Analysis of zz-www.sudokuoftheday.co.uk-20190128-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: ....37....536...9.....29.85..5...9.......1...18..6..5..1.....4.7.6......2.9...8.. initial
Autosolve
position: 892537164453618.9.671429385365...9..924.516..18796.45.518..6.4.7.6...5..2.9..58.6 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I4: 2,7 => CTR => I4: 1,8 * DIS # I7: 2,7 => CTR => I7: 3,9 * PRF # F8: 2,4 => SOL * DIS # F8: 3 => CTR => F8: 2,4 * PRF # F8: 4 => SOL * DIS # I5: 3,7 => CTR => I5: 8 * DIS # D5: 8 => CTR => D5: 3,7 * PRF # H9: 1 => SOL * DIS # I8: 2,3 => CTR => I8: 1,9 * DIS # F8: 2 => CTR => F8: 3,4 * DIS # I7: 7,9 => CTR => I7: 2,3 * DIS # I7: 2,7 => CTR => I7: 3,9 * PRF # D7: 2,7 => SOL * DIS # D7: 3 => CTR => D7: 2,7 * CNT 14 HDP CHAINS / 27 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I4: 2,7 => CTR => I4: 1,8 * DIS I4: 1,8 # I7: 2,7 => CTR => I7: 3,9 * PRF I4: 1,8 + I7: 3,9 # F8: 2,4 => SOL * STA I4: 1,8 + I7: 3,9 + F8: 2,4 * CNT 3 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....37....536...9.....29.85..5...9.......1...18..6..5..1.....4.7.6......2.9...8.. | initial |
| 892537164453618.9.671429385365...9..924.516..18796.45.518..6.4.7.6...5..2.9..58.6 | autosolve |
| 892537164453618297671429385365842971924751638187963452518296743736184529249375816 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) G2: 2,7 I2: 2,7 F4: 2,4 F6: 2,3 H5: 3,7 I6: 2,3 B8: 3,4 B9: 3,4 E7: 7,9 E9: 4,7 G7: 2,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H4,I4: 1.. / H4 = 1 => 0 pairs (X) / I4 = 1 => 15 pairs (_) D8,D9: 1.. / D8 = 1 => 0 pairs (*) / D9 = 1 => 0 pairs (X) D9,H9: 1.. / D9 = 1 => 14 pairs (_) / H9 = 1 => 0 pairs (*) I4,I8: 1.. / I4 = 1 => 15 pairs (_) / I8 = 1 => 0 pairs (X) G2,I2: 2.. / G2 = 2 => 13 pairs (_) / I2 = 2 => 0 pairs (X) F6,I6: 2.. / F6 = 2 => 0 pairs (X) / I6 = 2 => 0 pairs (_) G2,G7: 2.. / G2 = 2 => 13 pairs (_) / G7 = 2 => 0 pairs (X) H4,H8: 2.. / H4 = 2 => 0 pairs (X) / H8 = 2 => 0 pairs (_) D5,F6: 3.. / D5 = 3 => 0 pairs (X) / F6 = 3 => 0 pairs (_) B8,B9: 3.. / B8 = 3 => 0 pairs (*) / B9 = 3 => 0 pairs (X) F6,I6: 3.. / F6 = 3 => 0 pairs (*) / I6 = 3 => 0 pairs (X) D7,I7: 3.. / D7 = 3 => 0 pairs (X) / I7 = 3 => 0 pairs (_) F6,F8: 3.. / F6 = 3 => 0 pairs (*) / F8 = 3 => 0 pairs (X) E4,F4: 4.. / E4 = 4 => 0 pairs (*) / F4 = 4 => 0 pairs (X) B8,B9: 4.. / B8 = 4 => 12 pairs (_) / B9 = 4 => 0 pairs (*) B9,E9: 4.. / B9 = 4 => 0 pairs (*) / E9 = 4 => 0 pairs (X) F4,F8: 4.. / F4 = 4 => 12 pairs (_) / F8 = 4 => 0 pairs (*) G2,I2: 7.. / G2 = 7 => 0 pairs (X) / I2 = 7 => 13 pairs (_) G2,G7: 7.. / G2 = 7 => 0 pairs (X) / G7 = 7 => 13 pairs (_) I4,I5: 8.. / I4 = 8 => 0 pairs (X) / I5 = 8 => 12 pairs (_) D8,E8: 8.. / D8 = 8 => 18 pairs (_) / E8 = 8 => 18 pairs (_) D5,I5: 8.. / D5 = 8 => 0 pairs (X) / I5 = 8 => 12 pairs (_) E4,E8: 8.. / E4 = 8 => 18 