Analysis of zz-www.sudokuoftheday.co.uk-20190118-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: ..1.6..4..9.5.....54...........5.6..92......3............87...5.7.9....2.3...4.89 initial
Autosolve
position: 381269547.9.54....54....9...1..5269.92.....53.5..9.27.26987.4.5.7.9.5.62135624789 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C5: 6 => CTR => C5: 4,7 * DIS # F6: 3,6 => CTR => F6: 1,8 * DIS # E3: 1,8 => CTR => E3: 3 * DIS # I6: 1 => CTR => I6: 4,8 * DIS # C4: 4,8 => CTR => C4: 3,7 * DIS # G2: 3 => CTR => G2: 1,8 * DIS # C4: 4,8 => CTR => C4: 3,7 * PRF # F6: 1,3 => SOL * DIS # E3: 8 => CTR => E3: 1,3 * DIS # G2: 1,3 => CTR => G2: 8 * CNT 10 HDP CHAINS / 36 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C5: 6 => CTR => C5: 4,7 * DIS C5: 4,7 # F6: 3 => CTR => F6: 1,8 * PRF C5: 4,7 + F6: 1,8 # I6: 4,8 => SOL * STA C5: 4,7 + F6: 1,8 + I6: 4,8 * CNT 3 HDP CHAINS / 11 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..1.6..4..9.5.....54...........5.6..92......3............87...5.7.9....2.3...4.89 | initial |
| 381269547.9.54....54....9...1..5269.92.....53.5..9.27.26987.4.5.7.9.5.62135624789 | autosolve |
| 381269547692547831547138926713452698924786153856391274269873415478915362135624789 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) A2: 6,7 D5: 4,7 E5: 1,8 F5: 6,7 I4: 4,8 G5: 1,8 A8: 4,8 C8: 4,8 F7: 1,3 E8: 1,3 H7: 1,3 G8: 1,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G5,I6: 1.. / G5 = 1 => 13 pairs (_) / I6 = 1 => 0 pairs (X) F7,E8: 1.. / F7 = 1 => 0 pairs (X) / E8 = 1 => 13 pairs (_) H7,G8: 1.. / H7 = 1 => 13 pairs (_) / G8 = 1 => 0 pairs (X) E5,G5: 1.. / E5 = 1 => 0 pairs (X) / G5 = 1 => 13 pairs (_) F7,H7: 1.. / F7 = 1 => 0 pairs (X) / H7 = 1 => 13 pairs (_) E8,G8: 1.. / E8 = 1 => 13 pairs (_) / G8 = 1 => 0 pairs (X) D3,D6: 1.. / D3 = 1 => 17 pairs (_) / D6 = 1 => 0 pairs (X) C2,C3: 2.. / C2 = 2 => 14 pairs (_) / C3 = 2 => 19 pairs (_) H2,H3: 2.. / H2 = 2 => 19 pairs (_) / H3 = 2 => 14 pairs (_) C2,H2: 2.. / C2 = 2 => 14 pairs (_) / H2 = 2 => 19 pairs (_) C3,H3: 2.. / C3 = 2 => 19 pairs (_) / H3 = 2 => 14 pairs (_) C4,C6: 3.. / C4 = 3 => 15 pairs (_) / C6 = 3 => 15 pairs (_) F7,E8: 3.. / F7 = 3 => 13 pairs (_) / E8 = 3 => 0 pairs (X) H7,G8: 3.. / H7 = 3 => 0 pairs (X) / G8 = 3 => 13 pairs (_) C4,D4: 3.. / C4 = 3 => 15 pairs (_) / D4 = 3 => 15 pairs (_) F7,H7: 3.. / F7 = 3 => 13 pairs (_) / H7 = 3 => 0 pairs (X) E8,G8: 3.. / E8 = 3 => 0 pairs (X) / G8 = 3 => 