Analysis of zz-www.sudokuoftheday.co.uk-20060731-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006
level: medium
position: 4......8....7.54.6.7..1.9.28.93.2......9.........4...1..2.9.5...8.5.....39..6...4 initial
Autosolve
position: 4....9.8.9..7.54.6.7..1.9.28193.264....9.1.......4..91..2.9.5...8.5....9395.6...4 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 2,3 => CTR => B1: 5,6 * DIS # E2: 2,3 => CTR => E2: 8 * DIS # B1: 2,3 => CTR => B1: 5,6 * DIS # E2: 2,3 => CTR => E2: 8 * DIS # B1: 2,3 => CTR => B1: 5,6 * DIS # E8: 7 => CTR => E8: 2,3 * PRF # G1: 1,3 => SOL * DIS # C2: 8 => CTR => C2: 1,3 * DIS # H7: 1,3 => CTR => H7: 6,7 * DIS # H8: 1,3 => CTR => H8: 2,6,7 * PRF # I1: 7 => SOL * PRF # H5: 2,7 => SOL * DIS # C5: 3,7 => CTR => C5: 4,6 * DIS # G6: 3,7 => CTR => G6: 2,8 * DIS # E5: 8 => CTR => E5: 5,7 * DIS # F6: 7 => CTR => F6: 6,8 * DIS # D3: 6,8 => CTR => D3: 4 * DIS # I5: 5,7 => CTR => I5: 3,8 * DIS # I1: 3 => CTR => I1: 5,7 * DIS # C8: 7 => CTR => C8: 4,6 * DIS # B5: 3 => CTR => B5: 4,6 * DIS # F6: 7,8 => CTR => F6: 6 * CNT 22 HDP CHAINS / 53 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B1: 2,3 => CTR => B1: 5,6 * PRF B1: 5,6 # G1: 1,3 => SOL * STA B1: 5,6 + G1: 1,3 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 4......8....7.54.6.7..1.9.28.93.2......9.........4...1..2.9.5...8.5.....39..6...4 | initial |
| 4....9.8.9..7.54.6.7..1.9.28193.264....9.1.......4..91..2.9.5...8.5....9395.6...4 | autosolve |
| 453629187921785436678413952819372645264951378537846291742198563186534729395267814 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) B2: 2,3 A3: 5,6 D1: 2,6 E1: 2,3 H2: 1,3 H3: 3,5 B6: 3,5 C6: 3,7 E4: 5,7 D6: 6,8 I4: 5,7 B7: 4,6 F9: 7,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,C2: 1.. / C1 = 1 => 15 pairs (_) / C2 = 1 => 0 pairs (*) G1,H2: 1.. / G1 = 1 => 0 pairs (*) / H2 = 1 => 0 pairs (X) A7,A8: 1.. / A7 = 1 => 0 pairs (X) / A8 = 1 => 14 pairs (_) D7,D9: 1.. / D7 = 1 => 15 pairs (_) / D9 = 1 => 0 pairs (X) C1,G1: 1.. / C1 = 1 => 15 pairs (_) / G1 = 1 => 0 pairs (*) C2,H2: 1.. / C2 = 1 => 0 pairs (*) / H2 = 1 => 0 pairs (X) B1,B2: 2.. / B1 = 2 => 0 pairs (X) / B2 = 2 => 13 pairs (_) A5,A6: 2.. / A5 = 2 => 21 pairs (_) / A6 = 2 => 19 pairs (_) E8,D9: 2.. / E8 = 2 => 0 pairs (X) / D9 = 2 => 0 pairs (_) B2,E2: 2.. / B2 = 2 => 13 pairs (_) / E2 = 2 => 0 pairs (X) A6,G6: 2.. / A6 = 2 => 19 pairs (_) / G6 = 2 => 21 pairs (_) D1,D9: 