Analysis of zz-www.sudokuoftheday.co.uk-20190219-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019
level: medium
position: .......4..2.9..6.3..36......9.42......1....8......6.7..3..984..58..6..1...7...... initial
Autosolve
position: .......4..2.9..653..36......9.42......1..9.8......6.7.13..984..58..6..1...7...... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G3: 2,9 => CTR => G3: 1,7,8 * DIS # H9: 2,9 => CTR => H9: 3,6 * PRF # H9: 3,6 => SOL * DIS # B5: 4,5 => CTR => B5: 6,7 * DIS # C6: 4,5 => CTR => C6: 2 * PRF # C6: 2 => SOL * PRF # I6: 4,5 => SOL * DIS # B3: 4,5 => CTR => B3: 1,7 * PRF # H9: 3,6 => SOL * DIS # H9: 2,9 => CTR => H9: 3,6 * DIS # A9: 4,9 => CTR => A9: 2,6 * DIS # A9: 4,6 => CTR => A9: 2,9 * DIS # B5: 4,6 => CTR => B5: 5,7 * PRF # H9: 2,6 => SOL * CNT 14 HDP CHAINS / 34 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # G3: 2,9 => CTR => G3: 1,7,8 * DIS G3: 1,7,8 # H9: 2,9 => CTR => H9: 3,6 * PRF G3: 1,7,8 + H9: 3,6 => SOL * STA G3: 1,7,8 + H9: 3,6 * CNT 3 HDP CHAINS / 9 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .......4..2.9..6.3..36......9.42......1....8......6.7..3..984..58..6..1...7...... | initial |
| .......4..2.9..653..36......9.42......1..9.8......6.7.13..984..58..6..1...7...... | autosolve |
| 965372148724981653813645792698427531471539286352816974136798425589264317247153869 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) C2: 4,8 H3: 2,9 B6: 4,5 H4: 3,6 C7: 2,6 B9: 4,6 D7: 5,7 H7: 2,6 I7: 5,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,B3: 1.. / B1 = 1 => 9 pairs (_) / B3 = 1 => 9 pairs (_) E2,F2: 1.. / E2 = 1 => 10 pairs (_) / F2 = 1 => 11 pairs (_) D6,D9: 1.. / D6 = 1 => 9 pairs (_) / D9 = 1 => 9 pairs (_) C7,H7: 2.. / C7 = 2 => 0 pairs (X) / H7 = 2 => 0 pairs (_) H4,H9: 3.. / H4 = 3 => 10 pairs (_) / H9 = 3 => 0 pairs (X) I5,I6: 4.. / I5 = 4 => 10 pairs (_) / I6 = 4 => 0 pairs (*) C8,F8: 4.. / C8 = 4 => 0 pairs (X) / F8 = 4 => 12 pairs (_) D7,I7: 5.. / D7 = 5 => 13 pairs (_) / I7 = 5 => 10 pairs (_) C7,H7: 6.. / C7 = 6 => 0 pairs (*) / H7 = 6 => 0 pairs (X) A4,F4: 7.. / A4 = 7 => 0 pairs (X) / F4 = 7 => 15 pairs (_) D7,I7: 7.. / D7 = 7 => 10 pairs (_) / I7 = 7 => 13 pairs (_) A4,C4: 8.. / A4 = 8 => 0 pairs (X) / C4 = 8 => 13 pairs (_) D6,E6: 8.. / D6 = 8 => 9 pairs (_) / E6 = 8 => 9 pairs (_) G9,I9: 8.. / G9 = 8 => 10 pairs (_) / I9 = 8 => 10 pairs (_) D1,D6: 8.. / D1 = 8 => 9 pairs (_) / D6 = 8 => 9 pairs (_) G6,I6: 9.. / G6 = 9 => 9 pairs (_) / I6 = 9 => 11 pairs (_) C8,A9: 9.. / C8 = 9 => 12 pairs (_) / A9 = 9 => 0 pairs (X) C1,C8: 9.. / C1 = 9 => 0 pairs (X) / C8 = 9 => 12 pairs (_) H3,H9: 9.. / H3 = 9 => 18 pairs (_) / H9 = 9 => 0 pairs (X) * DURATION: 0:00:18.391647 START: 03:51:16.211024 END: 03:51:34.602671 2019-05-01 * CP COUNT: (19) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,B9,C2,C7,D7,H3,H4,H7,I7) * .......4..2.9..653..36......9.42......1..9.8......6.7.13..984..58..6..1...7...... * PAIR C2: 4,8 BLK 1 A2: 4,8,7 # reduction candidate for 4,8 A2: 4,8 # 13 pairs A3: 4,8,7,9 # reduction candidate for 4,8 A3: 4,8 # 19 pairs * PAIR C2: 4,8 ROW 2 E2: 4,8,1,7 # reduction candidate for 4,8 E2: 4,8 # 16 pairs E2: 1,7 # 10 pairs * PAIR H3: 2,9 BLK 3 G1: 2,9,1,7,8 # reduction candidate for 2,9 G1: 2,9 # 10 pairs I1: 2,9,1,7,8 # reduction candidate for 2,9 I1: 2,9 # 10 pairs G3: 2,9,1,7,8 # reduction candidate for 2,9 G3: 2,9 => CTR * 9......4..2.9.1653..36.592..9.427.3..71..9284.....6.79132.9846.589.64.1...7....9. G3: 1,7,8 # 9 pairs I3: 2,9,1,7,8 # reduction candidate for 2,9 I3: 2,9 # 20 pairs * PAIR H3: 2,9 COL H H9: 2,9,3,6 # reduction candidate for 2,9 H9: 2,9 => CTR * ..6....4..2.9..653..36.....79.42..36.61..9.84.....6.7.132.9846.58..6..1.647...... H9: 3,6 => SOLVED * 965372148724981653813645792698427531471539286352816974136798425589264317247153869 * PAIR B6: 4,5 BLK 4 B5: 4,5,6,7 # reduction candidate for 4,5 B5: 4,5 => CTR * 6.5....4..2.9..6539.36...2..9642..3.7.1..9.863.2..6.7.13..984..58..6..1...7...... B5: 6,7 # 10 pairs C6: 4,5,2 # reduction candidate for 4,5 C6: 4,5 => CTR * ..6....4..249..653..364.....9842...6671..9284245..6.7.132.9846.589.64.1.467...... C6: 2 => SOLVED * 965372148724981653813645792698427531471539286352816974136798425589264317247153869 * PAIR B6: 4,5 ROW 6 I6: 4,5,1,2,9 # reduction candidate for 4,5 I6: 4,5 => SOLVED * 965372148724981653813645792698427531471539286352816974136798425589264317247153869 I6: 1,2,9 # 10 pairs * PAIR B6: 4,5 COL B B3: 4,5,1,7 # reduction candidate for 4,5 B3: 4,5 => CTR * .1.....4..2.9..653..36......9.427.3..71..9.8......6.7.132.9846.58..6..1..67...... B3: 1,7 # 10 pairs * PAIR H4: 3,6 ROW 4 A4: 3,6,7,8 # reduction candidate for 3,6 A4: 3,6 # 23 pairs A4: 7,8 # 10 pairs * PAIR H4: 3,6 COL H H9: 3,6,2,9 # reduction candidate for 3,6 H9: 3,6 => SOLVED * 965372148724981653813645792698427531471539286352816974136798425589264317247153869 H9: 2,9 => CTR * ..6....4..2.9..653..36.....79.42..36.61..9.84.....6.7.132.9846.58..6..1.647...... * PAIR C7: 2,6 BLK 7 A9: 2,6,4,9 # reduction candidate for 2,6 A9: 4,9 => CTR * ..6....4..249..653..364.....9842...6671..9284245..6.7.132.9846.589.64.1.467...... A9: 2,6 # 15 pairs * PAIR B9: 4,6 BLK 7 A9: 4,6,2,9 # reduction candidate for 4,6 A9: 4,6 => CTR * ..6....4..2.9..653..36.....79.42..36.61.79.84.....6.7.132.9846.589.64.1.647...... A9: 2,9 # 10 pairs * PAIR B9: 4,6 COL B B5: 4,6,5,7 # reduction candidate for 4,6 B5: 4,6 => CTR * 6.5....4..2.9..6539.36...2..9.42......1..9.8..5...6.7.132.9846.589.64.1.467....9. B5: 5,7 # 12 pairs * PAIR D7: 5,7 COL D D1: 5,7,2,3,8 # reduction candidate for 5,7 D1: 5,7 # 15 pairs D5: 5,7,3 # reduction candidate for 5,7 D5: 5,7 # 11 pairs * PAIR H7: 2,6 BLK 9 H9: 2,6,3,9 # reduction candidate for 2,6 H9: 2,6 => SOLVED * 965372148724981653813645792698427531471539286352816974136798425589264317247153869 H9: 3,9 # 10 pairs I9: 2,6,5,8,9 # reduction candidate for 2,6 I9: 2,6 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190219-absurd-base-pr-000.dot * REASONING * DIS # G3: 2,9 => CTR => G3: 1,7,8 * DIS # H9: 2,9 => CTR => H9: 3,6 * PRF # H9: 3,6 => SOL * DIS # B5: 4,5 => CTR => B5: 6,7 * DIS # C6: 4,5 => CTR => C6: 2 * PRF # C6: 2 => SOL * PRF # I6: 4,5 => SOL * DIS # B3: 