Analysis of zz-www.sudokuoftheday.co.uk-20060512-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006
level: medium
position: ..9..46..34.......2..1....49..5.........61..5..5..97....69..18...26..9......824.. initial
Autosolve
position: ..9..46..34..56..926.19.5.49..5.........61.956.5..97....694.18248261.9...9..824.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A1: 7,8 => SOL * DIS # C4: 7,8 => CTR => C4: 1,3,4 * DIS # C5: 7,8 => CTR => C5: 3,4 * PRF # D2: 7 => SOL * DIS # H1: 3,7 => CTR => H1: 1,2 * DIS # H9: 3,7 => CTR => H9: 5,6 * DIS # C4: 7,8 => CTR => C4: 1,3,4 * DIS # C5: 7,8 => CTR => C5: 3,4 * DIS # D5: 7,8 => CTR => D5: 2,3,4 * PRF # A1: 7,8 => SOL * DIS # D5: 2,3 => CTR => D5: 4,7,8 * DIS # I4: 6 => CTR => I4: 1,8 * DIS # I1: 1,8 => CTR => I1: 3,7 * DIS # B7: 5,7 => CTR => B7: 3 * DIS # F7: 3 => CTR => F7: 5,7 * PRF # A1: 5,7 => SOL * PRF # C9: 3,7 => SOL * DIS # H9: 3,7 => CTR => H9: 5,6 * DIS # I9: 3,7 => CTR => I9: 6 * DIS # D5: 3,7 => CTR => D5: 2,4,8 * DIS # H9: 3,7 => CTR => H9: 5,6 * DIS # I9: 3,7 => CTR => I9: 6 * DIS # I1: 1,8 => CTR => I1: 3,7 * CNT 23 HDP CHAINS / 68 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A1: 7,8 => SOL * STA A1: 7,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..9..46..34.......2..1....49..5.........61..5..5..97....69..18...26..9......824.. | initial |
| ..9..46..34..56..926.19.5.49..5.........61.956.5..97....694.18248261.9...9..824.. | autosolve |
| 759824613341756829268193574924578361873461295615239748536947182482615937197382456 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) C3: 7,8 G2: 2,8 H3: 3,7 A5: 7,8 E6: 2,3 I6: 1,8 A7: 5,7 D9: 3,7 I8: 3,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A9,C9: 1.. / A9 = 1 => 0 pairs (*) / C9 = 1 => 0 pairs (X) C2,H2: 1.. / C2 = 1 => 0 pairs (*) / H2 = 1 => 0 pairs (X) A1,A9: 1.. / A1 = 1 => 19 pairs (_) / A9 = 1 => 0 pairs (*) G4,G5: 3.. / G4 = 3 => 12 pairs (_) / G5 = 3 => 11 pairs (_) B7,C9: 3.. / B7 = 3 => 18 pairs (_) / C9 = 3 => 0 pairs (X) F3,H3: 3.. / F3 = 3 => 24 pairs (_) / H3 = 3 => 10 pairs (_) B7,F7: 3.. / B7 = 3 => 18 pairs (_) / F7 = 3 => 0 pairs (X) C4,C5: 4.. / C4 = 4 => 11 pairs (_) / C5 = 4 => 0 pairs (X) D5,D6: 4.. / D5 = 4 => 11 pairs (_) / D6 = 4 => 0 pairs (X) H4,H6: 4.. / H4 = 4 => 0 pairs (X) / H6 = 4 => 11 pairs (_) C4,H4: 4.. / C4 = 4 => 11 pairs (_) / H4 = 4 => 0 pairs (X) C5,D5: 4.. / C5 = 4 => 0 pairs (X) / D5 = 4 => 11 pairs (_) D6,H6: 4.. / D6 = 4 => 0 pairs (X) / H6 = 4 => 11 pairs (_) A1,B1: 