2.. / D1 = 2 => 0 pairs (X) / D9 = 2 => 0 pairs (_) D3,F3: 4.. / D3 = 4 => 14 pairs (_) / F3 = 4 => 0 pairs (X) B5,C5: 4.. / B5 = 4 => 17 pairs (_) / C5 = 4 => 15 pairs (_) B7,C8: 4.. / B7 = 4 => 15 pairs (_) / C8 = 4 => 17 pairs (_) C8,F8: 4.. / C8 = 4 => 17 pairs (_) / F8 = 4 => 15 pairs (_) B5,B7: 4.. / B5 = 4 => 17 pairs (_) / B7 = 4 => 15 pairs (_) C5,C8: 4.. / C5 = 4 => 15 pairs (_) / C8 = 4 => 17 pairs (_) D3,D7: 4.. / D3 = 4 => 14 pairs (_) / D7 = 4 => 0 pairs (X) B1,A3: 5.. / B1 = 5 => 0 pairs (*) / A3 = 5 => 0 pairs (X) I1,H3: 5.. / I1 = 5 => 18 pairs (_) / H3 = 5 => 0 pairs (*) A6,B6: 5.. / A6 = 5 => 0 pairs (*) / B6 = 5 => 0 pairs (X) E4,E5: 5.. / E4 = 5 => 15 pairs (_) / E5 = 5 => 0 pairs (*) B1,I1: 5.. / B1 = 5 => 0 pairs (*) / I1 = 5 => 0 pairs (X) A3,H3: 5.. / A3 = 5 => 18 pairs (_) / H3 = 5 => 0 pairs (*) E4,I4: 5.. / E4 = 5 => 15 pairs (_) / I4 = 5 => 0 pairs (*) A3,A6: 5.. / A3 = 5 => 18 pairs (_) / A6 = 5 => 0 pairs (*) B1,B6: 5.. / B1 = 5 => 0 pairs (*) / B6 = 5 => 0 pairs (X) H3,H5: 5.. / H3 = 5 => 0 pairs (*) / H5 = 5 => 0 pairs (X) D6,F6: 6.. / D6 = 6 => 0 pairs (X) / F6 = 6 => 18 pairs (_) H7,H8: 6.. / H7 = 6 => 16 pairs (_) / H8 = 6 => 15 pairs (_) F3,F6: 6.. / F3 = 6 => 0 pairs (X) / F6 = 6 => 18 pairs (_) G1,I1: 7.. / G1 = 7 => 15 pairs (_) / I1 = 7 => 0 pairs (*) E4,I4: 7.. / E4 = 7 => 0 pairs (*) / I4 = 7 => 0 pairs (X) C2,C3: 8.. / C2 = 8 => 0 pairs (X) / C3 = 8 => 17 pairs (_) I7,G9: 8.. / I7 = 8 => 14 pairs (_) / G9 = 8 => 20 pairs (_) C2,E2: 8.. / C2 = 8 => 0 pairs (X) / E2 = 8 => 17 pairs (_) E2,E5: 8.. / E2 = 8 => 17 pairs (_) / E5 = 8 => 0 pairs (X) I5,I7: 8.. / I5 = 8 => 20 pairs (_) / I7 = 8 => 14 pairs (_) * DURATION: 0:00:44.994688 START: 01:26:29.166290 END: 01:27:14.160978 2019-05-01 * CP COUNT: (39) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B2,B6,B7,C6,D1,D6,E1,E4,F9,H2,H3,I4) * 4....9.8.9..7.54.6.7..1.9.28193.264....9.1.......4..91..2.9.5...8.5....9395.6...4 * PAIR B2: 2,3 BLK 1 B1: 2,3,5,6 # reduction candidate for 2,3 B1: 2,3 => CTR * 4.16.97859.87.5416576418932819352647...9.1.5..5.846.91..2.9.5...8.5....939526.174 B1: 5,6 # 25 pairs * PAIR B2: 2,3 ROW 2 E2: 2,3,8 # reduction candidate for 2,3 E2: 2,3 => CTR * 4....9.8.9.87.5416.7..1.9.28193.264....981......647891..2.9.5.8.8.57...939526...4 E2: 8 # 17 pairs * PAIR A3: 5,6 BLK 1 B1: 5,6,2,3 # reduction candidate for 5,6 B1: 2,3 => CTR * 4.16.97859.87.5416576418932819352647...9.1.5..5.846.91..2.9.5...8.5....939526.174 