13 pairs (_) E3,E8: 3.. / E3 = 3 => 13 pairs (_) / E8 = 3 => 0 pairs (X) G2,G8: 3.. / G2 = 3 => 0 pairs (X) / G8 = 3 => 13 pairs (_) I4,I6: 4.. / I4 = 4 => 15 pairs (_) / I6 = 4 => 14 pairs (_) A8,C8: 4.. / A8 = 4 => 12 pairs (_) / C8 = 4 => 16 pairs (_) C5,D5: 4.. / C5 = 4 => 14 pairs (_) / D5 = 4 => 14 pairs (_) I2,I3: 6.. / I2 = 6 => 18 pairs (_) / I3 = 6 => 14 pairs (_) F5,F6: 6.. / F5 = 6 => 13 pairs (_) / F6 = 6 => 0 pairs (X) C3,I3: 6.. / C3 = 6 => 18 pairs (_) / I3 = 6 => 14 pairs (_) C5,F5: 6.. / C5 = 6 => 0 pairs (X) / F5 = 6 => 13 pairs (_) A2,A6: 6.. / A2 = 6 => 17 pairs (_) / A6 = 6 => 17 pairs (_) A2,A4: 7.. / A2 = 7 => 17 pairs (_) / A4 = 7 => 17 pairs (_) E5,F6: 8.. / E5 = 8 => 13 pairs (_) / F6 = 8 => 0 pairs (X) A8,C8: 8.. / A8 = 8 => 16 pairs (_) / C8 = 8 => 12 pairs (_) E5,G5: 8.. / E5 = 8 => 13 pairs (_) / G5 = 8 => 0 pairs (X) E3,E5: 8.. / E3 = 8 => 0 pairs (X) / E5 = 8 => 13 pairs (_) G2,G5: 8.. / G2 = 8 => 13 pairs (_) / G5 = 8 => 0 pairs (X) * DURATION: 0:00:44.046421 START: 03:02:30.629578 END: 03:03:14.675999 2019-05-01 * CP COUNT: (33) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,C8,D5,E5,E8,F5,F7,G5,G8,H7,I4) * 381269547.9.54....54....9...1..5269.92.....53.5..9.27.26987.4.5.7.9.5.62135624789 * PAIR A2: 6,7 BLK 1 C2: 6,7,2 # reduction candidate for 6,7 C2: 6,7 # 19 pairs C3: 6,7,2 # reduction candidate for 6,7 C3: 6,7 # 14 pairs * PAIR D5: 4,7 BLK 5 D4: 4,7,3 # reduction candidate for 4,7 D4: 4,7 # 15 pairs D4: 3 # 15 pairs * PAIR D5: 4,7 ROW 5 C5: 4,7,6 # reduction candidate for 4,7 C5: 6 => CTR * 38126954769754..2.5427..9.671.35269.926487153.5319627.26987.415.7.915362135624789 C5: 4,7 # 13 pairs * PAIR E5: 1,8 BLK 5 F6: 1,8,3,6 # reduction candidate for 1,8 F6: 3,6 => CTR * 38126954769.54.8..54..38921.1.35269.92.487153.5319627.269873415.7.915362135624789 F6: 1,8 # 17 pairs * PAIR E5: 1,8 COL E E3: 1,8,3 # reduction candidate for 1,8 E3: 1,8 => CTR * 381269547.9.54731854718392671835269492.716853.53498271269871435.7.935162135624789 E3: 3 # 13 pairs * PAIR F5: 6,7 ROW 5 C5: 6,7,4 # reduction candidate for 6,7 C5: 6,7 # 14 pairs C5: 4 # 14 pairs * PAIR I4: 4,8 BLK 6 I6: 4,8,1 # reduction candidate for 4,8 I6: 1 => CTR * 381269547.92547318547183926718352694924.16853.5..98271269871435.7.935162135624789 I6: 4,8 # 13 pairs * PAIR I4: 4,8 ROW 4 A4: 4,8,7 # reduction candidate for 4,8 A4: 4,8 # 17 pairs C4: 4,8,3,7 # reduction candidate for 4,8 C4: 4,8 => CTR * 