Analysis of zz-www.sudokuoftheday.co.uk-20190328-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: ..1.3.94.........39....1.2.5.......6..3.9.2....41.....8.9.........42...54..8...61 initial
Autosolve
position: ..1.3.94..4.9....393..41.2.59...4..61.3.9.2.4..41....98.9.1.47231.42.8954..8.9361 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G2: 6 => CTR => G2: 1,5 * DIS # G2: 1 => CTR => G2: 5,6 * DIS # C4: 2 => CTR => C4: 7,8 * DIS # E2: 7,8 => CTR => E2: 5,6 * DIS # H6: 3 => CTR => H6: 5,8 * DIS # E6: 5,7 => CTR => E6: 6,8 * DIS # D7: 5,6 => CTR => D7: 3 * DIS # B1: 5,6 => CTR => B1: 2,7,8 * DIS # E2: 5,7 => CTR => E2: 6,8 * DIS # E6: 5,7 => CTR => E6: 6,8 * CNT 10 HDP CHAINS / 38 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # G2: 6 => CTR => G2: 1,5 * DIS G2: 1,5 # C3: 7,8 => CTR => C3: 5 * DIS G2: 1,5 + C3: 5 # C4: 2 => CTR => C4: 7,8 * PRF G2: 1,5 + C3: 5 + C4: 7,8 # F5: 5 => SOL * STA G2: 1,5 + C3: 5 + C4: 7,8 + F5: 5 * CNT 4 HDP CHAINS / 11 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..1.3.94.........39....1.2.5.......6..3.9.2....41.....8.9.........42...54..8...61 | initial |
| ..1.3.94..4.9....393..41.2.59...4..61.3.9.2.4..41....98.9.1.47231.42.8954..8.9361 | autosolve |
| 681532947742968513935741628598274136173695284264183759859316472316427895427859361 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) I1: 7,8 H2: 1,5 G3: 5,6 I3: 7,8 D4: 2,3 E4: 7,8 F6: 2,3 G4: 1,7 H5: 5,8 G6: 5,7 B7: 5,6 C8: 6,7 F8: 6,7 E9: 5,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G2,H2: 1.. / G2 = 1 => 0 pairs (X) / H2 = 1 => 14 pairs (_) G4,H4: 1.. / G4 = 1 => 14 pairs (_) / H4 = 1 => 0 pairs (X) G2,G4: 1.. / G2 = 1 => 0 pairs (X) / G4 = 1 => 14 pairs (_) H2,H4: 1.. / H2 = 1 => 14 pairs (_) / H4 = 1 => 0 pairs (X) D4,F6: 2.. / D4 = 2 => 14 pairs (_) / F6 = 2 => 0 pairs (X) B9,C9: 2.. / B9 = 2 => 16 pairs (_) / C9 = 2 => 16 pairs (_) C4,D4: 2.. / C4 = 2 => 0 pairs (X) / D4 = 2 => 14 pairs (_) D1,D4: 2.. / D1 = 2 => 0 pairs (X) / D4 = 2 => 14 pairs (_) D4,F6: 3.. / D4 = 3 => 0 pairs (X) / F6 = 3 => 14 pairs (_) H4,H6: 3.. / H4 = 3 => 14 pairs (_) / H6 = 3 => 0 pairs (X) D7,F7: 3.. / D7 = 3 => 14 pairs (_) / F7 = 3 => 0 pairs (X) D4,H4: 3.. / D4 = 3 => 0 pairs (X) / H4 = 3 => 14 pairs (_) F6,H6: 3.. / F6 = 3 => 14 pairs (_) / H6 = 3 => 0 pairs (X) D4,D7: 3.. / D4 = 3 => 0 pairs (X) / D7 = 3 => 14 pairs (_) F6,F7: 3.. / F6 = 3 => 14 pairs (_) / F7 = 3 => 0 pairs (X) G2,G3: 6.. / G2 = 6 => 0 pairs (X) / G3 = 6 => 15 pairs (_) B7,C8: 