B1: 5,6 # 25 pairs * PAIR D1: 2,6 ROW 1 B1: 2,6,3,5 # reduction candidate for 2,6 B1: 2,6 # 19 pairs B1: 3,5 # 15 pairs * PAIR E1: 2,3 BLK 2 E2: 2,3,8 # reduction candidate for 2,3 E2: 2,3 => CTR * 4....9.8.9.87.5416.7..1.9.28193.264....981......647891..2.9.5.8.8.57...939526...4 E2: 8 # 17 pairs * PAIR E1: 2,3 ROW 1 B1: 2,3,5,6 # reduction candidate for 2,3 B1: 2,3 => CTR * 4.16.97859.87.5416576418932819352647...9.1.5..5.846.91..2.9.5...8.5....939526.174 B1: 5,6 # 25 pairs * PAIR E1: 2,3 COL E E8: 2,3,7 # reduction candidate for 2,3 E8: 7 => CTR * 4..6.9.8.9..7.54.6.7..1.9.281935264....9.1.......4..91..2.9.5...8.57...9395268..4 E8: 2,3 # 17 pairs * PAIR H2: 1,3 BLK 3 G1: 1,3,7 # reduction candidate for 1,3 G1: 1,3 => SOLVED * 453629187921785436678413952819372645264951378537846291742198563186534729395267814 G1: 7 # 15 pairs * PAIR H2: 1,3 ROW 2 C2: 1,3,8 # reduction candidate for 1,3 C2: 8 => CTR * 4.1..9.8.9.87.5416.7..1.9.28193.264....981......647891..2.9.5.8.8.57...939526...4 C2: 1,3 # 17 pairs * PAIR H2: 1,3 COL H H7: 1,3,6,7 # reduction candidate for 1,3 H7: 1,3 => CTR * 45.239.8792.78543667..1.9528193.264....9.1...537.4.291..2.9.5...8452..69395.6..24 H7: 6,7 # 14 pairs H8: 1,3,2,6,7 # reduction candidate for 1,3 H8: 1,3 => CTR * 45...9.8.9..7.54.6.7.41.9528193.264...49.1...537.4.291.42.9.56..86524..9395.6..24 H8: 2,6,7 # 13 pairs * PAIR H3: 3,5 BLK 3 I1: 3,5,7 # reduction candidate for 3,5 I1: 7 => SOLVED * 453629187921785436678413952819372645264951378537846291742198563186534729395267814 I1: 3,5 # 15 pairs * PAIR H3: 3,5 COL H H5: 3,5,2,7 # reduction candidate for 3,5 H5: 2,7 => SOLVED * 453629187921785436678413952819372645264951378537846291742198563186534729395267814 H5: 3,5 # 20 pairs * PAIR B6: 3,5 COL B B1: 3,5,2,6 # reduction candidate for 3,5 B1: 2,6 # 19 pairs B1: 3,5 # 15 pairs * PAIR C6: 3,7 BLK 4 C5: 3,7,4,6 # reduction candidate for 3,7 C5: 3,7 => CTR * 4..239.859..7.54.657..1.93281935264764.9.1.5.25..4..91.62.9.5...845...69395.6..24 C5: 4,6 # 14 pairs * PAIR C6: 3,7 ROW 6 G6: 3,7,2,8 # reduction candidate for 3,7 G6: 3,7 => CTR * 4.1239785923785416578.1.9328193526476..9.1258257.4.391..2.9.5.3.845.31.9395167824 G6: 2,8 # 15 pairs * PAIR E4: 5,7 BLK 5 E5: 5,7,8 # reduction candidate for 5,7 E5: 8 => CTR * 4....9.8.9..7.54.6.7..1.9.2819352647...981......647891..2.9.5.8.8.57...939526...4 E5: 5,7 # 17 pairs * PAIR D6: 6,8 BLK 5 