Analysis of zz-www.sudokuoftheday.co.uk-20190319-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: 5...3.8....1....6..89....21.45..7.......894..9...........2...8......65.3...3.4..6 initial
Autosolve
position: 5..1328....1948765489765321.456271.....5894..9..41365....2.198....8.65.3...3.42.6 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B5: 6,7 => CTR => B5: 1,2,3 * PRF # B7: 6,7 => SOL * DIS # C5: 6,7 => CTR => C5: 2,3 * PRF # C5: 2,3 => SOL * DIS # C7: 6,7 => CTR => C7: 3,4 * DIS # A5: 2,3 => CTR => A5: 1,6,7 * DIS # B5: 2,3 => CTR => B5: 1,6,7 * DIS # A5: 2,7 => CTR => A5: 1,3,6 * PRF # A5: 1,3,6 => SOL * DIS # B5: 2,7 => CTR => B5: 1,3,6 * DIS # C5: 2,7 => CTR => C5: 3,6 * PRF # C6: 2,7 => SOL * DIS # C6: 8 => CTR => C6: 2,7 * DIS # I6: 2,7 => CTR => I6: 8 * PRF # I6: 8 => SOL * DIS # B8: 2,7 => CTR => B8: 1,9 * DIS # A5: 3,7 => CTR => A5: 1,2,6 * PRF # A5: 1,2,6 => SOL * DIS # B5: 3,7 => CTR => B5: 1,2,6 * PRF # C5: 3,7 => SOL * DIS # C5: 2,6 => CTR => C5: 3,7 * DIS # I6: 2,7 => CTR => I6: 8 * PRF # I6: 8 => SOL * DIS # A5: 2,7 => CTR => A5: 1,3,6 * PRF # A5: 1,3,6 => SOL * DIS # B5: 2,7 => CTR => B5: 1,3,6 * DIS # C5: 2,7 => CTR => C5: 3,6 * DIS # A9: 1 => CTR => A9: 7,8 * PRF # C6: 7,8 => SOL * DIS # C6: 2 => CTR => C6: 7,8 * DIS # B7: 5,7 => CTR => B7: 3,6 * DIS # B8: 1,2 => CTR => B8: 7,9 * DIS # H8: 1 => CTR => H8: 4,7 * PRF # C7: 4,7 => SOL * DIS # C7: 3,6 => CTR => C7: 4,7 * DIS # H8: 1,7 => CTR => H8: 4 * PRF # H8: 4 => SOL * PRF # A9: 1,7 => SOL * DIS # A9: 8 => CTR => A9: 1,7 * CNT 39 HDP CHAINS / 54 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B5: 6,7 => CTR => B5: 1,2,3 * PRF B5: 1,2,3 # B7: 6,7 => SOL * STA B5: 1,2,3 + B7: 6,7 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 5...3.8....1....6..89....21.45..7.......894..9...........2...8......65.3...3.4..6 | initial |
| 5..1328....1948765489765321.456271.....5894..9..41365....2.198....8.65.3...3.42.6 | autosolve |
| 576132894231948765489765321845627139613589472927413658364251987192876543758394216 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) B1: 6,7 C1: 6,7 A2: 2,3 B2: 2,3 H1: 4,9 I1: 4,9 A4: 3,8 B6: 2,7 H4: 3,9 I4: 8,9 H5: 3,7 I5: 2,7 B9: 5,9 C9: 7,8 E7: 5,7 E8: 7,9 E9: 5,9 I7: 4,7 H9: 1,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A5,B5: 1.. / A5 = 1 => 0 pairs (X) / B5 = 1 => 19 pairs (_) H8,H9: 1.. / H8 = 1 => 0 pairs (X) / H9 = 1 => 23 pairs (_) A9,H9: 1.. / A9 = 1 => 0 pairs (X) / H9 = 1 => 23 pairs (_) B5,B8: 1.. / B5 = 1 => 19 pairs (_) / B8 = 1 => 0 pairs (X) A2,B2: 2.. / A2 = 2 => 18 pairs (_) / B2 = 2 => 0 pairs (X) I5,I6: 2.. / I5 = 2 => 19 pairs (_) / I6 = 2 => 0 pairs (X) A2,B2: 3.. / A2 = 3 => 0 pairs (X) / B2 = 3 => 18 pairs (_) H4,H5: 3.. / H4 = 3 => 0 pairs (*) / H5 = 3 => 0 pairs (X) A4,H4: 3.. / A4 = 3 => 0 pairs (X) / H4 = 3 => 0 pairs (_) C5,C7: 3.. / C5 = 3 => 0 pairs (*) / C7 = 3 => 0 pairs (X) H1,I1: 4.. / H1 = 4 => 0 pairs (X) / I1 = 4 => 0 pairs (_) C7,C8: 4.. / C7 = 4 => 0 pairs (*) / C8 = 4 => 0 pairs (X) I7,H8: 4.. / I7 = 4 => 0 pairs (X) / H8 = 4 => 0 pairs (_) C7,I7: 4.. / C7 = 4 => 0 pairs (*) / I7 = 4 => 0 pairs (X) C8,H8: 4.. / C8 = 4 => 0 pairs (X) / H8 = 4 => 0 pairs (_) H1,H8: 4.. / H1 = 4 => 0 pairs (X) / H8 = 4 => 0 pairs (_) I1,I7: 4.. / I1 = 4 => 0 pairs (*) / I7 = 4 => 0 pairs (X) B7,B9: 5.. / B7 = 5 => 0 pairs (X) / B9 = 5 => 18 pairs (_) E7,E9: 5.. / E7 = 5 => 18 pairs (_) / E9 = 5 => 0 pairs (X) B7,E7: 5.. / B7 = 5 => 0 pairs (X) / E7 = 5 => 18 pairs (_) B9,E9: 5.. / B9 = 5 => 18 pairs (_) / E9 = 5 => 0 pairs (X) B1,C1: 6.. / B1 = 6 => 0 pairs (X) / C1 = 6 => 0 pairs (_) A5,A7: 6.. / A5 = 6 => 0 pairs (*) / A7 = 6 => 0 pairs (X) B1,C1: 7.. / B1 = 7 => 0 pairs (*) / C1 = 7 => 0 pairs (X) E7,E8: 7.. / E7 = 7 => 0 pairs (X) / E8 = 7 => 18 pairs (_) A4,C6: 8.. / A4 = 8 => 0 pairs (*) / C6 = 8 => 0 pairs (X) I4,I6: 8.. / I4 = 8 => 0 pairs (X) / I6 = 8 => 0 pairs (_) A9,C9: 8.. / A9 = 8 => 0 pairs (X) / C9 = 8 => 0 pairs (_) A4,I4: 8.. / A4 = 8 => 0 pairs (*) / I4 = 8 => 0 pairs (X) C6,I6: 8.. / C6 = 8 => 0 pairs (X) / I6 = 8 => 0 pairs (_) A4,A9: 8.. / A4 = 8 => 0 pairs (*) / A9 = 8 => 0 pairs (X) C6,C9: 8.. / C6 = 8 => 0 pairs (X) / C9 = 8 => 0 pairs (_) H1,I1: 9.. / H1 = 9 => 0 pairs (*) / I1 = 9 => 0 pairs (X) H4,I4: 9.. / H4 = 9 => 0 pairs (X) / I4 = 9 => 0 pairs (_) B8,B9: 9.. / B8 = 9 => 18 pairs (_) / B9 = 9 => 0 pairs (X) E8,E9: 9.. / E8 = 9 => 0 pairs (X) / E9 = 9 => 18 pairs (_) B8,E8: 9.. / B8 = 9 => 18 pairs (_) / E8 = 9 => 0 pairs (X) B9,E9: 9.. / B9 = 9 => 0 pairs (X) / E9 = 9 => 18 pairs (_) H1,H4: 9.. / H1 = 9 => 0 pairs (*) / H4 = 9 => 0 pairs (X) I1,I4: 9.. / I1 = 9 => 0 pairs (X) / I4 = 9 => 0 pairs (_) * DURATION: 0:00:48.111271 START: 04:38:26.938428 END: 04:39:15.049699 2019-05-01 * CP COUNT: (40) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,B1,B2,B6,B9,C1,C9,E7,E8,E9,H1,H4,H5,H9,I1,I4,I5,I7) * 5..1328....1948765489765321.456271.....5894..9..41365....2.198....8.65.3...3.42.6 * PAIR B1: 6,7 COL B B5: 6,7,1,2,3 # reduction candidate for 6,7 B5: 6,7 => CTR * 5..1328....1948765489765321.456271..1..5894..9..41365.653271984.14896573798354216 B5: 1,2,3 # 19 pairs B7: 6,7,3,5 # reduction candidate for 6,7 B7: 6,7 => SOLVED * 576132894231948765489765321845627139613589472927413658364251987192876543758394216 B7: 3,5 # 20 pairs * PAIR C1: 6,7 COL C C5: 6,7,2,3 # reduction candidate for 6,7 C5: 6,7 => CTR * 5..132849..1948765489765321.45627198...58943.9..41365...32.1984..48.65.3...3.42.6 C5: 2,3 => SOLVED * 576132894231948765489765321845627139613589472927413658364251987192876543758394216 C7: 6,7,3,4 # reduction candidate for 6,7 C7: 6,7 => CTR * 5..1328....1948765489765321.456271....35894729..41365....2.198....8.65.3...3.42.6 C7: 3,4 # 20 pairs * PAIR A2: 2,3 COL A A5: 2,3,1,6,7 # reduction candidate for 2,3 A5: 2,3 => CTR * 567132849.31948765489765321.45627198.1658943797.41365.6.32.1984..48.65.3...3.42.6 