6.. / B7 = 6 => 0 pairs (X) / C8 = 6 => 22 pairs (_) C8,F8: 6.. / C8 = 6 => 22 pairs (_) / F8 = 6 => 0 pairs (X) E2,E6: 6.. / E2 = 6 => 22 pairs (_) / E6 = 6 => 0 pairs (X) I1,I3: 7.. / I1 = 7 => 13 pairs (_) / I3 = 7 => 14 pairs (_) G4,G6: 7.. / G4 = 7 => 0 pairs (X) / G6 = 7 => 14 pairs (_) F8,E9: 7.. / F8 = 7 => 22 pairs (_) / E9 = 7 => 0 pairs (X) C8,F8: 7.. / C8 = 7 => 0 pairs (X) / F8 = 7 => 22 pairs (_) I1,I3: 8.. / I1 = 8 => 14 pairs (_) / I3 = 8 => 13 pairs (_) C3,I3: 8.. / C3 = 8 => 14 pairs (_) / I3 = 8 => 13 pairs (_) * DURATION: 0:00:31.194597 START: 04:52:16.974728 END: 04:52:48.169325 2019-05-01 * CP COUNT: (25) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,C8,D4,E4,E9,F6,F8,G3,G4,G6,H2,H5,I1,I3) * ..1.3.94..4.9....393..41.2.59...4..61.3.9.2.4..41....98.9.1.47231.42.8954..8.9361 * PAIR I1: 7,8 ROW 1 B1: 7,8,2,5,6 # reduction candidate for 7,8 B1: 7,8 # 18 pairs F1: 7,8,2,5,6 # reduction candidate for 7,8 F1: 7,8 # 17 pairs * PAIR H2: 1,5 BLK 3 G2: 1,5,6 # reduction candidate for 1,5 G2: 6 => CTR * 6.1.3.94.74.9..61393864152759...4136163.9.284284163759859316472316427895472859361 G2: 1,5 # 15 pairs * PAIR G3: 5,6 BLK 3 G2: 5,6,1 # reduction candidate for 5,6 G2: 1 => CTR * ..123.94..4.9..15393574162859.3847161.3.9.284.841725398596134723164278954..859361 G2: 5,6 # 14 pairs * PAIR G3: 5,6 ROW 3 C3: 5,6,7,8 # reduction candidate for 5,6 C3: 5,6 # 15 pairs D3: 5,6,7 # reduction candidate for 5,6 D3: 5,6 # 16 pairs * PAIR I3: 7,8 ROW 3 C3: 7,8,5,6 # reduction candidate for 7,8 C3: 7,8 # 16 pairs C3: 5,6 # 15 pairs * PAIR E4: 7,8 BLK 5 F5: 7,8,5,6 # reduction candidate for 7,8 F5: 7,8 # 18 pairs E6: 7,8,5,6 # reduction candidate for 7,8 E6: 7,8 # 22 pairs * PAIR E4: 7,8 ROW 4 C4: 7,8,2 # reduction candidate for 7,8 C4: 2 => CTR * .712359482459....3938.41.275923847161.379.284.841.25398.9.1347231.42.89542.8.9361 C4: 7,8 # 14 pairs * PAIR E4: 7,8 COL E E2: 7,8,5,6 # reduction candidate for 7,8 E2: 7,8 => CTR * ..153.94..4.97...393.64152.59.284.361637952842841637598593164723164278954..859361 E2: 5,6 # 16 pairs * PAIR H5: 5,8 BLK 6 H6: 5,8,3 # reduction candidate for 5,8 H6: 3 => CTR * .712359482459....3938.41.275923847161.379.284.841.25398.9.1347231.42.89542.8.9361 H6: 5,8 # 14 pairs * PAIR H5: 5,8 ROW 5 F5: 5,8,6,7 # reduction candidate for 5,8 F5: 5,8 # 17 pairs F5: 6,7 # 16 pairs * PAIR G6: 5,7 ROW 6 E6: 5,7,6,8 # reduction candidate for 5,7 E6: 5,7 => CTR * .61.3894774896215393574162859..84716173.9.284.8417.539859.13472316427895427859361 