38126954769754..215427..93671.35269.926487153.5319627.2698734.5.7.9.5.62135624789 C4: 3,7 # 13 pairs * PAIR G5: 1,8 BLK 6 I6: 1,8,4 # reduction candidate for 1,8 I6: 1,8 # 15 pairs I6: 4 # 14 pairs * PAIR G5: 1,8 COL G G2: 1,8,3 # reduction candidate for 1,8 G2: 3 => CTR * 381269547.92547318547183926718352694924.16853.5..98271269871435.7.935162135624789 G2: 1,8 # 13 pairs * PAIR A8: 4,8 COL A A4: 4,8,7 # reduction candidate for 4,8 A4: 4,8 # 17 pairs A6: 4,8,6 # reduction candidate for 4,8 A6: 4,8 # 17 pairs * PAIR C8: 4,8 COL C C4: 4,8,3,7 # reduction candidate for 4,8 C4: 4,8 => CTR * 38126954769754..215427..93671.35269.926487153.5319627.2698734.5.7.9.5.62135624789 C4: 3,7 # 13 pairs C6: 4,8,3,6 # reduction candidate for 4,8 C6: 4,8 # 15 pairs * PAIR F7: 1,3 COL F F2: 1,3,7,8 # reduction candidate for 1,3 F2: 1,3 # 18 pairs F3: 1,3,7,8 # reduction candidate for 1,3 F3: 1,3 # 19 pairs F6: 1,3,6,8 # reduction candidate for 1,3 F6: 1,3 => SOLVED * 381269547692547831547138926713452698924786153856391274269873415478915362135624789 F6: 6,8 # 14 pairs * PAIR E8: 1,3 COL E E3: 1,3,8 # reduction candidate for 1,3 E3: 8 => CTR * 381269547.92547318547183926718352694924.16853.5..98271269871435.7.935162135624789 E3: 1,3 # 13 pairs * PAIR H7: 1,3 COL H H2: 1,3,2 # reduction candidate for 1,3 H2: 1,3 # 14 pairs H3: 1,3,2 # reduction candidate for 1,3 H3: 1,3 # 19 pairs * PAIR G8: 1,3 COL G G2: 1,3,8 # reduction candidate for 1,3 G2: 1,3 => CTR * 381269547.92547318547183926718352694924.16853.5..98271269871435.7.935162135624789 G2: 8 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190118-absurd-base-pr-000.dot * REASONING * DIS # C5: 6 => CTR => C5: 4,7 * DIS # F6: 3,6 => CTR => F6: 1,8 * DIS # E3: 1,8 => CTR => E3: 3 * DIS # I6: 1 => CTR => I6: 4,8 * DIS # C4: 4,8 => CTR => C4: 3,7 * DIS # G2: 3 => CTR => G2: 1,8 * DIS # C4: 4,8 => CTR => C4: 3,7 * PRF # F6: 1,3 => SOL * DIS # E3: 8 => CTR => E3: 1,3 * DIS # G2: 1,3 => CTR => G2: 8 * CNT 10 HDP CHAINS / 36 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,C8,D5,E5,E8,F5,F7,G5,G8,H7,I4) * 381269547.9.54....54....9...1..5269.92.....53.5..9.27.26987.4.5.7.9.5.62135624789 * PAIR A2: 6,7 BLK 1 C2: 6,7,2 # reduction candidate for 6,7 C2: 6,7 # 19 pairs C3: 6,7,2 # reduction candidate for 6,7 C3: 6,7 # 14 pairs * PAIR D5: 4,7 BLK 5 D4: 4,7,3 # reduction candidate for 4,7 D4: 4,7 # 15 pairs D4: 3 # 15 pairs * PAIR D5: 4,7 ROW 5 C5: 4,7,6 # reduction candidate for 4,7 C5: 