Analysis of zz-www.sudokuoftheday.co.uk-20190314-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...8.....62..43.4........5.7..6............85.3..14.....9.897.....3.....34..5 initial
Autosolve
position: 1..34..8.5...623.43.4......2.5.7.86.7........6.85.3..1453...9.897....43.8..934..5 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B3: 8,9 => CTR => B3: 2,6 * DIS # C1: 7,9 => CTR => C1: 2,6 * PRF # C1: 2,6 => SOL * DIS # H3: 1,9 => CTR => H3: 2,5 * PRF # B5: 1,9 => SOL * DIS # E5: 1,9 => CTR => E5: 2,8 * DIS # F5: 1,9 => CTR => F5: 6,8 * DIS # B4: 4,9 => CTR => B4: 1,3 * DIS # B5: 4,9 => CTR => B5: 1,3 * DIS # H6: 4,9 => CTR => H6: 2,7 * PRF # H6: 2,7 => SOL * DIS # D5: 1,4 => CTR => D5: 2,6,8 * DIS # B4: 1,4 => CTR => B4: 3,9 * DIS # E5: 1,9 => CTR => E5: 2,8 * DIS # F5: 1,9 => CTR => F5: 6,8 * PRF # E5: 2,9 => SOL * DIS # I5: 2 => CTR => I5: 3,9 * DIS # B4: 1,4 => CTR => B4: 3,9 * DIS # H5: 2,5 => CTR => H5: 4,9 * DIS # G3: 2,5 => CTR => G3: 1,6 * PRF # H6: 2,7 => SOL * DIS # H6: 4,9 => CTR => H6: 2,7 * DIS # E8: 1,2 => CTR => E8: 5,8 * PRF # E5: 1,2 => SOL * PRF # H9: 1,2 => SOL * DIS # H3: 1,2 => CTR => H3: 5,9 * DIS # G9: 2,6 => CTR => G9: 1,7 * DIS # C8: 2,6 => CTR => C8: 1 * PRF # C8: 1 => SOL * CNT 29 HDP CHAINS / 64 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B3: 8,9 => CTR => B3: 2,6 * DIS B3: 2,6 # C1: 7,9 => CTR => C1: 2,6 * PRF B3: 2,6 + C1: 2,6 => SOL * STA B3: 2,6 + C1: 2,6 * CNT 3 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1..3...8.....62..43.4........5.7..6............85.3..14.....9.897.....3.....34..5 | initial |
| 1..34..8.5...623.43.4......2.5.7.86.7........6.85.3..1453...9.897....43.8..934..5 | autosolve |
| 192345687587162394364789152235471869719826543648593271453617928971258436826934715 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) B2: 8,9 C2: 7,9 H2: 1,9 C5: 1,9 B6: 4,9 D4: 1,4 F4: 1,9 E6: 2,9 I4: 3,9 G5: 2,5 G6: 2,7 D7: 6,7 E7: 1,2 F7: 6,7 H7: 1,2 I8: 2,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D2,H2: 1.. / D2 = 1 => 15 pairs (_) / H2 = 1 => 0 pairs (X) E7,H7: 1.. / E7 = 1 => 0 pairs (*) / H7 = 1 => 0 pairs (X) G3,G9: 1.. / G3 = 1 => 16 pairs (_) / G9 = 1 => 0 pairs (X) E7,H7: 2.. / E7 = 2 => 0 pairs (X) / H7 = 2 => 0 pairs (_) D5,D8: 2.. / D5 = 2 => 0 pairs (X) / D8 = 2 => 0 pairs (_) B4,B5: 3.. / B4 = 3 => 14 pairs (_) / B5 = 3 => 16 pairs (_) I4,I5: 3.. / I4 = 3 => 16 pairs (_) / I5 = 3 => 14 pairs (_) B4,I4: 3.. / B4 = 3 => 14 pairs (_) / I4 = 3 => 16 pairs (_) B5,I5: 3.. / B5 = 3 => 16 pairs (_) / I5 = 3 => 14 pairs (_) D4,D5: 4.. / D4 = 4 => 15 pairs (_) / D5 = 4 => 0 pairs (X) H5,H6: 4.. / H5 = 4 => 15 pairs (_) / H6 = 4 => 0 pairs (X) B4,D4: 4.. / B4 = 4 => 0 pairs (X) / D4 = 4 => 15 pairs (_) B6,H6: 4.. / B6 = 4 => 15 pairs (_) / H6 = 4 => 0 pairs (X) G5,H5: 5.. / G5 = 5 => 17 pairs (_) / H5 = 5 => 0 pairs (X) E8,F8: 5.. / E8 = 5 => 17 pairs (_) / F8 = 5 => 0 pairs (X) F1,G1: 5.. / F1 = 5 => 18 pairs (_) / G1 = 5 => 0 pairs (X) E3,E8: 5.. / E3 = 5 => 0 pairs (X) / E8 = 5 => 17 pairs (_) H3,H5: 5.. / H3 = 5 => 17 pairs (_) / H5 = 5 => 0 pairs (X) D5,F5: 6.. / D5 = 6 => 0 pairs (X) / F5 = 6 => 15 pairs (_) D7,F7: 6.. / D7 = 6 => 15 pairs (_) / F7 = 6 => 0 pairs (X) I8,G9: 6.. / I8 = 6 => 16 pairs (_) / G9 = 6 => 0 pairs (X) C8,I8: 6.. / C8 = 6 => 0 pairs (X) / I8 = 6 => 16 pairs (_) D5,D7: 6.. / D5 = 6 => 0 pairs (X) / D7 = 6 => 15 pairs (_) F5,F7: 6.. / F5 = 6 => 15 pairs (_) / F7 = 6 => 0 pairs (X) C1,C2: 7.. / C1 = 7 => 0 pairs (X) / C2 = 7 => 16 pairs (_) I1,I3: 7.. / I1 = 7 => 17 pairs (_) / I3 = 7 => 17 pairs (_) G6,H6: 7.. / G6 = 7 => 15 pairs (_) / H6 = 7 => 0 pairs (*) D7,F7: 7.. / D7 = 7 => 0 pairs (X) / F7 = 7 => 15 pairs (_) G9,H9: 7.. / G9 = 7 => 0 pairs (*) / H9 = 7 => 0 pairs (X) C2,D2: 7.. / C2 = 7 => 16 pairs (_) / D2 = 7 => 0 pairs (X) G6,G9: 7.. / G6 = 7 => 15 pairs (_) / G9 = 7 => 0 pairs (*) H6,H9: 7.. / H6 = 7 => 0 pairs (*) / H9 = 7 => 0 pairs (X) B2,B3: 8.. / B2 = 8 => 16 pairs (_) / B3 = 8 => 0 pairs (X) B2,D2: 8.. / B2 = 8 => 16 pairs (_) / D2 = 8 => 0 pairs (X) * DURATION: 0:00:43.776042 START: 04:30:43.313385 END: 04:31:27.089427 2019-05-01 * CP COUNT: (34) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B6,C2,C5,D4,D7,E6,E7,F4,F7,G5,G6,H2,H7,I4,I8) * 1..34..8.5...623.43.4......2.5.7.86.7........6.85.3..1453...9.897....43.8..934..5 * PAIR B2: 8,9 BLK 1 B3: 8,9,2,6 # reduction candidate for 8,9 B3: 8,9 => CTR * 1..34.58.5...623.43.4......2.5.7.86.7.....25.6.8523741453.1.9289712..4368..934175 B3: 2,6 # 17 pairs * PAIR C2: 7,9 BLK 1 C1: 7,9,2,6 # reduction candidate for 7,9 C1: 7,9 => CTR * 1..34.58.5..1623943.4.5.12.2.547186.7.1.8.25.6.85.3..1453...91897..1543.81.934..5 C1: 2,6 => SOLVED * 192345687587162394364789152235471869719826543648593271453617928971258436826934715 * PAIR H2: 1,9 BLK 3 H3: 1,9,2,5 # reduction candidate for 1,9 H3: 1,9 => CTR * 1..34..8.5...623.43.4......2.5.7.86.7.....25.698523741453.1.928971...43.8..934.75 H3: 2,5 # 17 pairs * PAIR C5: 1,9 BLK 4 B4: 1,9,3,4 # reduction candidate for 1,9 B4: 1,9 # 16 pairs B5: 1,9,3,4 # reduction candidate for 1,9 B5: 1,9 => SOLVED * 192345687587162394364789152235471869719826543648593271453617928971258436826934715 B5: 3,4 # 17 pairs * PAIR C5: 1,9 ROW 5 E5: 1,9,2,8 # reduction candidate for 1,9 E5: 1,9 => CTR * 1..34..8.5...623.43.4......2.547186.7.1.9....6.85237.1453.1.9.897....43.8..934..5 E5: 2,8 # 17 pairs F5: 1,9,6,8 # reduction candidate for 1,9 F5: 1,9 => CTR * 1..34..8959786231438419.65.2.547.86.7.9681...6485237914537169289712584368..934175 F5: 6,8 # 17 pairs * PAIR B6: 4,9 BLK 4 B4: 4,9,1,3 # reduction candidate