 => CTR => E6: 4 * DIS # D8: 5,6 => CTR => D8: 7,8 * DIS # E6: 6 => CTR => E6: 4,5 * PRF # I5: 4,9 => SOL * DIS # I5: 3,8 => CTR => I5: 4,9 * DIS # G5: 4,8 => CTR => G5: 3 * PRF # G5: 3 => SOL * DIS # I5: 4,8 => CTR => I5: 3,9 * PRF # D8: 5,8 => SOL * PRF # D3: 7 => SOL * CNT 14 HDP CHAINS / 34 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,C3,C5,C9,D6,D7,E5,F4,F6,H1,H5,I4) * .651.......24.6.514....2.962.738.56.65.2.7...893...127..6...97...9....1..2.9..63. * PAIR C3: 1,8 BLK 1 B3: 1,8,3,7 # reduction candidate for 1,8 B3: 1,8 => CTR * .651.8243..24.6851481.32796217389564654217389893...127.46...97...976.41..289..635 B3: 3,7 => SOLVED * 765198243982436751431752896217389564654217389893645127346521978579863412128974635 * DURATION: 0:00:02.453484 START: 02:40:23.128295 END: 02:40:25.581779 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190102-absurd-base-pr-001.dot * REASONING * DIS # B3: 1,8 => CTR => B3: 3,7 * PRF B3: 3,7 => SOL * STA B3: 3,7 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190102, absurd
Solution
position: 765198243982436751431752896217389564654217389893645127346521978579863412128974635 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 # B3: 1,8 => CTR => B3: 3,7 * PRF # B3: 3,7 => SOL * DIS # G1: 4,8 => CTR => G1: 2,3,7 * INC # G1: 2,3,7 => UNS * DIS # I1: 4,8 => CTR => I1: 2,3 * INC # I1: 2,3 => UNS * DIS # E6: 5,6 => CTR => E6: 4 * INC # E6: 4 => UNS * DIS # D8: 5,6 => CTR => D8: 7,8 * INC # D8: 7,8 => UNS * INC # E6: 4,5 => UNS * DIS # E6: 6 => CTR => E6: 4,5 * INC # F7: 4,5 => UNS * INC # F8: 4,5 => UNS * INC # F9: 4,5 => UNS * PRF # I5: 4,9 => SOL * DIS # I5: 3,8 => CTR => I5: 4,9 * DIS # G5: 4,8 => CTR => G5: 3 * PRF # G5: 3 => SOL * DIS # I5: 4,8 => CTR => I5: 3,9 * INC # I5: 3,9 => UNS * INC # B7: 4,8 => UNS * INC # B8: 4,8 => UNS * INC # F9: 4,8 => UNS * INC # I9: 4,8 => UNS * INC # F7: 5,8 => UNS * PRF # D8: 5,8 => SOL * INC # D8: 6,7 => UNS * INC # F8: 5,8 => UNS * INC # F9: 5,8 => UNS * INC # I7: 5,8 => UNS * INC # I7: 2,4 => UNS * INC # D3: 5,8 => UNS * PRF # D3: 7 => SOL * CNT 34 HDP CHAINS / 34 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B3: 1,8 => CTR => B3: 3,7 * PRF B3: 3,7 => SOL * STA B3: 3,7 * CNT 2 HDP CHAINS / 1 HYP OPENED