6 => CTR * 38126954769754..2.5427..9.671.35269.926487153.5319627.26987.415.7.915362135624789 * PAIR RESTART * PAIR D5: 4,7 BLK 5 D4: 4,7,3 # reduction candidate for 4,7 D4: 4,7 # 15 pairs D4: 3 # 14 pairs * PAIR E5: 1,8 BLK 5 F6: 1,8,3 # reduction candidate for 1,8 F6: 3 => CTR * 381269547.9.54....54....9...1..5269.92..86153.5.19327.2698714.5.7.9.5.62135624789 * PAIR I4: 4,8 BLK 6 I6: 4,8,1 # reduction candidate for 4,8 I6: 4,8 => SOLVED * 381269547692547831547138926713452698924786153856391274269873415478915362135624789 * DURATION: 0:00:08.239146 START: 03:03:40.196294 END: 03:03:48.435440 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190118-absurd-base-pr-001.dot * REASONING * DIS # C5: 6 => CTR => C5: 4,7 * DIS C5: 4,7 # F6: 3 => CTR => F6: 1,8 * PRF C5: 4,7 + F6: 1,8 # I6: 4,8 => SOL * STA C5: 4,7 + F6: 1,8 + I6: 4,8 * CNT 3 HDP CHAINS / 11 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190118, absurd
Solution
position: 381269547692547831547138926713452698924786153856391274269873415478915362135624789 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 # C2: 6,7 => UNS * INC # C3: 6,7 => UNS * INC # D4: 4,7 => UNS * INC # D4: 3 => UNS * INC # C5: 4,7 => UNS * DIS # C5: 6 => CTR => C5: 4,7 * INC # F6: 1,8 => UNS * DIS # F6: 3,6 => CTR => F6: 1,8 * DIS # E3: 1,8 => CTR => E3: 3 * INC # E3: 3 => UNS * INC # C5: 6,7 => UNS * INC # C5: 4 => UNS * INC # I6: 4,8 => UNS * DIS # I6: 1 => CTR => I6: 4,8 * INC # A4: 4,8 => UNS * DIS # C4: 4,8 => CTR => C4: 3,7 * INC # C4: 3,7 => UNS * INC # I6: 1,8 => UNS * INC # I6: 4 => UNS * INC # G2: 1,8 => UNS * DIS # G2: 3 => CTR => G2: 1,8 * INC # A4: 4,8 => UNS * INC # A6: 4,8 => UNS * DIS # C4: 4,8 => CTR => C4: 3,7 * INC # C4: 3,7 => UNS * INC # C6: 4,8 => UNS * INC # F2: 1,3 => UNS * INC # F3: 1,3 => UNS * PRF # F6: 1,3 => SOL * INC # F6: 6,8 => UNS * INC # E3: 1,3 => UNS * DIS # E3: 8 => CTR => E3: 1,3 * INC # H2: 1,3 => UNS * INC # H3: 1,3 => UNS * DIS # G2: 1,3 => CTR => G2: 8 * INC # G2: 8 => UNS * CNT 36 HDP CHAINS / 36 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C2: 6,7 => UNS * INC # C3: 6,7 => UNS * INC # D4: 4,7 => UNS * INC # D4: 3 => UNS * INC # C5: 4,7 => UNS * DIS # C5: 6 => CTR => C5: 4,7 * INC C5: 4,7 # D4: 4,7 => UNS * INC C5: 4,7 # D4: 3 => UNS * INC C5: 4,7 # F6: 1,8 => UNS * DIS C5: 4,7 # F6: 3 => CTR => F6: 1,8 * PRF C5: 4,7 + F6: 1,8 # I6: 4,8 => SOL * STA C5: 4,7 + F6: 1,8 + I6: 4,8 * CNT 11 HDP CHAINS / 11 HYP OPENED