for 4,9 B4: 4,9 => CTR * 1..34.58.5..1623943.4.5.12.2.5471863731.8....6.85.3..1453...91897..1543.81.934..5 B4: 1,3 # 16 pairs B5: 4,9,1,3 # reduction candidate for 4,9 B5: 4,9 => CTR * 1..34.58.5..1623943.4.5.12.2354718697.1.8.2536.85.3..1453...91897..1543.81.934..5 B5: 1,3 # 17 pairs * PAIR B6: 4,9 ROW 6 H6: 4,9,2,7 # reduction candidate for 4,9 H6: 4,9 => CTR * 1..34..8.597862314384.9.6522.5.7.86.7.9.8....648523791453.1.9289712584368..934175 H6: 2,7 => SOLVED * 192345687587162394364789152235471869719826543648593271453617928971258436826934715 * PAIR D4: 1,4 BLK 5 D5: 1,4,2,6,8 # reduction candidate for 1,4 D5: 1,4 => CTR * 1..345.8959786231438479....2.5.79863739186.426485237914536179289712584368..934175 D5: 2,6,8 # 15 pairs * PAIR D4: 1,4 ROW 4 B4: 1,4,3,9 # reduction candidate for 1,4 B4: 1,4 => CTR * 1..34..89597862314384.9....215479863739.8..42648523791453.1.9289712584368..934175 B4: 3,9 # 16 pairs * PAIR F4: 1,9 BLK 5 E5: 1,9,2,8 # reduction candidate for 1,9 E5: 1,9 => CTR * 1..34..8.5...623.43.4......2.547186.7.1.9....6.85237.1453.1.9.897....43.8..934..5 E5: 2,8 # 17 pairs F5: 1,9,6,8 # reduction candidate for 1,9 F5: 1,9 => CTR * 1..34..8959786231438419.65.2.547.86.7.9681...6485237914537169289712584368..934175 F5: 6,8 # 17 pairs * PAIR F4: 1,9 ROW 4 B4: 1,9,3,4 # reduction candidate for 1,9 B4: 3,4 # 17 pairs B4: 1,9 # 16 pairs * PAIR F4: 1,9 COL F F3: 1,9,5,7,8 # reduction candidate for 1,9 F3: 1,9 # 20 pairs F3: 5,7,8 # 16 pairs * PAIR E6: 2,9 BLK 5 E5: 2,9,1,8 # reduction candidate for 2,9 E5: 2,9 => SOLVED * 192345687587162394364789152235471869719826543648593271453617928971258436826934715 E5: 1,8 # 17 pairs * PAIR E6: 2,9 ROW 6 H6: 2,9,4,7 # reduction candidate for 2,9 H6: 4,7 # 17 pairs H6: 2,9 # 15 pairs * PAIR I4: 3,9 BLK 6 I5: 3,9,2 # reduction candidate for 3,9 I5: 2 => CTR * 1..345.8.5978623143.4......215479863739.8.542648523791453.1.9289712584368..934175 I5: 3,9 # 17 pairs * PAIR I4: 3,9 ROW 4 B4: 3,9,1,4 # reduction candidate for 3,9 B4: 1,4 => CTR * 1..34..89597862314384.9....215479863739.8..42648523791453.1.9289712584368..934175 B4: 3,9 # 16 pairs * PAIR G5: 2,5 BLK 6 H5: 2,5,4,9 # reduction candidate for 2,5 H5: 2,5 => CTR * 1..34..8.5...623.43.4......2.5.7.86.7........698523741453.1.928971...43.8..934.75 H5: 4,9 # 18 pairs * PAIR G5: 2,5 COL G G1: 2,5,6 # reduction candidate for 2,5 G1: 2,5 # 19 pairs G3: 2,5,1,6 # reduction candidate for 2,5 G3: 2,5 => CTR * 192345687587162394364....122.547.86.7........6.85.37.1453.1.928971...436826934175 G3: 1,6 # 17 pairs * PAIR G6: 2,7 BLK 6 H6: 2,7,4,9 # reduction candidate for 2,7 H6: 2,7 => SOLVED * 192345687587162394364789152235471869719826543648593271453617928971258436826934715 H6: 4,9 => CTR * 1..34..8.597862314384.9.6522.5.7.86.7.9.8....648523791453.1.9289712584368..934175 * PAIR