5.. / A1 = 5 => 0 pairs (X) / B1 = 5 => 10 pairs (_) F7,F8: 5.. / F7 = 5 => 17 pairs (_) / F8 = 5 => 20 pairs (_) H8,H9: 5.. / H8 = 5 => 17 pairs (_) / H9 = 5 => 20 pairs (_) F8,H8: 5.. / F8 = 5 => 20 pairs (_) / H8 = 5 => 17 pairs (_) A9,H9: 5.. / A9 = 5 => 17 pairs (_) / H9 = 5 => 20 pairs (_) B1,B7: 5.. / B1 = 5 => 10 pairs (_) / B7 = 5 => 0 pairs (X) H4,I4: 6.. / H4 = 6 => 17 pairs (_) / I4 = 6 => 0 pairs (X) H9,I9: 6.. / H9 = 6 => 0 pairs (X) / I9 = 6 => 17 pairs (_) H4,H9: 6.. / H4 = 6 => 17 pairs (_) / H9 = 6 => 0 pairs (X) I4,I9: 6.. / I4 = 6 => 0 pairs (X) / I9 = 6 => 17 pairs (_) E1,E4: 7.. / E1 = 7 => 19 pairs (_) / E4 = 7 => 11 pairs (_) I1,G2: 8.. / I1 = 8 => 0 pairs (X) / G2 = 8 => 13 pairs (_) C3,F3: 8.. / C3 = 8 => 12 pairs (_) / F3 = 8 => 16 pairs (_) D6,I6: 8.. / D6 = 8 => 20 pairs (_) / I6 = 8 => 13 pairs (_) A1,A5: 8.. / A1 = 8 => 0 pairs (X) / A5 = 8 => 9 pairs (_) F3,F4: 8.. / F3 = 8 => 16 pairs (_) / F4 = 8 => 12 pairs (_) * DURATION: 0:00:33.373366 START: 23:05:52.811231 END: 23:06:26.184597 2019-04-30 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A7,C3,D9,E6,G2,H3,I6,I8) * ..9..46..34..56..926.19.5.49..5.........61.956.5..97....694.18248261.9...9..824.. * PAIR C3: 7,8 BLK 1 A1: 7,8,1,5 # reduction candidate for 7,8 A1: 7,8 => SOLVED * 759824613341756829268193574924578361873461295615239748536947182482615937197382456 A1: 1,5 # 12 pairs C2: 7,8,1 # reduction candidate for 7,8 C2: 7,8 # 16 pairs * PAIR C3: 7,8 ROW 3 F3: 7,8,3 # reduction candidate for 7,8 F3: 3 # 24 pairs F3: 7,8 # 10 pairs * PAIR C3: 7,8 COL C C4: 7,8,1,3,4 # reduction candidate for 7,8 C4: 7,8 => CTR * ..9..46..34..56..926.19.5.49..5...46..4.61.956.54.97.8..694.18248261.9...937824.. C4: 1,3,4 # 10 pairs C5: 7,8,3,4 # reduction candidate for 7,8 C5: 7,8 => CTR * ..9..46..341.56.7926.19.5349.45...6....461.956.5..974...69431824826159...937824.6 C5: 3,4 # 10 pairs * PAIR G2: 2,8 ROW 2 D2: 2,8,7 # reduction candidate for 2,8 D2: 7 => SOLVED * 759824613341756829268193574924578361873461295615239748536947182482615937197382456 D2: 2,8 # 12 pairs * PAIR G2: 2,8 COL G G4: 2,8,3 # reduction candidate for 2,8 G4: 2,8 # 11 pairs G5: 2,8,3 # reduction candidate for 2,8 G5: 2,8 # 12 pairs * PAIR H3: 3,7 BLK 3 H1: 3,7,1,2 # reduction candidate for 3,7 H1: 3,7 => CTR * 159..46.834..5621926.19.5.491.5....68...613956.58.974173694518248261.95.591.8246. H1: 1,2 # 10 pairs I1: 3,7,1,8 # reduction candidate for 3,7 I1: 3,7 # 17 pairs * PAIR H3: 3,7 ROW 3 F3: 3,7,8 # reduction candidate for 3,7 F3: 8 # 16 pairs F3: 3,7 # 12 pairs * PAIR H3: 3,7 COL H H8: 3,7,5 # reduction candidate for 3,7 H8: 3,7 # 20 pairs H9: 3,7,5,6 # reduction candidate for 3,7 H9: 3,7 => CTR * 159..462.34.25681926819.5.49.45.8361873461295615329748736945182482613957591782436 H9: 5,6 # 10 pairs * PAIR A5: 7,8 BLK 4 C4: 7,8,1,3,4 # reduction candidate for 7,8 C4: 7,8 => CTR * ..9..46..34..56..926.19.5.49..5...46..4.61.956.54.97.8..694.18248261.9...937824.. C4: 1,3,4 # 10 pairs C5: 7,8,3,4 # reduction candidate for 7,8 C5: 7,8 => CTR * ..9..46..341.56.7926.19.5349.45...6....461.956.5..974...69431824826159...937824.6 C5: 3,4 # 10 pairs * PAIR A5: 7,8 ROW 5 D5: 7,8,2,3,4 # reduction candidate for 7,8 D5: 7,8 => CTR * ..9..46.1341.568.926.19.5.491.5...46..4.61.956.54.9718..694.18248261.95..9..8246. D5: 2,3,4 # 9 pairs * PAIR A5: 7,8 COL A A1: 7,8,1,5 # reduction candidate for 7,8 A1: 7,8 => SOLVED * 759824613341756829268193574924578361873461295615239748536947182482615937197382456 A1: 1,5 # 12 pairs * PAIR E6: 2,3 BLK 5 E4: 2,3,7 # reduction candidate for 2,3 E4: 2,3 # 19 pairs D5: 2,3,4,7,8 # reduction candidate for 2,3 D5: 2,3 => CTR * ..98.46.1341.568.926819.5.4913578246874261395625439718.3694.18248261.9...9..8246. D5: 4,7,8 # 9 pairs D6: 2,3,4,8 # reduction candidate for 2,3 D6: 2,3 # 17 pairs * PAIR E6: 2,3 ROW 6 B6: 2,3,1 # reduction candidate for 2,3 B6: 1 # 17 pairs B6: 2,3 # 13 pairs * PAIR E6: 2,3 COL E E1: 2,3,7 # reduction candidate for 2,3 E1: 7 # 19 pairs E1: 2,3 # 11 pairs * PAIR I6: 1,8 BLK 6 I4: 1,8,6 # reduction candidate for 1,8 I4: 6 => CTR * 159..46.834..5621926.19.5.491.5..8.687.261395625..97.173694518248261.95.591.8246. I4: 1,8 # 17 pairs * PAIR I6: 1,8 COL I I1: 1,8,3,7 # reduction candidate for 1,8 I1: 1,8 => CTR * 159..46.834..5621926.19.5.49..5....68...613956.58.974173694518248261.95.591.8246. I1: 3,7 # 17 pairs * PAIR A7: 5,7 BLK 7 B7: 5,7,3 # reduction candidate for 5,7 B7: 5,7 => CTR * ..9..46.7347.5681926819.5349..5...6.....61.956.5..974...6943182482615973193782456 B7: 3 # 18 pairs A9: 5,7,1 # reduction candidate for 5,7 A9: 5,7 # 19 pairs * PAIR A7: 5,7 ROW 7 F7: 5,7,3 # reduction candidate for 5,7 F7: 3 => CTR * ..9..46.7347.5681926819.5349..5...6.....61.956.5..974...6943182482615973193782456 F7: 5,7 # 18 pairs * PAIR A7: 5,7 COL A A1: 5,7,1,8 # reduction candidate for 5,7 A1: 5,7 => SOLVED * 759824613341756829268193574924578361873461295615239748536947182482615937197382456 A1: 1,8 # 12 pairs * PAIR D9: 