E6: 6,8 # 17 pairs * PAIR B7: 5,6 ROW 7 D7: 5,6,3 # reduction candidate for 5,6 D7: 5,6 => CTR * .712359482459....3938.41.275923847161.379.284.841.25398.9.1347231.42.89542.8.9361 D7: 3 # 14 pairs F7: 5,6,3 # reduction candidate for 5,6 F7: 5,6 # 14 pairs * PAIR B7: 5,6 COL B B1: 5,6,2,7,8 # reduction candidate for 5,6 B1: 5,6 => CTR * 261.3.94.748962..393574162859.2.4.36173.9.2.46.41....9859.1.4723164278954..859361 B1: 2,7,8 # 16 pairs * PAIR C8: 6,7 COL C C2: 6,7,2,5,8 # reduction candidate for 6,7 C2: 6,7 # 20 pairs C3: 6,7,5,8 # reduction candidate for 6,7 C3: 6,7 # 19 pairs * PAIR F8: 6,7 COL F F1: 6,7,2,5,8 # reduction candidate for 6,7 F1: 6,7 # 19 pairs F2: 6,7,2,5,8 # reduction candidate for 6,7 F2: 6,7 # 20 pairs F5: 6,7,5,8 # reduction candidate for 6,7 F5: 6,7 # 16 pairs * PAIR E9: 5,7 ROW 9 B9: 5,7,2 # reduction candidate for 5,7 B9: 5,7 # 16 pairs C9: 5,7,2 # reduction candidate for 5,7 C9: 5,7 # 16 pairs * PAIR E9: 5,7 COL E E2: 5,7,6,8 # reduction candidate for 5,7 E2: 5,7 => CTR * ..153.94..4.97...393.64152.59.284.361637952842841637598593164723164278954..859361 E2: 6,8 # 15 pairs E6: 5,7,6,8 # reduction candidate for 5,7 E6: 5,7 => CTR * .61.3894774896215393574162859..84716173.9.284.8417.539859.13472316427895427859361 E6: 6,8 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190328-absurd-base-pr-000.dot * REASONING * DIS # G2: 6 => CTR => G2: 1,5 * DIS # G2: 1 => CTR => G2: 5,6 * DIS # C4: 2 => CTR => C4: 7,8 * DIS # E2: 7,8 => CTR => E2: 5,6 * DIS # H6: 3 => CTR => H6: 5,8 * DIS # E6: 5,7 => CTR => E6: 6,8 * DIS # D7: 5,6 => CTR => D7: 3 * DIS # B1: 5,6 => CTR => B1: 2,7,8 * DIS # E2: 5,7 => CTR => E2: 6,8 * DIS # E6: 5,7 => CTR => E6: 6,8 * CNT 10 HDP CHAINS / 38 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,C8,D4,E4,E9,F6,F8,G3,G4,G6,H2,H5,I1,I3) * ..1.3.94..4.9....393..41.2.59...4..61.3.9.2.4..41....98.9.1.47231.42.8954..8.9361 * PAIR I1: 7,8 ROW 1 B1: 7,8,2,5,6 # reduction candidate for 7,8 B1: 7,8 # 18 pairs F1: 7,8,2,5,6 # reduction candidate for 7,8 F1: 7,8 # 17 pairs * PAIR H2: 1,5 BLK 3 G2: 1,5,6 # reduction candidate for 1,5 G2: 6 => CTR * 6.1.3.94.74.9..61393864152759...4136163.9.284284163759859316472316427895472859361 * PAIR I3: 7,8 ROW 3 C3: 7,8,5 # reduction candidate for 7,8 C3: 7,8 => CTR * .51.3.94..4698...393.54162.59...4..61.3.9.2.4..41....9869315472317426895425879361 * PAIR RESTART * PAIR E4: 7,8 BLK 5 F5: 7,8,5,6 # reduction candidate for 7,8 F5: 7,8 # 18 pairs E6: 7,8,5,6 # reduction candidate for 7,8 