Analysis of zz-www.sudokuoftheday.co.uk-20190108-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: ..49...6.....2..7.9......3....536.9............74....1..2...9...78..2...4..75...2 initial
Autosolve
position: 7.491..6.....2..799....7.3.2.153679....271.....7489.21..2...9.7.78.92...4..75...2 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A2: 5,6 => CTR => A2: 1,3,8 * DIS # B2: 5,6 => CTR => B2: 1,3,8 * DIS # C5: 5,6 => CTR => C5: 3,9 * PRF # D2: 6,8 => SOL * DIS # D2: 3 => CTR => D2: 6,8 * DIS # D7: 6,8 => CTR => D7: 1,3 * DIS # B1: 2,8 => CTR => B1: 3,5 * PRF # B1: 3,5 => SOL * PRF # I3: 5,8 => SOL * DIS # I3: 4 => CTR => I3: 5,8 * DIS # B1: 5,8 => CTR => B1: 2,3 * PRF # F1: 5,8 => SOL * DIS # F1: 3 => CTR => F1: 5,8 * DIS # B5: 3,5,6,9 => CTR => B5: 4,8 * DIS # I3: 4,8 => CTR => I3: 5 * PRF # I3: 5 => SOL * DIS # B5: 3,6 => CTR => B5: 4,5,8,9 * DIS # C5: 3,6 => CTR => C5: 5,9 * PRF # D7: 3,8 => SOL * DIS # F7: 3,8 => CTR => F7: 4 * PRF # F7: 4 => SOL * DIS # F1: 3,8 => CTR => F1: 5 * PRF # F1: 5 => SOL * PRF # F2: 3,8 => SOL * DIS # G8: 3,6 => CTR => G8: 4,5 * DIS # H7: 5 => CTR => H7: 1,8 * CNT 26 HDP CHAINS / 49 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A2: 5,6 => CTR => A2: 1,3,8 * DIS A2: 1,3,8 # B2: 5,6 => CTR => B2: 1,3,8 * DIS A2: 1,3,8 + B2: 1,3,8 # C2: 3 => CTR => C2: 5,6 * PRF A2: 1,3,8 + B2: 1,3,8 + C2: 5,6 # D2: 6,8 => SOL * STA A2: 1,3,8 + B2: 1,3,8 + C2: 5,6 + D2: 6,8 * CNT 4 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..49...6.....2..7.9......3....536.9............74....1..2...9...78..2...4..75...2 | initial |
| 7.491..6.....2..799....7.3.2.153679....271.....7489.21..2...9.7.78.92...4..75...2 | autosolve |
| 734915268815623479926847135281536794349271856567489321152364987678192543493758612 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) B3: 1,2 C3: 5,6 D3: 6,8 E3: 4,6 G1: 2,8 I1: 5,8 G3: 1,2 B4: 4,8 I4: 4,8 I5: 3,6 E7: 4,6 F9: 3,8 I8: 3,6 H9: 1,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G2,G3: 1.. / G2 = 1 => 0 pairs (X) / G3 = 1 => 12 pairs (_) D7,D8: 1.. / D7 = 1 => 21 pairs (_) / D8 = 1 => 15 pairs (_) B3,G3: 1.. / B3 = 1 => 0 pairs (X) / G3 = 1 => 12 pairs (_) B9,H9: 1.. / B9 = 1 => 0 pairs (X) / H9 = 1 => 15 pairs (_) B1,B3: 2.. / B1 = 2 => 0 pairs (X) / B3 = 2 => 12 pairs (_) G1,G3: 2.. / G1 = 2 => 12 pairs (_) / G3 = 2 => 0 pairs (X) B1,G1: 2.. / B1 = 2 => 0 pairs (X) / G1 = 2 => 12 pairs (_) B3,G3: 2.. / B3 = 2 => 12 pairs (_) / G3 = 2 => 0 pairs (X) B1,F1: 3.. / B1 = 3 => 0 pairs (*) / F1 = 3 => 0 pairs (X) I5,I8: 3.. / I5 = 3 => 0 pairs (X) / I8 = 3 => 15 pairs (_) F2,E3: 4.. / F2 = 4 => 0 pairs (X) / E3 = 4 => 0 pairs (_) G2,I3: 4.. / G2 = 4 => 0 pairs (*) / I3 = 4 => 0 pairs (X) B4,B5: 4.. / B4 = 4 => 0 pairs (X) / B5 = 4 => 0 pairs (_) E7,F7: 4.. / E7 = 4 => 0 pairs (X) / F7 = 4 => 0 pairs (_) G8,H8: 4.. / G8 = 4 => 0 pairs (X) / H8 = 4 => 15 pairs (_) F2,G2: 4.. / F2 = 4 => 0 pairs (X) / G2 = 4 => 0 pairs (_) E3,I3: 4.. / E3 = 4 => 0 pairs (*) / I3 = 4 => 0 pairs (X) B4,I4: 4.. / B4 = 4 => 0 pairs (X) / I4 = 4 => 0 pairs (_) E3,E7: 4.. / E3 = 4 => 0 pairs (*) / E7 = 4 => 0 pairs (X) F2,F7: 4.. / F2 = 4 => 0 pairs (X) / F7 = 4 => 0 pairs (_) H5,H8: 4.. / H5 = 4 => 0 pairs (X) / H8 = 4 => 15 pairs (_) I3,I4: 4.. / I3 = 4 => 0 pairs (X) / I4 = 4 => 0 pairs (_) F1,F2: 5.. / F1 = 5 => 0 pairs (*) / F2 = 5 => 0 pairs (X) I1,I3: 5.. / I1 = 5 => 0 pairs (X) / I3 = 5 => 0 pairs (_) C3,I3: 5.. / C3 = 5 => 0 pairs (X) / I3 = 5 => 0 pairs (_) E3,E7: 6.. / E3 = 6 => 0 pairs (X) / E7 = 6 => 0 pairs (_) I5,I8: 6.. / I5 = 6 => 15 pairs (_) / I8 = 6 => 0 pairs (X) D3,I3: 8.. / D3 = 8 => 16 pairs (_) / I3 = 8 => 0 pairs (X) B4,I4: 8.. / B4 = 8 => 0 pairs (*) / I4 = 8 => 0 pairs (X) A2,A5: 8.. / A2 = 8 => 20 pairs (_) / A5 = 8 => 0 pairs (X) B5,C5: 9.. / B5 = 9 => 0 pairs (X) / C5 = 9 => 16 pairs (_) B9,C9: 9.. / B9 = 9 => 16 pairs (_) / C9 = 9 => 0 pairs (X) B5,B9: 9.. / B5 = 9 => 0 pairs (X) / B9 = 9 => 16 pairs (_) C5,C9: 9.. / C5 = 9 => 16 pairs (_) / C9 = 9 => 0 pairs (X) * DURATION: 0:00:41.301949 START: 02:47:52.303601 END: 02:48:33.605550 2019-05-01 * CP COUNT: (34) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B4,C3,D3,E3,E7,F9,G1,G3,H9,I1,I4,I5,I8) * 7.491..6.....2..799....7.3.2.153679....271.....7489.21..2...9.7.78.92...4..75...2 * PAIR C3: 5,6 BLK 1 A2: 5,6,1,3,8 # reduction candidate for 5,6 A2: 5,6 => CTR * 7.491..65....254799....7.3.2415367988..271.....7489.21..2...9.7.78.92...4..75...2 A2: 1,3,8 # 14 pairs B2: 5,6,1,3,8 # reduction candidate for 5,6 B2: 5,6 => CTR * 7.4913.65..3.254799.5.47138281536794.49271.....7489.21..2.649.7.78.92.4.496758312 B2: 1,3,8 # 14 pairs C2: 5,6,3 # reduction candidate for 5,6 C2: 5,6 # 17 pairs * PAIR C3: 5,6 COL C C5: 5,6,3,9 # reduction candidate for 5,6 C5: 5,6 => CTR * 7.4913.65..3.254799....7.3.24153679889.271.....7489.21..2...9.7.78.92...4.975...2 C5: 3,9 # 15 pairs * PAIR D3: 6,8 BLK 2 D2: 6,8,3 # reduction candidate for 6,8 D2: 6,8 => SOLVED * 734915268815623479926847135281536794349271856567489321152364987678192543493758612 D2: 3 => CTR * 73491.26....32.479925.47138281536794.49271.....7489.21..28649.7.78192.4.49375...2 * PAIR D3: 6,8 COL D D7: 6,8,1,3 # reduction candidate for 6,8 D7: 6,8 => CTR * 