Analysis of zz-www.sudokuoftheday.co.uk-20190325-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019
level: medium
position: 43.7....5......8..8.9....3..2.......6.4.....118...674..6.5.9........3..8.926..... initial
Autosolve
position: 4367....52.....8..8.9....3.92.......6.4.....118...674..685.9...541273..8.926..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 5,7 => CTR => B2: 1 * PRF # C4: 3 => SOL * DIS # D2: 1,4 => CTR => D2: 3,9 * DIS # E2: 1,4 => CTR => E2: 3,5,6,9 * DIS # E3: 1,4 => CTR => E3: 2,5,6 * DIS # F3: 1,4 => CTR => F3: 2,5 * DIS # D4: 3,8 => CTR => D4: 1,4 * PRF # C4: 3 => SOL * DIS # F5: 2 => CTR => F5: 5,7 * DIS # B2: 5,7 => CTR => B2: 1 * DIS # C4: 7 => CTR => C4: 3,5 * PRF # E6: 2,9 => SOL * DIS # D5: 3,9 => CTR => D5: 8 * DIS # E6: 3,9 => CTR => E6: 2,5 * PRF # I6: 3,9 => SOL * DIS # D2: 1,4 => CTR => D2: 3,9 * DIS # E9: 1,4 => CTR => E9: 8 * DIS # E2: 1,4 => CTR => E2: 3,5,6,9 * DIS # E3: 1,4 => CTR => E3: 2,5,6 * DIS # H2: 1,7 => CTR => H2: 6,9 * CNT 20 HDP CHAINS / 56 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B2: 5,7 => CTR => B2: 1 * PRF B2: 1 # C4: 3 => SOL * STA B2: 1 + C4: 3 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 43.7....5......8..8.9....3..2.......6.4.....118...674..6.5.9........3..8.926..... | initial |
| 4367....52.....8..8.9....3.92.......6.4.....118...674..685.9...541273..8.926..... | autosolve |
| 436798215217354869859162437923417586674835921185926743368549172541273698792681354 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) C2: 5,7 D3: 1,4 B5: 5,7 C6: 3,5 D6: 3,9 I4: 3,6 A7: 3,7 A9: 3,7 E7: 1,4 G8: 6,9 H8: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,B3: 1.. / B2 = 1 => 13 pairs (_) / B3 = 1 => 0 pairs (X) E6,I6: 2.. / E6 = 2 => 0 pairs (*) / I6 = 2 => 0 pairs (X) D2,E2: 3.. / D2 = 3 => 18 pairs (_) / E2 = 3 => 12 pairs (_) C4,C6: 3.. / C4 = 3 => 0 pairs (*) / C6 = 3 => 0 pairs (X) A7,A9: 3.. / A7 = 3 => 11 pairs (_) / A9 = 3 => 11 pairs (_) G9,H9: 5.. / G9 = 5 => 0 pairs (X) / H9 = 5 => 12 pairs (_) C6,E6: 5.. / C6 = 5 => 0 pairs (*) / E6 = 5 => 0 pairs (X) E2,E3: 6.. / E2 = 6 => 0 pairs (X) / E3 = 6 => 11 pairs (_) G8,H8: 6.. / G8 = 6 => 11 pairs (_) / H8 = 6 => 11 pairs (_) C4,B5: 7.. / C4 = 7 => 0 pairs (X) / B5 = 7 => 25 pairs (_) F4,F5: 7.. / F4 = 7 => 25 pairs (_) / F5 = 7 => 0 pairs (X) A7,A9: 7.. / A7 = 7 => 11 pairs (_) / A9 = 7 => 11 pairs (_) B3,I3: 7.. / B3 = 7 => 0 pairs (X) / I3 = 7 => 13 pairs (_) C4,F4: 7.. / C4 = 7 => 0 pairs (X) / F4 = 7 => 25 pairs (_) B5,F5: 7.. / B5 = 7 => 25 pairs (_) / F5 = 7 => 0 pairs (X) C2,C4: 7.. / C2 = 7 => 25 pairs (_) / C4 = 7 => 0 pairs (X) E1,F1: 8.. / E1 = 8 => 0 pairs (X) / F1 = 8 => 12 pairs (_) D4,D5: 8.. / D4 = 8 => 0 pairs (X) / D5 = 8 => 11 pairs (_) H4,H5: 8.. / H4 = 8 => 11 pairs (_) / H5 = 8 => 0 pairs (X) E9,F9: 