3,7 BLK 8 F7: 3,7,5 # reduction candidate for 3,7 F7: 3,7 # 20 pairs F8: 3,7,5 # reduction candidate for 3,7 F8: 3,7 # 17 pairs * PAIR D9: 3,7 ROW 9 C9: 3,7,1 # reduction candidate for 3,7 C9: 3,7 => SOLVED * 759824613341756829268193574924578361873461295615239748536947182482615937197382456 C9: 1 # 19 pairs H9: 3,7,5,6 # reduction candidate for 3,7 H9: 3,7 => CTR * 159..462.34.25681926819.5.49.45.8361873461295615329748736945182482613957591782436 H9: 5,6 # 10 pairs I9: 3,7,6 # reduction candidate for 3,7 I9: 3,7 => CTR * 159..46.834..5621926.19.5.491.5..8.687.261395625..97.173694518248261.95.591.8246. I9: 6 # 17 pairs * PAIR D9: 3,7 COL D D1: 3,7,2,8 # reduction candidate for 3,7 D1: 3,7 # 13 pairs D5: 3,7,2,4,8 # reduction candidate for 3,7 D5: 3,7 => CTR * ..98.46.134125687926819753491.5782468.4.61.956.54.9718..694.18248261.9...9..8246. D5: 2,4,8 # 9 pairs * PAIR I8: 3,7 BLK 9 H8: 3,7,5 # reduction candidate for 3,7 H8: 3,7 # 20 pairs H9: 3,7,5,6 # reduction candidate for 3,7 H9: 3,7 => CTR * 159..462.34.25681926819.5.49.45.8361873461295615329748736945182482613957591782436 H9: 5,6 # 10 pairs I9: 3,7,6 # reduction candidate for 3,7 I9: 3,7 => CTR * 159..46.834..5621926.19.5.491.5..8.687.261395625..97.173694518248261.95.591.8246. I9: 6 # 17 pairs * PAIR I8: 3,7 ROW 8 F8: 3,7,5 # reduction candidate for 3,7 F8: 5 # 20 pairs F8: 3,7 # 17 pairs * PAIR I8: 3,7 COL I I1: 3,7,1,8 # reduction candidate for 3,7 I1: 1,8 => CTR * 159..46.834..5621926.19.5.49..5....68...613956.58.974173694518248261.95.591.8246. I1: 3,7 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060512-absurd-base-pr-000.dot * REASONING * PRF # A1: 7,8 => SOL * DIS # C4: 7,8 => CTR => C4: 1,3,4 * DIS # C5: 7,8 => CTR => C5: 3,4 * PRF # D2: 7 => SOL * DIS # H1: 3,7 => CTR => H1: 1,2 * DIS # H9: 3,7 => CTR => H9: 5,6 * DIS # C4: 7,8 => CTR => C4: 1,3,4 * DIS # C5: 7,8 => CTR => C5: 3,4 * DIS # D5: 7,8 => CTR => D5: 2,3,4 * PRF # A1: 7,8 => SOL * DIS # D5: 2,3 => CTR => D5: 4,7,8 * DIS # I4: 6 => CTR => I4: 1,8 * DIS # I1: 1,8 => CTR => I1: 3,7 * DIS # B7: 5,7 => CTR => B7: 3 * DIS # F7: 3 => CTR => F7: 5,7 * PRF # A1: 5,7 => SOL * PRF # C9: 3,7 => SOL * DIS # H9: 3,7 => CTR => H9: 5,6 * DIS # I9: 3,7 => CTR => I9: 6 * DIS # D5: 3,7 => CTR => D5: 2,4,8 * DIS # H9: 3,7 => CTR => H9: 5,6 * DIS # I9: 3,7 => CTR => I9: 6 * DIS # I1: 1,8 => CTR => I1: 3,7 * CNT 23 HDP CHAINS / 68 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A7,C3,D9,E6,G2,H3,I6,I8) * ..9..46..34..56..926.19.5.49..5.........61.956.5..97....694.18248261.9...9..824.. * PAIR