73491.26....32.479925.47138281536794.49271.....7489.21..28649.7.78192.4.49375...2 D7: 1,3 # 16 pairs * PAIR G1: 2,8 ROW 1 B1: 2,8,3,5 # reduction candidate for 2,8 B1: 2,8 => CTR * 7.4913.65....254799.5.47138281536794.49271.....7489.21..2.649.7.78.92.4.49.758.12 B1: 3,5 => SOLVED * 734915268815623479926847135281536794349271856567489321152364987678192543493758612 * PAIR I1: 5,8 BLK 3 I3: 5,8,4 # reduction candidate for 5,8 I3: 5,8 => SOLVED * 734915268815623479926847135281536794349271856567489321152364987678192543493758612 I3: 4 => CTR * 7.491..65....254799....7.3.2.153679....271.....7489.21..2...9.7.78.92...4..75...2 * PAIR I1: 5,8 ROW 1 B1: 5,8,2,3 # reduction candidate for 5,8 B1: 5,8 => CTR * 7.491326.....25479925647138281536794.49271.....7489.21..2.649.7.78.92.4.49.758.12 B1: 2,3 # 17 pairs F1: 5,8,3 # reduction candidate for 5,8 F1: 5,8 => SOLVED * 734915268815623479926847135281536794349271856567489321152364987678192543493758612 F1: 3 => CTR * 7.491326.....25479925647138281536794.49271.....7489.21..2.649.7.78.92.4.49.758.12 * PAIR B4: 4,8 BLK 4 B5: 4,8,3,5,6,9 # reduction candidate for 4,8 B5: 3,5,6,9 => CTR * 7.491..65....254799....7.3.2415367988..271.....7489.21..2...9.7.78.92...4..75...2 B5: 4,8 # 20 pairs * PAIR I4: 4,8 BLK 6 G5: 4,8,3,5,6 # reduction candidate for 4,8 G5: 4,8 # 18 pairs H5: 4,8,5 # reduction candidate for 4,8 H5: 4,8 # 15 pairs * PAIR I4: 4,8 COL I I3: 4,8,5 # reduction candidate for 4,8 I3: 4,8 => CTR * 7.4918265816325479925647138281536794.49271....67489.21.528649.7.78.92.4.49.75..12 I3: 5 => SOLVED * 734915268815623479926847135281536794349271856567489321152364987678192543493758612 * PAIR I5: 3,6 BLK 6 G5: 3,6,4,5,8 # reduction candidate for 3,6 G5: 3,6 # 20 pairs G6: 3,6,5 # reduction candidate for 3,6 G6: 3,6 # 15 pairs * PAIR I5: 3,6 ROW 5 A5: 3,6,5,8 # reduction candidate for 3,6 A5: 3,6 # 22 pairs B5: 3,6,4,5,8,9 # reduction candidate for 3,6 B5: 3,6 => CTR * 7.491..65....254799....7.3.2415367988.9271.....7489.21..2...9.7.78.92...49.75..12 B5: 4,5,8,9 # 14 pairs C5: 3,6,5,9 # reduction candidate for 3,6 C5: 3,6 => CTR * 7.491..65....254799....7.3.24153679889.271.....7489.21..2...9.7.78.92...4.975...2 C5: 5,9 # 15 pairs * PAIR F9: 3,8 BLK 8 D7: 3,8,1,6 # reduction candidate for 3,8 D7: 3,8 => SOLVED * 734915268815623479926847135281536794349271856567489321152364987678192543493758612 D7: 1,6 # 16 pairs F7: 3,8,4 # reduction candidate for 3,8 F7: 3,8 => CTR * 7.4915.6.....24.799...67.34241536798...271.....7489.21..2.4.9.7.78.92...4..75...2 F7: 4 => SOLVED * 734915268815623479926847135281536794349271856567489321152364987678192543493758612 * PAIR