A5: 1,6,7 # 19 pairs * PAIR B2: 2,3 COL B B5: 2,3,1,6,7 # reduction candidate for 2,3 B5: 2,3 => CTR * 567132849..19487654897653218456271..1.65894..9..41365.6.32.1984.14896573798354216 B5: 1,6,7 # 19 pairs * PAIR B6: 2,7 BLK 4 A5: 2,7,1,3,6 # reduction candidate for 2,7 A5: 2,7 => CTR * 567132849.31948765489765321345627198.1658943.9..41365.6.32.1984..48.65.3...3.42.6 A5: 1,3,6 => SOLVED * 576132894231948765489765321845627139613589472927413658364251987192876543758394216 B5: 2,7,1,3,6 # reduction candidate for 2,7 B5: 2,7 => CTR * 5..1328....1948765489765321.456271..1.658943.9..41365.6.32.1984.14896573798354216 B5: 1,3,6 # 19 pairs C5: 2,7,3,6 # reduction candidate for 2,7 C5: 2,7 => CTR * 576132849.319487654897653213456271987..58943.9.841365...32.1984..48.65.38.73.4216 C5: 3,6 # 20 pairs C6: 2,7,8 # reduction candidate for 2,7 C6: 2,7 => SOLVED * 576132894231948765489765321845627139613589472927413658364251987192876543758394216 C6: 8 => CTR * 5761328....19487654897653213456271987..5894..9.841365....2.198....8.65.38.73.4216 * PAIR B6: 2,7 ROW 6 I6: 2,7,8 # reduction candidate for 2,7 I6: 2,7 => CTR * 5761328.9..19487654897653213456271987..5894..9.841365....2.198....8.65.38.73.4216 I6: 8 => SOLVED * 576132894231948765489765321845627139613589472927413658364251987192876543758394216 * PAIR B6: 2,7 COL B B8: 2,7,1,9 # reduction candidate for 2,7 B8: 2,7 => CTR * 567132849.31948765489765321.45627198.1.58943.9.841365..5.271984..48965.3.9.3542.6 B8: 1,9 # 20 pairs * PAIR H5: 3,7 ROW 5 A5: 3,7,1,2,6 # reduction candidate for 3,7 A5: 3,7 => CTR * 567132849.31948765489765321.45627198.165894329..41365.6.32.1984..48.65.3...3.42.6 A5: 1,2,6 => SOLVED * 576132894231948765489765321845627139613589472927413658364251987192876543758394216 B5: 3,7,1,2,6 # reduction candidate for 3,7 B5: 3,7 => CTR * 5..1328....1948765489765321.456271..1.65894.29..41365.6.32.1984.14896573798354216 B5: 1,2,6 # 19 pairs C5: 3,7,2,6 # reduction candidate for 3,7 C5: 3,7 => SOLVED * 576132894231948765489765321845627139613589472927413658364251987192876543758394216 C5: 2,6 => CTR * 576132849.319487654897653213456271987..58943.9.841365...32.1984..48.65.38.73.4216 * PAIR I5: 2,7 BLK 6 I6: 2,7,8 # reduction candidate for 2,7 I6: 2,7 => CTR * 5761328.9..19487654897653213456271987..5894..9.841365....2.198....8.65.38.73.4216 I6: 8 => SOLVED * 576132894231948765489765321845627139613589472927413658364251987192876543758394216 * PAIR I5: 2,7 ROW 5 A5: 2,7,1,3,6 # reduction candidate for 2,7 A5: 2,7 => CTR * 567132849.31948765489765321345627198.1658943.9..41365.6.32.1984..48.65.3...3.42.6 A5: 1,3,6 => SOLVED * 576132894231948765489765321845627139613589472927413658364251987192876543758394216 B5: 2,7,1,3,6 # reduction candidate for 2,7 B5: 2,7 => CTR * 5..1328....1948765489765321.456271..1.658943.9..41365.6.32.1984.14896573798354216 B5: 1,3,6 # 19 pairs C5: 2,7,3,6 # reduction candidate for 2,7 C5: 2,7 => CTR * 