G6: 2,7 COL G G9: 2,7,1,6 # reduction candidate for 2,7 G9: 2,7 # 21 pairs G9: 1,6 # 17 pairs * PAIR E7: 1,2 BLK 8 D8: 1,2,8 # reduction candidate for 1,2 D8: 1,2 # 19 pairs E8: 1,2,5,8 # reduction candidate for 1,2 E8: 1,2 => CTR * 1..34..8.5...623.43.4.5....2.5.7.86.7...8..5.6.8593.41453...9.897....43.8..934..5 E8: 5,8 # 17 pairs * PAIR E7: 1,2 COL E E5: 1,2,8,9 # reduction candidate for 1,2 E5: 1,2 => SOLVED * 192345687587162394364789152235471869719826543648593271453617928971258436826934715 E5: 8,9 # 17 pairs * PAIR H7: 1,2 BLK 9 G9: 1,2,6,7 # reduction candidate for 1,2 G9: 1,2 # 16 pairs H9: 1,2,7 # reduction candidate for 1,2 H9: 1,2 => SOLVED * 192345687587162394364789152235471869719826543648593271453617928971258436826934715 H9: 7 # 15 pairs * PAIR H7: 1,2 COL H H3: 1,2,5,9 # reduction candidate for 1,2 H3: 1,2 => CTR * 1..34..8.5...623943.4......2.5.7.86.7.....25.698523741453.1.928971...43.8..934.75 H3: 5,9 # 17 pairs * PAIR I8: 2,6 BLK 9 G9: 2,6,1,7 # reduction candidate for 2,6 G9: 2,6 => CTR * 1..345.875871623943.478.1..2.547.86.7..2.654.64859372145362791897.8..43.8..934.75 G9: 1,7 # 17 pairs * PAIR I8: 2,6 ROW 8 C8: 2,6,1 # reduction candidate for 2,6 C8: 2,6 => CTR * 1..345.875871623943.478.1..2.547.86.7..2.654.648593..145362791897.8..43.8..934..5 C8: 1 => SOLVED * 192345687587162394364789152235471869719826543648593271453617928971258436826934715 * PAIR I8: 2,6 COL I I1: 2,6,7,9 # reduction candidate for 2,6 I1: 2,6 # 19 pairs I3: 2,6,7,9 # reduction candidate for 2,6 I3: 2,6 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190314-absurd-base-pr-000.dot * REASONING * DIS # B3: 8,9 => CTR => B3: 2,6 * DIS # C1: 7,9 => CTR => C1: 2,6 * PRF # C1: 2,6 => SOL * DIS # H3: 1,9 => CTR => H3: 2,5 * PRF # B5: 1,9 => SOL * DIS # E5: 1,9 => CTR => E5: 2,8 * DIS # F5: 1,9 => CTR => F5: 6,8 * DIS # B4: 4,9 => CTR => B4: 1,3 * DIS # B5: 4,9 => CTR => B5: 1,3 * DIS # H6: 4,9 => CTR => H6: 2,7 * PRF # H6: 2,7 => SOL * DIS # D5: 1,4 => CTR => D5: 2,6,8 * DIS # B4: 1,4 => CTR => B4: 3,9 * DIS # E5: 1,9 => CTR => E5: 2,8 * DIS # F5: 1,9 => CTR => F5: 6,8 * PRF # E5: 2,9 => SOL * DIS # I5: 2 => CTR => I5: 3,9 * DIS # B4: 1,4 => CTR => B4: 3,9 * DIS # H5: 2,5 => CTR => H5: 4,9 * DIS # G3: 2,5 => CTR => G3: 1,6 * PRF # H6: 2,7 => SOL * DIS # H6: 4,9 => CTR => H6: 2,7 * DIS # E8: 1,2 => CTR => E8: 5,8 * PRF # E5: 1,2 => SOL * PRF # H9: 1,2 => SOL * DIS # H3: 1,2 => CTR => H3: 5,9 * DIS # G9: 2,6 => CTR => G9: 1,7 * DIS # C8: 2,6 => CTR => C8: 1 * PRF # C8: 1 => SOL * CNT 29 HDP CHAINS / 64 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B6,C2,C5,D4,D7,E6,E7,F4,F7,G5,G6,H2,H7,I4,I8) * 1..34..8.5...623.43.4......2.5.7.86.7........6.85.3..1453...9.897....43.8..934..5 * PAIR B2: 8,9 BLK 1 B3: 8,9,2,6 # reduction candidate for 8,9 B3: 8,9 => CTR * 