F9: 3,8 ROW 9 G9: 3,8,6 # reduction candidate for 3,8 G9: 3,8 # 19 pairs G9: 6 # 17 pairs * PAIR F9: 3,8 COL F F1: 3,8,5 # reduction candidate for 3,8 F1: 3,8 => CTR * 734918265816325479925647138281536794.49271....67489.213.2.649.7.78.92.4.49.75..12 F1: 5 => SOLVED * 734915268815623479926847135281536794349271856567489321152364987678192543493758612 F2: 3,8,4,5 # reduction candidate for 3,8 F2: 3,8 => SOLVED * 734915268815623479926847135281536794349271856567489321152364987678192543493758612 F2: 4,5 # 15 pairs * PAIR I8: 3,6 BLK 9 G8: 3,6,4,5 # reduction candidate for 3,6 G8: 3,6 => CTR * 7.491.26.8...2..7992...713.281536794.4927158..57489.211.2...957578192.4.496753812 G8: 4,5 # 17 pairs G9: 3,6,8 # reduction candidate for 3,6 G9: 3,6 # 17 pairs * PAIR I8: 3,6 ROW 8 A8: 3,6,1,5 # reduction candidate for 3,6 A8: 3,6 # 20 pairs D8: 3,6,1 # reduction candidate for 3,6 D8: 3,6 # 21 pairs * PAIR H9: 1,8 BLK 9 H7: 1,8,5 # reduction candidate for 1,8 H7: 5 => CTR * 73491.26.186325479925.471382.153679...3271..66574893213.2...957578.92..34.9753..2 H7: 1,8 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190108-absurd-base-pr-000.dot * REASONING * DIS # A2: 5,6 => CTR => A2: 1,3,8 * DIS # B2: 5,6 => CTR => B2: 1,3,8 * DIS # C5: 5,6 => CTR => C5: 3,9 * PRF # D2: 6,8 => SOL * DIS # D2: 3 => CTR => D2: 6,8 * DIS # D7: 6,8 => CTR => D7: 1,3 * DIS # B1: 2,8 => CTR => B1: 3,5 * PRF # B1: 3,5 => SOL * PRF # I3: 5,8 => SOL * DIS # I3: 4 => CTR => I3: 5,8 * DIS # B1: 5,8 => CTR => B1: 2,3 * PRF # F1: 5,8 => SOL * DIS # F1: 3 => CTR => F1: 5,8 * DIS # B5: 3,5,6,9 => CTR => B5: 4,8 * DIS # I3: 4,8 => CTR => I3: 5 * PRF # I3: 5 => SOL * DIS # B5: 3,6 => CTR => B5: 4,5,8,9 * DIS # C5: 3,6 => CTR => C5: 5,9 * PRF # D7: 3,8 => SOL * DIS # F7: 3,8 => CTR => F7: 4 * PRF # F7: 4 => SOL * DIS # F1: 3,8 => CTR => F1: 5 * PRF # F1: 5 => SOL * PRF # F2: 3,8 => SOL * DIS # G8: 3,6 => CTR => G8: 4,5 * DIS # H7: 5 => CTR => H7: 1,8 * CNT 26 HDP CHAINS / 49 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B4,C3,D3,E3,E7,F9,G1,G3,H9,I1,I4,I5,I8) * 7.491..6.....2..799....7.3.2.153679....271.....7489.21..2...9.7.78.92...4..75...2 * PAIR C3: 5,6 BLK 1 A2: 5,6,1,3,8 # reduction candidate for 5,6 A2: 5,6 => CTR * 7.491..65....254799....7.3.2415367988..271.....7489.21..2...9.7.78.92...4..75...2 B2: 5,6,1,3,8 # reduction candidate for 5,6 B2: 5,6 => CTR * 7.4913.65..3.254799.5.47138281536794.49271.....7489.21..2.649.7.78.92.4.496758312 C2: 5,6,3 # reduction candidate for 5,6 C2: 5,6 # 17 pairs * RESTART * PAIR C3: 5,6 BLK 1 C2: 5,6,3 # reduction candidate for 5,6 C2: 3 => CTR * 