E6: 7,8 # 22 pairs * PAIR E4: 7,8 ROW 4 C4: 7,8,2 # reduction candidate for 7,8 C4: 2 => CTR * ..1.3.947.48962..39357416285923.4..61.3.9.2.4..41....98.9.1.47231.42.8954..8.9361 * PAIR RESTART * PAIR E4: 7,8 BLK 5 F5: 7,8,5 # reduction candidate for 7,8 F5: 5 => SOLVED * 681532947742968513935741628598274136173695284264183759859316472316427895427859361 * DURATION: 0:00:09.444034 START: 04:53:13.056728 END: 04:53:22.500762 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190328-absurd-base-pr-001.dot * REASONING * DIS # G2: 6 => CTR => G2: 1,5 * DIS G2: 1,5 # C3: 7,8 => CTR => C3: 5 * DIS G2: 1,5 + C3: 5 # C4: 2 => CTR => C4: 7,8 * PRF G2: 1,5 + C3: 5 + C4: 7,8 # F5: 5 => SOL * STA G2: 1,5 + C3: 5 + C4: 7,8 + F5: 5 * CNT 4 HDP CHAINS / 11 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190328, absurd
Solution
position: 681532947742968513935741628598274136173695284264183759859316472316427895427859361 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:
* INC # B1: 7,8 => UNS * INC # F1: 7,8 => UNS * INC # G2: 1,5 => UNS * DIS # G2: 6 => CTR => G2: 1,5 * INC # G2: 5,6 => UNS * DIS # G2: 1 => CTR => G2: 5,6 * INC # C3: 5,6 => UNS * INC # D3: 5,6 => UNS * INC # C3: 7,8 => UNS * INC # C3: 5,6 => UNS * INC # F5: 7,8 => UNS * INC # E6: 7,8 => UNS * INC # C4: 7,8 => UNS * DIS # C4: 2 => CTR => C4: 7,8 * DIS # E2: 7,8 => CTR => E2: 5,6 * INC # E2: 5,6 => UNS * INC # H6: 5,8 => UNS * DIS # H6: 3 => CTR => H6: 5,8 * INC # F5: 5,8 => UNS * INC # F5: 6,7 => UNS * DIS # E6: 5,7 => CTR => E6: 6,8 * INC # E6: 6,8 => UNS * DIS # D7: 5,6 => CTR => D7: 3 * INC # D7: 3 => UNS * INC # F7: 5,6 => UNS * DIS # B1: 5,6 => CTR => B1: 2,7,8 * INC # B1: 2,7,8 => UNS * INC # C2: 6,7 => UNS * INC # C3: 6,7 => UNS * INC # F1: 6,7 => UNS * INC # F2: 6,7 => UNS * INC # F5: 6,7 => UNS * INC # B9: 5,7 => UNS * INC # C9: 5,7 => UNS * DIS # E2: 5,7 => CTR => E2: 6,8 * INC # E2: 6,8 => UNS * DIS # E6: 5,7 => CTR => E6: 6,8 * INC # E6: 6,8 => UNS * CNT 38 HDP CHAINS / 38 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 7,8 => UNS * INC # F1: 7,8 => UNS * INC # G2: 1,5 => UNS * DIS # G2: 6 => CTR => G2: 1,5 * DIS G2: 1,5 # C3: 7,8 => CTR => C3: 5 * INC G2: 1,5 + C3: 5 # F5: 7,8 => UNS * INC G2: 1,5 + C3: 5 # E6: 7,8 => UNS * INC G2: 1,5 + C3: 5 # C4: 7,8 => UNS * DIS G2: 1,5 + C3: 5 # C4: 2 => CTR => C4: 7,8 * INC G2: 1,5 + C3: 5 + C4: 7,8 # F5: 7,8 => UNS * PRF G2: 1,5 + C3: 5 + C4: 7,8 # F5: 5 => SOL * STA G2: 1,5 + C3: 5 + C4: 7,8 + F5: 5 * CNT 11 HDP CHAINS / 11 HYP OPENED