4,5 => CTR => B3: 1,7 * PRF # H9: 3,6 => SOL * DIS # H9: 2,9 => CTR => H9: 3,6 * DIS # A9: 4,9 => CTR => A9: 2,6 * DIS # A9: 4,6 => CTR => A9: 2,9 * DIS # B5: 4,6 => CTR => B5: 5,7 * PRF # H9: 2,6 => SOL * CNT 14 HDP CHAINS / 34 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,B9,C2,C7,D7,H3,H4,H7,I7) * .......4..2.9..653..36......9.42......1..9.8......6.7.13..984..58..6..1...7...... * PAIR C2: 4,8 BLK 1 A2: 4,8,7 # reduction candidate for 4,8 A2: 4,8 # 13 pairs A3: 4,8,7,9 # reduction candidate for 4,8 A3: 4,8 # 19 pairs * PAIR C2: 4,8 ROW 2 E2: 4,8,1,7 # reduction candidate for 4,8 E2: 4,8 # 16 pairs E2: 1,7 # 10 pairs * PAIR H3: 2,9 BLK 3 G1: 2,9,1,7,8 # reduction candidate for 2,9 G1: 2,9 # 10 pairs I1: 2,9,1,7,8 # reduction candidate for 2,9 I1: 2,9 # 10 pairs G3: 2,9,1,7,8 # reduction candidate for 2,9 G3: 2,9 => CTR * 9......4..2.9.1653..36.592..9.427.3..71..9284.....6.79132.9846.589.64.1...7....9. I3: 2,9,1,7,8 # reduction candidate for 2,9 I3: 2,9 # 20 pairs * PAIR H3: 2,9 COL H H9: 2,9,3,6 # reduction candidate for 2,9 H9: 2,9 => CTR * ..6....4..2.9..653..36.....79.42..36.61..9.84.....6.7.132.9846.58..6..1.647...... H9: 3,6 => SOLVED * 965372148724981653813645792698427531471539286352816974136798425589264317247153869 * DURATION: 0:00:06.780987 START: 03:51:56.562255 END: 03:52:03.343242 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190219-absurd-base-pr-001.dot * REASONING * DIS # G3: 2,9 => CTR => G3: 1,7,8 * DIS G3: 1,7,8 # H9: 2,9 => CTR => H9: 3,6 * PRF G3: 1,7,8 + H9: 3,6 => SOL * STA G3: 1,7,8 + H9: 3,6 * CNT 3 HDP CHAINS / 9 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190219, absurd
Solution
position: 965372148724981653813645792698427531471539286352816974136798425589264317247153869 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 # A2: 4,8 => UNS * INC # A3: 4,8 => UNS * INC # E2: 4,8 => UNS * INC # E2: 1,7 => UNS * INC # G1: 2,9 => UNS * INC # I1: 2,9 => UNS * DIS # G3: 2,9 => CTR => G3: 1,7,8 * INC # G3: 1,7,8 => UNS * INC # I3: 2,9 => UNS * DIS # H9: 2,9 => CTR => H9: 3,6 * PRF # H9: 3,6 => SOL * DIS # B5: 4,5 => CTR => B5: 6,7 * INC # B5: 6,7 => UNS * DIS # C6: 4,5 => CTR => C6: 2 * PRF # C6: 2 => SOL * PRF # I6: 4,5 => SOL * INC # I6: 1,2,9 => UNS * DIS # B3: 4,5 => CTR => B3: 1,7 * INC # B3: 1,7 => UNS * INC # A4: 3,6 => UNS * INC # A4: 7,8 => UNS * PRF # H9: 3,6 => SOL * DIS # H9: 2,9 => CTR => H9: 3,6 * INC # A9: 2,6 => UNS * DIS # A9: 4,9 => CTR => A9: 2,6 * DIS # A9: 4,6 => CTR => A9: 2,9 * INC # A9: 2,9 => UNS * DIS # B5: 4,6 => CTR => B5: 5,7 * INC # B5: 5,7 => UNS * INC # D1: 5,7 => UNS * INC # D5: 5,7 => UNS * PRF # H9: 2,6 => SOL * INC # H9: 3,9 => UNS * INC # I9: 2,6 => UNS * CNT 34 HDP CHAINS / 34 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A2: 4,8 => UNS * INC # A3: 4,8 => UNS * INC # E2: 4,8 => UNS * INC # E2: 1,7 => UNS * INC # G1: 2,9 => UNS * INC # I1: 2,9 => UNS * DIS # G3: 2,9 => CTR => G3: 1,7,8 * INC G3: 1,7,8 # I3: 2,9 => UNS * DIS G3: 1,7,8 # H9: 2,9 => CTR => H9: 3,6 * PRF G3: 1,7,8 + H9: 3,6 => SOL * STA G3: 1,7,8 + H9: 3,6 * CNT 10 HDP CHAINS / 9 HYP OPENED