7.491..6...36254799.68471352.1536794.4.271.....7489.21..2...9.7.78.92...4..75...2 * PAIR D3: 6,8 BLK 2 D2: 6,8,3 # reduction candidate for 6,8 D2: 6,8 => SOLVED * 734915268815623479926847135281536794349271856567489321152364987678192543493758612 * DURATION: 0:00:05.406682 START: 02:49:08.228080 END: 02:49:13.634762 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190108-absurd-base-pr-001.dot * REASONING * DIS # A2: 5,6 => CTR => A2: 1,3,8 * DIS A2: 1,3,8 # B2: 5,6 => CTR => B2: 1,3,8 * DIS A2: 1,3,8 + B2: 1,3,8 # C2: 3 => CTR => C2: 5,6 * PRF A2: 1,3,8 + B2: 1,3,8 + C2: 5,6 # D2: 6,8 => SOL * STA A2: 1,3,8 + B2: 1,3,8 + C2: 5,6 + D2: 6,8 * CNT 4 HDP CHAINS / 6 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190108, absurd
Solution
position: 734915268815623479926847135281536794349271856567489321152364987678192543493758612 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 # A2: 5,6 => CTR => A2: 1,3,8 * INC # A2: 1,3,8 => UNS * DIS # B2: 5,6 => CTR => B2: 1,3,8 * INC # B2: 1,3,8 => UNS * INC # C2: 5,6 => UNS * DIS # C5: 5,6 => CTR => C5: 3,9 * INC # C5: 3,9 => UNS * PRF # D2: 6,8 => SOL * DIS # D2: 3 => CTR => D2: 6,8 * DIS # D7: 6,8 => CTR => D7: 1,3 * INC # D7: 1,3 => UNS * DIS # B1: 2,8 => CTR => B1: 3,5 * PRF # B1: 3,5 => SOL * PRF # I3: 5,8 => SOL * DIS # I3: 4 => CTR => I3: 5,8 * DIS # B1: 5,8 => CTR => B1: 2,3 * INC # B1: 2,3 => UNS * PRF # F1: 5,8 => SOL * DIS # F1: 3 => CTR => F1: 5,8 * INC # B5: 4,8 => UNS * DIS # B5: 3,5,6,9 => CTR => B5: 4,8 * INC # G5: 4,8 => UNS * INC # H5: 4,8 => UNS * DIS # I3: 4,8 => CTR => I3: 5 * PRF # I3: 5 => SOL * INC # G5: 3,6 => UNS * INC # G6: 3,6 => UNS * INC # A5: 3,6 => UNS * DIS # B5: 3,6 => CTR => B5: 4,5,8,9 * INC # B5: 4,5,8,9 => UNS * DIS # C5: 3,6 => CTR => C5: 5,9 * INC # C5: 5,9 => UNS * PRF # D7: 3,8 => SOL * INC # D7: 1,6 => UNS * DIS # F7: 3,8 => CTR => F7: 4 * PRF # F7: 4 => SOL * INC # G9: 3,8 => UNS * INC # G9: 6 => UNS * DIS # F1: 3,8 => CTR => F1: 5 * PRF # F1: 5 => SOL * PRF # F2: 3,8 => SOL * INC # F2: 4,5 => UNS * DIS # G8: 3,6 => CTR => G8: 4,5 * INC # G8: 4,5 => UNS * INC # G9: 3,6 => UNS * INC # A8: 3,6 => UNS * INC # D8: 3,6 => UNS * INC # H7: 1,8 => UNS * DIS # H7: 5 => CTR => H7: 1,8 * CNT 49 HDP CHAINS / 49 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A2: 5,6 => CTR => A2: 1,3,8 * DIS A2: 1,3,8 # B2: 5,6 => CTR => B2: 1,3,8 * INC A2: 1,3,8 + B2: 1,3,8 # C2: 5,6 => UNS * INC A2: 1,3,8 + B2: 1,3,8 # C2: 5,6 => UNS * DIS A2: 1,3,8 + B2: 1,3,8 # C2: 3 => CTR => C2: 5,6 * PRF A2: 1,3,8 + B2: 1,3,8 + C2: 5,6 # D2: 6,8 => SOL * STA A2: 1,3,8 + B2: 1,3,8 + C2: 5,6 + D2: 6,8 * CNT 6 HDP CHAINS / 6 HYP OPENED