576132849.319487654897653213456271987..58943.9.841365...32.1984..48.65.38.73.4216 C5: 3,6 # 20 pairs * PAIR C9: 7,8 BLK 7 A9: 7,8,1 # reduction candidate for 7,8 A9: 1 => CTR * 5..1328....1948765489765321845627139...5894729..413658...2.19877..8.65.3...3.42.6 A9: 7,8 # 23 pairs * PAIR C9: 7,8 COL C C6: 7,8,2 # reduction candidate for 7,8 C6: 7,8 => SOLVED * 576132894231948765489765321845627139613589472927413658364251987192876543758394216 C6: 2 => CTR * 5..1328....1948765489765321845627139...589472972413658...2.1987...876543...3.42.6 * PAIR E7: 5,7 ROW 7 B7: 5,7,3,6 # reduction candidate for 5,7 B7: 5,7 => CTR * 576132849.319487654897653213456271987..58943.9.841365...32.1984..48.65.38.73.4216 B7: 3,6 # 19 pairs * PAIR E8: 7,9 ROW 8 B8: 7,9,1,2 # reduction candidate for 7,9 B8: 1,2 => CTR * 576132849.319487654897653213456271987..58943.9.841365..53271984..48965.3897354216 B8: 7,9 # 23 pairs * PAIR I7: 4,7 BLK 9 H8: 4,7,1 # reduction candidate for 4,7 H8: 1 => CTR * 5..132849..1948765489765321.45627198...58943.9.841365...32.1984..48.6513...3.42.6 H8: 4,7 # 23 pairs * PAIR I7: 4,7 ROW 7 C7: 4,7,3,6 # reduction candidate for 4,7 C7: 4,7 => SOLVED * 576132894231948765489765321845627139613589472927413658364251987192876543758394216 C7: 3,6 => CTR * 576132849.319487654897653213456271987..58943.9.841365...32.1984..48.65.38.73.4216 * PAIR H9: 1,7 BLK 9 H8: 1,7,4 # reduction candidate for 1,7 H8: 1,7 => CTR * 576132849.319487654897653213456271987..58943.9.841365...32.1984..48.65.38.73.4216 H8: 4 => SOLVED * 576132894231948765489765321845627139613589472927413658364251987192876543758394216 * PAIR H9: 1,7 ROW 9 A9: 1,7,8 # reduction candidate for 1,7 A9: 1,7 => SOLVED * 576132894231948765489765321845627139613589472927413658364251987192876543758394216 A9: 8 => CTR * 5761328....19487654897653213456271987..5894..9..41365....2.198....8.65.38.73.4216 * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190319-absurd-base-pr-000.dot * REASONING * DIS # B5: 6,7 => CTR => B5: 1,2,3 * PRF # B7: 6,7 => SOL * DIS # C5: 6,7 => CTR => C5: 2,3 * PRF # C5: 2,3 => SOL * DIS # C7: 6,7 => CTR => C7: 3,4 * DIS # A5: 2,3 => CTR => A5: 1,6,7 * DIS # B5: 2,3 => CTR => B5: 1,6,7 * DIS # A5: 2,7 => CTR => A5: 1,3,6 * PRF # A5: 1,3,6 => SOL * DIS # B5: 2,7 => CTR => B5: 1,3,6 * DIS # C5: 2,7 => CTR => C5: 3,6 * PRF # C6: 2,7 => SOL * DIS # C6: 8 => CTR => C6: 2,7 * DIS # I6: 2,7 => CTR => I6: 8 * PRF # I6: 8 => SOL * DIS # B8: 2,7 => CTR => B8: 1,9 * DIS # A5: 3,7 => CTR => A5: 1,2,6 * PRF # A5: 1,2,6 => SOL * DIS # B5: 3,7 => CTR => B5: 1,2,6 * PRF # C5: 3,7 => SOL * DIS # C5: 2,6 => CTR => C5: 3,7 * DIS # I6: 2,7 => CTR => I6: 8 * PRF # I6: 8 => SOL * DIS # A5: 2,7 => CTR => A5: 1,3,6 * PRF # A5: 1,3,6 => SOL * DIS # B5: 2,7 => CTR => B5: 1,3,6 * DIS # C5: 2,7 => CTR => C5: 3,6 * DIS # A9: 1 => CTR => A9: 7,8 * PRF # C6: 7,8 => SOL * DIS # C6: 2 => CTR => C6: 7,8 * DIS # B7: 5,7 => CTR => B7: 3,6 * DIS # B8: 1,2 => CTR => B8: 7,9 * DIS # H8: 1 => CTR => H8: 4,7 * PRF # C7: 4,7 => SOL * DIS # C7: 3,6 => CTR => C7: 4,7 * DIS # H8: 1,7 => CTR => H8: 4 * PRF # H8: 4 => SOL * PRF # A9: 1,7 => SOL * DIS # A9: 8 => CTR => A9: 1,7 * CNT 39 HDP CHAINS / 54 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,B1,B2,B6,B9,C1,C9,E7,E8,E9,H1,H4,H5,H9,I1,I4,I5,I7) * 5..1328....1948765489765321.456271.....5894..9..41365....2.198....8.65.3...3.42.6 * PAIR B1: 6,7 COL B B5: 6,7,1,2,3 # reduction candidate for 6,7 B5: 6,7 => CTR * 5..1328....1948765489765321.456271..1..5894..9..41365.653271984.14896573798354216 B7: 6,7,3,5 # reduction candidate for 6,7 B7: 6,7 => SOLVED * 576132894231948765489765321845627139613589472927413658364251987192876543758394216 * DURATION: 0:00:02.312372 START: 04:39:53.824889 END: 04:39:56.137261 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190319-absurd-base-pr-001.dot * REASONING * DIS # B5: 6,7 => CTR => B5: 1,2,3 * PRF B5: 1,2,3 # B7: 6,7 => SOL * STA B5: 1,2,3 + B7: 6,7 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190319, absurd
Solution
position: 576132894231948765489765321845627139613589472927413658364251987192876543758394216 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 # B5: 6,7 => CTR => B5: 1,2,3 * INC # B5: 1,2,3 => UNS * PRF # B7: 6,7 => SOL * INC # B7: 3,5 => UNS * DIS # C5: 6,7 => CTR => C5: 2,3 * PRF # C5: 2,3 => SOL * DIS # C7: 6,7 => CTR => C7: 3,4 * INC # C7: 3,4 => UNS * DIS # A5: 2,3 => CTR => A5: 1,6,7 * INC # A5: 1,6,7 => UNS * DIS # B5: 2,3 => CTR => B5: 1,6,7 * INC # B5: 1,6,7 => UNS * DIS # A5: 2,7 => CTR => A5: 1,3,6 * PRF # A5: 1,3,6 => SOL * DIS # B5: 2,7 => CTR => B5: 1,3,6 * INC # B5: 1,3,6 => UNS * DIS # C5: 2,7 => CTR => C5: 3,6 * INC # C5: 3,6 => UNS * PRF # C6: 2,7 => SOL * DIS # C6: 8 => CTR => C6: 2,7 * DIS # I6: 2,7 => CTR => I6: 8 * PRF # I6: 8 => SOL * DIS # B8: 2,7 => CTR => B8: 1,9 * INC # B8: 1,9 => UNS * DIS # A5: 3,7 => CTR => A5: 1,2,6 * PRF # A5: 1,2,6 => SOL * DIS # B5: 3,7 => CTR => B5: 1,2,6 * INC # B5: 1,2,6 => UNS * PRF # C5: 3,7 => SOL * DIS # C5: 2,6 => CTR => C5: 3,7 * DIS # I6: 2,7 => CTR => I6: 8 * PRF # I6: 8 => SOL * DIS # A5: 2,7 => CTR => A5: 1,3,6 * PRF # A5: 1,3,6 => SOL * DIS # B5: 2,7 => CTR => B5: 1,3,6 * INC # B5: 1,3,6 => UNS * DIS # C5: 2,7 => CTR => C5: 3,6 * INC # C5: 3,6 => UNS * INC # A9: 7,8 => UNS * DIS # A9: 1 => CTR => A9: 7,8 * PRF # C6: 7,8 => SOL * DIS # C6: 2 => CTR => C6: 7,8 * DIS # B7: 5,7 => CTR => B7: 3,6 * INC # B7: 3,6 => UNS * INC # B8: 7,9 => UNS * DIS # B8: 1,2 => CTR => B8: 7,9 * INC # H8: 4,7 => UNS * DIS # H8: 1 => CTR => H8: 4,7 * PRF # C7: 4,7 => SOL * DIS # C7: 3,6 => CTR => C7: 4,7 * DIS # H8: 1,7 => CTR => H8: 4 * PRF # H8: 4 => SOL * PRF # A9: 1,7 => SOL * DIS # A9: 8 => CTR => A9: 1,7 * CNT 54 HDP CHAINS / 54 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B5: 6,7 => CTR => B5: 1,2,3 * PRF B5: 1,2,3 # B7: 6,7 => SOL * STA B5: 1,2,3 + B7: 6,7 * CNT 2 HDP CHAINS / 2 HYP OPENED