8.. / E9 = 8 => 12 pairs (_) / F9 = 8 => 0 pairs (X) D4,H4: 8.. / D4 = 8 => 0 pairs (X) / H4 = 8 => 11 pairs (_) D5,H5: 8.. / D5 = 8 => 11 pairs (_) / H5 = 8 => 0 pairs (X) E1,E9: 8.. / E1 = 8 => 0 pairs (X) / E9 = 8 => 12 pairs (_) F1,F9: 8.. / F1 = 8 => 12 pairs (_) / F9 = 8 => 0 pairs (X) G8,H8: 9.. / G8 = 9 => 11 pairs (_) / H8 = 9 => 11 pairs (_) I2,I6: 9.. / I2 = 9 => 20 pairs (_) / I6 = 9 => 0 pairs (X) * DURATION: 0:00:24.748918 START: 04:47:43.216969 END: 04:48:07.965887 2019-05-01 * CP COUNT: (26) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A9,B5,C2,C6,D3,D6,E7,G8,H8,I4) * 4367....52.....8..8.9....3.92.......6.4.....118...674..685.9...541273..8.926..... * PAIR C2: 5,7 BLK 1 B2: 5,7,1 # reduction candidate for 5,7 B2: 5,7 => CTR * 4367....52...3.864819465237923..7..66.4.....118.3267493685.9.72541273..87926....3 B2: 1 # 13 pairs B3: 5,7,1 # reduction candidate for 5,7 B3: 5,7 # 13 pairs * PAIR C2: 5,7 COL C C4: 5,7,3 # reduction candidate for 5,7 C4: 3 => SOLVED * 436798215217354869859162437923417586674835921185926743368549172541273698792681354 C4: 5,7 # 22 pairs * PAIR D3: 1,4 BLK 2 D2: 1,4,3,9 # reduction candidate for 1,4 D2: 1,4 => CTR * 436798..52...358..859.62.3792.......674.....118...674..685.9...541273..8.9268.... D2: 3,9 # 13 pairs E2: 1,4,3,5,6,9 # reduction candidate for 1,4 E2: 1,4 => CTR * 436798..52..3.5869859.62.3792.....866748....118.9.674..685.9...541273698.9268.... E2: 3,5,6,9 # 11 pairs F2: 1,4,5 # reduction candidate for 1,4 F2: 1,4 # 16 pairs E3: 1,4,2,5,6 # reduction candidate for 1,4 E3: 1,4 => CTR * 436798..52..36.8.98.9..2.3.92.......6.48....118.9.674..685.9...541273..8.9268.... E3: 2,5,6 # 11 pairs F3: 1,4,2,5 # reduction candidate for 1,4 F3: 1,4 => CTR * 4367....521...58.4859....3792.....866748.2..118...674..685.9...541273..8.926..... F3: 2,5 # 12 pairs * PAIR D3: 1,4 ROW 3 G3: 1,4,2,6 # reduction candidate for 1,4 G3: 1,4 # 15 pairs G3: 2,6 # 14 pairs * PAIR D3: 1,4 COL D D4: 1,4,3,8 # reduction candidate for 1,4 D4: 3,8 => CTR * 4367....52....58..859..2.3792.......674.....118...674..685.9...541273..8.926..... D4: 1,4 # 13 pairs * PAIR B5: 5,7 BLK 4 C4: 5,7,3 # reduction candidate for 5,7 C4: 3 => SOLVED * 436798215217354869859162437923417586674835921185926743368549172541273698792681354 C4: 5,7 # 22 pairs * PAIR B5: 5,7 ROW 5 F5: 5,7,2 # reduction candidate for 5,7 F5: 2 => CTR * 436798..52.7...8.98.9.2..3792...7..6674..2..118...6742.685.9...541273..8.926..... F5: 5,7 # 13 pairs * PAIR B5: 5,7 COL B B2: 5,7,1 # reduction candidate for 5,7 B2: 5,7 => CTR * 4367....52...3.864819465237923..7..66.4.....118.3267493685.9.72541273..87926....3 B2: 1 # 13 pairs B3: 5,7,1 # reduction candidate for 5,7 B3: 5,7 # 13 pairs * PAIR C6: 3,5 BLK 4 C4: 3,5,7 # reduction candidate for 3,5 C4: 7 => CTR * 