1..34.58.5...623.43.4......2.5.7.86.7.....25.6.8523741453.1.9289712..4368..934175 * PAIR C2: 7,9 BLK 1 C1: 7,9,2,6 # reduction candidate for 7,9 C1: 7,9 => CTR * 1..34.58.58.1623943.4.5912.2.547186.7.1.862..6.85.3..1453...91897..1543.81.934..5 C1: 2,6 => SOLVED * 192345687587162394364789152235471869719826543648593271453617928971258436826934715 * DURATION: 0:00:04.509210 START: 04:32:16.344314 END: 04:32:20.853524 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190314-absurd-base-pr-001.dot * REASONING * DIS # B3: 8,9 => CTR => B3: 2,6 * DIS B3: 2,6 # C1: 7,9 => CTR => C1: 2,6 * PRF B3: 2,6 + C1: 2,6 => SOL * STA B3: 2,6 + C1: 2,6 * CNT 3 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190314, absurd
Solution
position: 192345687587162394364789152235471869719826543648593271453617928971258436826934715 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: 8,9 => CTR => B3: 2,6 * INC # B3: 2,6 => UNS * DIS # C1: 7,9 => CTR => C1: 2,6 * PRF # C1: 2,6 => SOL * DIS # H3: 1,9 => CTR => H3: 2,5 * INC # H3: 2,5 => UNS * INC # B4: 1,9 => UNS * PRF # B5: 1,9 => SOL * INC # B5: 3,4 => UNS * DIS # E5: 1,9 => CTR => E5: 2,8 * INC # E5: 2,8 => UNS * DIS # F5: 1,9 => CTR => F5: 6,8 * INC # F5: 6,8 => UNS * DIS # B4: 4,9 => CTR => B4: 1,3 * INC # B4: 1,3 => UNS * DIS # B5: 4,9 => CTR => B5: 1,3 * INC # B5: 1,3 => UNS * DIS # H6: 4,9 => CTR => H6: 2,7 * PRF # H6: 2,7 => SOL * DIS # D5: 1,4 => CTR => D5: 2,6,8 * INC # D5: 2,6,8 => UNS * DIS # B4: 1,4 => CTR => B4: 3,9 * INC # B4: 3,9 => UNS * DIS # E5: 1,9 => CTR => E5: 2,8 * INC # E5: 2,8 => UNS * DIS # F5: 1,9 => CTR => F5: 6,8 * INC # F5: 6,8 => UNS * INC # B4: 1,9 => UNS * INC # B4: 3,4 => UNS * INC # F3: 1,9 => UNS * INC # F3: 5,7,8 => UNS * PRF # E5: 2,9 => SOL * INC # E5: 1,8 => UNS * INC # H6: 2,9 => UNS * INC # H6: 4,7 => UNS * INC # I5: 3,9 => UNS * DIS # I5: 2 => CTR => I5: 3,9 * INC # B4: 3,9 => UNS * DIS # B4: 1,4 => CTR => B4: 3,9 * DIS # H5: 2,5 => CTR => H5: 4,9 * INC # H5: 4,9 => UNS * INC # G1: 2,5 => UNS * DIS # G3: 2,5 => CTR => G3: 1,6 * INC # G3: 1,6 => UNS * PRF # H6: 2,7 => SOL * DIS # H6: 4,9 => CTR => H6: 2,7 * INC # G9: 2,7 => UNS * INC # G9: 1,6 => UNS * INC # D8: 1,2 => UNS * DIS # E8: 1,2 => CTR => E8: 5,8 * INC # E8: 5,8 => UNS * PRF # E5: 1,2 => SOL * INC # E5: 8,9 => UNS * INC # G9: 1,2 => UNS * PRF # H9: 1,2 => SOL * INC # H9: 7 => UNS * DIS # H3: 1,2 => CTR => H3: 5,9 * INC # H3: 5,9 => UNS * DIS # G9: 2,6 => CTR => G9: 1,7 * INC # G9: 1,7 => UNS * DIS # C8: 2,6 => CTR => C8: 1 * PRF # C8: 1 => SOL * INC # I1: 2,6 => UNS * INC # I3: 2,6 => UNS * CNT 64 HDP CHAINS / 64 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B3: 8,9 => CTR => B3: 2,6 * DIS B3: 2,6 # C1: 7,9 => CTR => C1: 2,6 * PRF B3: 2,6 + C1: 2,6 => SOL * STA B3: 2,6 + C1: 2,6 * CNT 3 HDP CHAINS / 2 HYP OPENED