F6: 6,8,7 # reduction candidate for 6,8 F6: 7 => CTR * 4....9.8.9..7.54.6.7..169.28193.264....9.1......647891..2.9.5.8.8.57...939526...4 F6: 6,8 # 17 pairs * PAIR D6: 6,8 COL D D3: 6,8,4 # reduction candidate for 6,8 D3: 6,8 => CTR * 4..239.8.92.7854.6.786149328193.264..4.9.1.5..37846291.6249.5...8452..6939516..24 D3: 4 # 14 pairs * PAIR I4: 5,7 BLK 6 H5: 5,7,2,3 # reduction candidate for 5,7 H5: 5,7 # 15 pairs I5: 5,7,3,8 # reduction candidate for 5,7 I5: 5,7 => CTR * 45162978392.7.541667..1.9528193.264.2..9.183.537846291..2.935.8.8.57...9395.6...4 I5: 3,8 # 14 pairs * PAIR I4: 5,7 COL I I1: 5,7,3 # reduction candidate for 5,7 I1: 3 => CTR * 45162978392.7854166784139528193.264.2..9.183.537846291..2.9.5...8.5...2939526.174 I1: 5,7 # 16 pairs * PAIR B7: 4,6 BLK 7 C8: 4,6,7 # reduction candidate for 4,6 C8: 7 => CTR * 4.1..9.859..7.54.657.41.932819352647.64971.5.753.4.291.42.93578.87524369395.67124 C8: 4,6 # 18 pairs * PAIR B7: 4,6 COL B B5: 4,6,3 # reduction candidate for 4,6 B5: 3 => CTR * 46.239.8592.7854.6578416932819352647634971.58257648391.428935...865.4..9395.6...4 B5: 4,6 # 14 pairs * PAIR F9: 7,8 BLK 8 F7: 7,8,3,4 # reduction candidate for 7,8 F7: 7,8 # 20 pairs F7: 3,4 # 14 pairs * PAIR F9: 7,8 ROW 9 G9: 7,8,1,2 # reduction candidate for 7,8 G9: 7,8 # 16 pairs G9: 1,2 # 15 pairs * PAIR F9: 7,8 COL F F6: 7,8,6 # reduction candidate for 7,8 F6: 7,8 => CTR * 461239785923785416578416932819352647.34971.58.57648391.4289.5...8.52...9395.67.24 F6: 6 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060731-absurd-base-pr-000.dot * REASONING * DIS # B1: 2,3 => CTR => B1: 5,6 * DIS # E2: 2,3 => CTR => E2: 8 * DIS # B1: 2,3 => CTR => B1: 5,6 * DIS # E2: 2,3 => CTR => E2: 8 * DIS # B1: 2,3 => CTR => B1: 5,6 * DIS # E8: 7 => CTR => E8: 2,3 * PRF # G1: 1,3 => SOL * DIS # C2: 8 => CTR => C2: 1,3 * DIS # H7: 1,3 => CTR => H7: 6,7 * DIS # H8: 1,3 => CTR => H8: 2,6,7 * PRF # I1: 7 => SOL * PRF # H5: 2,7 => SOL * DIS # C5: 3,7 => CTR => C5: 4,6 * DIS # G6: 3,7 => CTR => G6: 2,8 * DIS # E5: 8 => CTR => E5: 5,7 * DIS # F6: 7 => CTR => F6: 6,8 * DIS # D3: 6,8 => CTR => D3: 4 * DIS # I5: 5,7 => CTR => I5: 3,8 * DIS # I1: 3 => CTR => I1: 5,7 * DIS # C8: 7 => CTR => C8: 4,6 * DIS # B5: 3 => CTR => B5: 4,6 * DIS # F6: 7,8 => CTR => F6: 6 * CNT 22 HDP CHAINS / 53 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B2,B6,B7,C6,D1,D6,E1,E4,F9,H2,H3,I4) * 4....9.8.9..7.54.6.7..1.9.28193.264....9.1.......4..91..2.9.5...8.5....9395.6...4 * PAIR B2: 2,3 BLK 1 B1: 2,3,5,6 # reduction candidate for 2,3 B1: 2,3 => CTR * 4.16.97859.87.5416576418932819352647...9.1.5..5.846.91..2.9.5...8.5....939526.174 * PAIR H2: 1,3 BLK 3 G1: 1,3,7 # reduction candidate for 1,3 G1: 1,3 => SOLVED * 453629187921785436678413952819372645264951378537846291742198563186534729395267814 * DURATION: 0:00:03.381754 START: 01:27:45.190111 END: 01:27:48.571865 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060731-absurd-base-pr-001.dot * REASONING * DIS # B1: 2,3 => CTR => B1: 5,6 * PRF B1: 5,6 # G1: 1,3 => SOL * STA B1: 5,6 + G1: 1,3 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060731, absurd
Solution
position: 453629187921785436678413952819372645264951378537846291742198563186534729395267814 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 # B1: 2,3 => CTR => B1: 5,6 * INC # B1: 5,6 => UNS * DIS # E2: 2,3 => CTR => E2: 8 * INC # E2: 8 => UNS * INC # B1: 5,6 => UNS * DIS # B1: 2,3 => CTR => B1: 5,6 * INC # B1: 2,6 => UNS * INC # B1: 3,5 => UNS * DIS # E2: 2,3 => CTR => E2: 8 * INC # E2: 8 => UNS * DIS # B1: 2,3 => CTR => B1: 5,6 * INC # B1: 5,6 => UNS * INC # E8: 2,3 => UNS * DIS # E8: 7 => CTR => E8: 2,3 * PRF # G1: 1,3 => SOL * INC # G1: 7 => UNS * INC # C2: 1,3 => UNS * DIS # C2: 8 => CTR => C2: 1,3 * DIS # H7: 1,3 => CTR => H7: 6,7 * INC # H7: 6,7 => UNS * DIS # H8: 1,3 => CTR => H8: 2,6,7 * INC # H8: 2,6,7 => UNS * INC # I1: 3,5 => UNS * PRF # I1: 7 => SOL * INC # H5: 3,5 => UNS * PRF # H5: 2,7 => SOL * INC # B1: 3,5 => UNS * INC # B1: 2,6 => UNS * DIS # C5: 3,7 => CTR => C5: 4,6 * INC # C5: 4,6 => UNS * DIS # G6: 3,7 => CTR => G6: 2,8 * INC # G6: 2,8 => UNS * INC # E5: 5,7 => UNS * DIS # E5: 8 => CTR => E5: 5,7 * INC # F6: 6,8 => UNS * DIS # F6: 7 => CTR => F6: 6,8 * DIS # D3: 6,8 => CTR => D3: 4 * INC # D3: 4 => UNS * INC # H5: 5,7 => UNS * DIS # I5: 5,7 => CTR => I5: 3,8 * INC # I5: 3,8 => UNS * INC # I1: 5,7 => UNS * DIS # I1: 3 => CTR => I1: 5,7 * INC # C8: 4,6 => UNS * DIS # C8: 7 => CTR => C8: 4,6 * INC # B5: 4,6 => UNS * DIS # B5: 3 => CTR => B5: 4,6 * INC # F7: 7,8 => UNS * INC # F7: 3,4 => UNS * INC # G9: 7,8 => UNS * INC # G9: 1,2 => UNS * DIS # F6: 7,8 => CTR => F6: 6 * INC # F6: 6 => UNS * CNT 53 HDP CHAINS / 53 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B1: 2,3 => CTR => B1: 5,6 * PRF B1: 5,6 # G1: 1,3 => SOL * STA B1: 5,6 + G1: 1,3 * CNT 2 HDP CHAINS / 2 HYP OPENED