43679...52.5...8.98.9..5.3.927......654.27..1183956742.685.9...541273..8.926..... C4: 3,5 # 25 pairs * PAIR C6: 3,5 ROW 6 E6: 3,5,2,9 # reduction candidate for 3,5 E6: 2,9 => SOLVED * 436798215217354869859162437923417586674835921185926743368549172541273698792681354 E6: 3,5 # 20 pairs * PAIR D6: 3,9 BLK 5 D5: 3,9,8 # reduction candidate for 3,9 D5: 3,9 => CTR * 4367....52....58..859..2.3792.8.....674....8118...674..685.9...541273..8.926..... D5: 8 # 11 pairs E5: 3,9,2,5 # reduction candidate for 3,9 E5: 3,9 # 15 pairs E6: 3,9,2,5 # reduction candidate for 3,9 E6: 3,9 => CTR * 4367....52.7...8.98.9....37923..7..6674...391185936742.685.9...541273968.926..... E6: 2,5 # 12 pairs * PAIR D6: 3,9 ROW 6 I6: 3,9,2 # reduction candidate for 3,9 I6: 3,9 => SOLVED * 436798215217354869859162437923417586674835921185926743368549172541273698792681354 I6: 2 # 20 pairs * PAIR D6: 3,9 COL D D2: 3,9,1,4 # reduction candidate for 3,9 D2: 1,4 => CTR * 436798..52...358..859.62.3792.......674.....118...674..685.9...541273..8.9268.... D2: 3,9 # 13 pairs * PAIR I4: 3,6 BLK 6 G4: 3,6,5 # reduction candidate for 3,6 G4: 3,6 # 28 pairs G4: 5 # 13 pairs * PAIR A7: 3,7 ROW 7 I7: 3,7,2,4 # reduction candidate for 3,7 I7: 3,7 # 13 pairs I7: 2,4 # 12 pairs * PAIR A9: 3,7 ROW 9 I9: 3,7,4 # reduction candidate for 3,7 I9: 4 # 17 pairs I9: 3,7 # 13 pairs * PAIR E7: 1,4 BLK 8 E9: 1,4,8 # reduction candidate for 1,4 E9: 1,4 => CTR * 43678...52...3.8..8.9.6..3.923.57...6.4.....118.326749.685.9...541273..8.926.8... E9: 8 # 12 pairs F9: 1,4,8 # reduction candidate for 1,4 F9: 1,4 # 12 pairs * PAIR E7: 1,4 ROW 7 G7: 1,4,2,3 # reduction candidate for 1,4 G7: 1,4 # 13 pairs G7: 2,3 # 12 pairs * PAIR E7: 1,4 COL E E2: 1,4,3,5,6,9 # reduction candidate for 1,4 E2: 1,4 => CTR * 436798..52..3.5869859.62.3792.....866748....118.9.674..685.9...541273698.9268.... E2: 3,5,6,9 # 11 pairs E3: 1,4,2,5,6 # reduction candidate for 1,4 E3: 1,4 => CTR * 436798..52..36.8.98.9..2.3.92.......6.48....118.9.674..685.9...541273..8.9268.... E3: 2,5,6 # 11 pairs E4: 1,4,3,5 # reduction candidate for 1,4 E4: 1,4 # 14 pairs * PAIR H8: 6,9 COL H H2: 6,9,1,7 # reduction candidate for 6,9 H2: 1,7 => CTR * 4367....52153.48798791.5.3.9274.15866548273.1183956742.685.9...541273968.926...5. H2: 6,9 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190325-absurd-base-pr-000.dot * REASONING * DIS # B2: 5,7 => CTR => B2: 1 * PRF # C4: 3 => SOL * DIS # D2: 1,4 => CTR => D2: 3,9 * DIS # E2: 1,4 => CTR => E2: 3,5,6,9 * DIS # E3: 1,4 => CTR => E3: 2,5,6 * DIS # F3: 1,4 => CTR => F3: 2,5 * DIS # D4: 3,8 => CTR => D4: 1,4 * PRF # C4: 3 => SOL * DIS # F5: 2 => CTR => F5: 5,7 * DIS # B2: 5,7 => CTR => B2: 1 * DIS # C4: 7 => CTR => C4: 3,5 * PRF # E6: 2,9 => SOL * DIS # D5: 3,9 => CTR => D5: 8 * DIS # E6: 3,9 => CTR => E6: 2,5 * PRF # I6: 3,9 => SOL * DIS # D2: 1,4 => CTR => D2: 3,9 * DIS # E9: 1,4 => CTR => E9: 8 * DIS # E2: 1,4 => CTR => E2: 3,5,6,9 * DIS # E3: 1,4 => CTR => E3: 2,5,6 * DIS # H2: 1,7 => CTR => H2: 6,9 * CNT 20 HDP CHAINS / 56 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A9,B5,C2,C6,D3,D6,E7,G8,H8,I4) * 4367....52.....8..8.9....3.92.......6.4.....118...674..685.9...541273..8.926..... * PAIR C2: 5,7 BLK 1 B2: 5,7,1 # reduction candidate for 5,7 B2: 5,7 => CTR * 4367....52...3.864819465237923..7..66.4.....118.3267493685.9.72541273..87926....3 * RESTART * PAIR C2: 5,7 COL C C4: 5,7,3 # reduction candidate for 5,7 C4: 3 => SOLVED * 436798215217354869859162437923417586674835921185926743368549172541273698792681354 * DURATION: 0:00:03.063116 START: 04:48:37.782229 END: 04:48:40.845345 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190325-absurd-base-pr-001.dot * REASONING * DIS # B2: 5,7 => CTR => B2: 1 * PRF B2: 1 # C4: 3 => SOL * STA B2: 1 + C4: 3 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190325, absurd
Solution
position: 436798215217354869859162437923417586674835921185926743368549172541273698792681354 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 # B2: 5,7 => CTR => B2: 1 * INC # B2: 1 => UNS * INC # B3: 5,7 => UNS * INC # C4: 5,7 => UNS * PRF # C4: 3 => SOL * DIS # D2: 1,4 => CTR => D2: 3,9 * INC # D2: 3,9 => UNS * DIS # E2: 1,4 => CTR => E2: 3,5,6,9 * INC # E2: 3,5,6,9 => UNS * INC # F2: 1,4 => UNS * DIS # E3: 1,4 => CTR => E3: 2,5,6 * INC # E3: 2,5,6 => UNS * DIS # F3: 1,4 => CTR => F3: 2,5 * INC # F3: 2,5 => UNS * INC # G3: 1,4 => UNS * INC # G3: 2,6 => UNS * INC # D4: 1,4 => UNS * DIS # D4: 3,8 => CTR => D4: 1,4 * INC # C4: 5,7 => UNS * PRF # C4: 3 => SOL * INC # F5: 5,7 => UNS * DIS # F5: 2 => CTR => F5: 5,7 * DIS # B2: 5,7 => CTR => B2: 1 * INC # B2: 1 => UNS * INC # B3: 5,7 => UNS * INC # C4: 3,5 => UNS * DIS # C4: 7 => CTR => C4: 3,5 * INC # E6: 3,5 => UNS * PRF # E6: 2,9 => SOL * DIS # D5: 3,9 => CTR => D5: 8 * INC # D5: 8 => UNS * INC # E5: 3,9 => UNS * DIS # E6: 3,9 => CTR => E6: 2,5 * INC # E6: 2,5 => UNS * PRF # I6: 3,9 => SOL * INC # I6: 2 => UNS * INC # D2: 3,9 => UNS * DIS # D2: 1,4 => CTR => D2: 3,9 * INC # G4: 3,6 => UNS * INC # G4: 5 => UNS * INC # I7: 3,7 => UNS * INC # I7: 2,4 => UNS * INC # I9: 3,7 => UNS * INC # I9: 4 => UNS * DIS # E9: 1,4 => CTR => E9: 8 * INC # E9: 8 => UNS * INC # F9: 1,4 => UNS * INC # G7: 1,4 => UNS * INC # G7: 2,3 => UNS * DIS # E2: 1,4 => CTR => E2: 3,5,6,9 * INC # E2: 3,5,6,9 => UNS * DIS # E3: 1,4 => CTR => E3: 2,5,6 * INC # E3: 2,5,6 => UNS * INC # E4: 1,4 => UNS * INC # H2: 6,9 => UNS * DIS # H2: 1,7 => CTR => H2: 6,9 * CNT 56 HDP CHAINS / 56 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B2: 5,7 => CTR => B2: 1 * INC B2: 1 # C4: 5,7 => UNS * PRF B2: 1 # C4: 3 => SOL * STA B2: 1 + C4: 3 * CNT 3 HDP CHAINS / 3 HYP OPENED