pairs (_) / E8 = 8 => 18 pairs (_) E7,E8: 9.. / E7 = 9 => 15 pairs (_) / E8 = 9 => 0 pairs (X) I7,I8: 9.. / I7 = 9 => 0 pairs (X) / I8 = 9 => 15 pairs (_) E7,I7: 9.. / E7 = 9 => 15 pairs (_) / I7 = 9 => 0 pairs (X) E8,I8: 9.. / E8 = 9 => 0 pairs (X) / I8 = 9 => 15 pairs (_) * DURATION: 0:00:33.882666 START: 03:16:41.985195 END: 03:17:15.867861 2019-05-01 * CP COUNT: (27) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,B9,E7,E9,F4,F6,G2,G7,H5,I2,I6) * 892537164453618.9.671429385365...9..924.516..18796.45.518..6.4.7.6...5..2.9..58.6 * PAIR I2: 2,7 COL I I4: 2,7,1,8 # reduction candidate for 2,7 I4: 2,7 => CTR * 892537164453618297671429385365...912924.51678187962453518..6.4.7.6...5212.91.58.6 I4: 1,8 # 12 pairs I7: 2,7,3,9 # reduction candidate for 2,7 I7: 2,7 => CTR * 892537164453618.9.671429385365...9.1924.516.81879634525183962477.6...5.92.9..58.6 I7: 3,9 # 12 pairs * PAIR F4: 2,4 COL F F8: 2,4,3 # reduction candidate for 2,4 F8: 2,4 => SOLVED * 892537164453618297671429385365842971924751638187963452518296743736184529249375816 F8: 3 => CTR * 892537164453618.9.671429385365..49..924.516..1879624535183.6.4.7.6...5..2.9..58.6 * PAIR F6: 2,3 COL F F8: 2,3,4 # reduction candidate for 2,3 F8: 4 => SOLVED * 892537164453618297671429385365842971924751638187963452518296743736184529249375816 F8: 2,3 # 12 pairs * PAIR H5: 3,7 BLK 6 I5: 3,7,8 # reduction candidate for 3,7 I5: 3,7 => CTR * 892537164453618.9.671429385365...9.89248516..187963452518..6.4.7.6.8.52.2.9..58.6 I5: 8 # 12 pairs * PAIR H5: 3,7 ROW 5 D5: 3,7,8 # reduction candidate for 3,7 D5: 8 => CTR * 892537164453618.9.671429385365...9..9248516..187963452518..6.4.7.6.8.5292.9..5816 D5: 3,7 # 12 pairs * PAIR H5: 3,7 COL H H9: 3,7,1 # reduction candidate for 3,7 H9: 1 => SOLVED * 892537164453618297671429385365842971924751638187963452518296743736184529249375816 H9: 3,7 # 14 pairs * PAIR I6: 2,3 COL I I7: 2,3,7,9 # reduction candidate for 2,3 I7: 2,3 # 13 pairs I8: 2,3,1,9 # reduction candidate for 2,3 I8: 2,3 => CTR * 892537164453618.97671429385365.849.1924.516.818796.45.518376.497.6.9.5..2.9..58.6 I8: 1,9 # 12 pairs * PAIR B8: 3,4 ROW 8 F8: 3,4,2 # reduction candidate for 3,4 F8: 2 => CTR * 892537164453618.9.671429385365..49..924.516..187963452518..6.4.7.6..25..2.9..58.6 F8: 3,4 # 15 pairs * PAIR E7: 7,9 ROW 7 I7: 7,9,2,3 # reduction candidate for 7,9 I7: 7,9 => CTR * 892537164453618792671429385365...921924.516.818796.45.5183.624.7.6...5..2.9..58.6 I7: 2,3 # 13 pairs * PAIR E9: 4,7 COL E E4: 4,7,8 # reduction candidate for 4,7 E4: 8 # 18 pairs E4: 4,7 # 18 pairs * PAIR G7: 2,7 BLK 9 I7: 2,7,3,9 # reduction candidate for 2,7 I7: 2,7 => CTR * 892537164453618.9.671429385365...9.1924.516.81879634525183962477.6...5.92.9..58.6 I7: 3,9 # 12 pairs * PAIR G7: 2,7 ROW 7 D7: 2,7,3 # reduction candidate for 2,7 D7: 2,7 => SOLVED * 892537164453618297671429385365842971924751638187963452518296743736184529249375816 D7: 3 => CTR * 892537164453618.9.671429385365...9..924.516..1879634525183.624.7.6...5..2.9..58.6 * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190128-absurd-base-pr-000.dot * REASONING * DIS # I4: 2,7 => CTR => I4: 1,8 * DIS # I7: 2,7 => CTR => I7: 3,9 * PRF # F8: 2,4 => SOL * DIS # F8: 3 => CTR => F8: 2,4 * PRF # F8: 4 => SOL * DIS # I5: 3,7 => CTR => I5: 8 * DIS # D5: 8 => CTR => D5: 3,7 * PRF # H9: 1 => SOL * DIS # I8: 2,3 => CTR => I8: 1,9 * DIS # F8: 2 => CTR => F8: 3,4 * DIS # I7: 7,9 => CTR => I7: 2,3 * DIS # I7: 2,7 => CTR => I7: 3,9 * PRF # D7: 2,7 => SOL * DIS # D7: 3 => CTR => D7: 2,7 * CNT 14 HDP CHAINS / 27 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,B9,E7,E9,F4,F6,G2,G7,H5,I2,I6) * 892537164453618.9.671429385365...9..924.516..18796.45.518..6.4.7.6...5..2.9..58.6 * PAIR I2: 2,7 COL I I4: 2,7,1,8 # reduction candidate for 2,7 I4: 2,7 => CTR * 892537164453618297671429385365...912924.51678187962453518..6.4.7.6...5212.91.58.6 I7: 2,7,3,9 # reduction candidate for 2,7 I7: 2,7 => CTR * 892537164453618.9.671429385365...9.1924.516.81879634525183962477.6...5.92.9..58.6 * RESTART * PAIR RESTART * PAIR F4: 2,4 COL F F8: 2,4,3 # reduction candidate for 2,4 F8: 2,4 => SOLVED * 892537164453618297671429385365842971924751638187963452518296743736184529249375816 * DURATION: 0:00:03.040811 START: 03:17:35.007339 END: 03:17:38.048150 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190128-absurd-base-pr-001.dot * REASONING * DIS # I4: 2,7 => CTR => I4: 1,8 * DIS I4: 1,8 # I7: 2,7 => CTR => I7: 3,9 * PRF I4: 1,8 + I7: 3,9 # F8: 2,4 => SOL * STA I4: 1,8 + I7: 3,9 + F8: 2,4 * CNT 3 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190128, absurd
Solution
position: 892537164453618297671429385365842971924751638187963452518296743736184529249375816 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 # I4: 2,7 => CTR => I4: 1,8 * INC # I4: 1,8 => UNS * DIS # I7: 2,7 => CTR => I7: 3,9 * INC # I7: 3,9 => UNS * PRF # F8: 2,4 => SOL * DIS # F8: 3 => CTR => F8: 2,4 * INC # F8: 2,3 => UNS * PRF # F8: 4 => SOL * DIS # I5: 3,7 => CTR => I5: 8 * INC # I5: 8 => UNS * INC # D5: 3,7 => UNS * DIS # D5: 8 => CTR => D5: 3,7 * INC # H9: 3,7 => UNS * PRF # H9: 1 => SOL * INC # I7: 2,3 => UNS * DIS # I8: 2,3 => CTR => I8: 1,9 * INC # I8: 1,9 => UNS * INC # F8: 3,4 => UNS * DIS # F8: 2 => CTR => F8: 3,4 * DIS # I7: 7,9 => CTR => I7: 2,3 * INC # I7: 2,3 => UNS * INC # E4: 4,7 => UNS * INC # E4: 8 => UNS * DIS # I7: 2,7 => CTR => I7: 3,9 * INC # I7: 3,9 => UNS * PRF # D7: 2,7 => SOL * DIS # D7: 3 => CTR => D7: 2,7 * CNT 27 HDP CHAINS / 27 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # I4: 2,7 => CTR => I4: 1,8 * DIS I4: 1,8 # I7: 2,7 => CTR => I7: 3,9 * PRF I4: 1,8 + I7: 3,9 # F8: 2,4 => SOL * STA I4: 1,8 + I7: 3,9 + F8: 2,4 * CNT 3 HDP CHAINS / 3 HYP OPENED