C3: 7,8 BLK 1 A1: 7,8,1,5 # reduction candidate for 7,8 A1: 7,8 => SOLVED * 759824613341756829268193574924578361873461295615239748536947182482615937197382456 * DURATION: 0:00:01.777887 START: 23:07:09.957539 END: 23:07:11.735426 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060512-absurd-base-pr-001.dot * REASONING * PRF # A1: 7,8 => SOL * STA A1: 7,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060512, absurd
Solution
position: 759824613341756829268193574924578361873461295615239748536947182482615937197382456 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:
* PRF # A1: 7,8 => SOL * INC # A1: 1,5 => UNS * INC # C2: 7,8 => UNS * INC # F3: 7,8 => UNS * INC # F3: 3 => UNS * DIS # C4: 7,8 => CTR => C4: 1,3,4 * INC # C4: 1,3,4 => UNS * DIS # C5: 7,8 => CTR => C5: 3,4 * INC # C5: 3,4 => UNS * INC # D2: 2,8 => UNS * PRF # D2: 7 => SOL * INC # G4: 2,8 => UNS * INC # G5: 2,8 => UNS * DIS # H1: 3,7 => CTR => H1: 1,2 * INC # H1: 1,2 => UNS * INC # I1: 3,7 => UNS * INC # F3: 3,7 => UNS * INC # F3: 8 => UNS * INC # H8: 3,7 => UNS * DIS # H9: 3,7 => CTR => H9: 5,6 * INC # H9: 5,6 => UNS * DIS # C4: 7,8 => CTR => C4: 1,3,4 * INC # C4: 1,3,4 => UNS * DIS # C5: 7,8 => CTR => C5: 3,4 * INC # C5: 3,4 => UNS * DIS # D5: 7,8 => CTR => D5: 2,3,4 * INC # D5: 2,3,4 => UNS * PRF # A1: 7,8 => SOL * INC # A1: 1,5 => UNS * INC # E4: 2,3 => UNS * DIS # D5: 2,3 => CTR => D5: 4,7,8 * INC # D5: 4,7,8 => UNS * INC # D6: 2,3 => UNS * INC # B6: 2,3 => UNS * INC # B6: 1 => UNS * INC # E1: 2,3 => UNS * INC # E1: 7 => UNS * INC # I4: 1,8 => UNS * DIS # I4: 6 => CTR => I4: 1,8 * DIS # I1: 1,8 => CTR => I1: 3,7 * INC # I1: 3,7 => UNS * DIS # B7: 5,7 => CTR => B7: 3 * INC # B7: 3 => UNS * INC # A9: 5,7 => UNS * INC # F7: 5,7 => UNS * DIS # F7: 3 => CTR => F7: 5,7 * PRF # A1: 5,7 => SOL * INC # A1: 1,8 => UNS * INC # F7: 3,7 => UNS * INC # F8: 3,7 => UNS * PRF # C9: 3,7 => SOL * INC # C9: 1 => UNS * DIS # H9: 3,7 => CTR => H9: 5,6 * INC # H9: 5,6 => UNS * DIS # I9: 3,7 => CTR => I9: 6 * INC # I9: 6 => UNS * INC # D1: 3,7 => UNS * DIS # D5: 3,7 => CTR => D5: 2,4,8 * INC # D5: 2,4,8 => UNS * INC # H8: 3,7 => UNS * DIS # H9: 3,7 => CTR => H9: 5,6 * INC # H9: 5,6 => UNS * DIS # I9: 3,7 => CTR => I9: 6 * INC # I9: 6 => UNS * INC # F8: 3,7 => UNS * INC # F8: 5 => UNS * INC # I1: 3,7 => UNS * DIS # I1: 1,8 => CTR => I1: 3,7 * CNT 68 HDP CHAINS / 68 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A1: 7,8 => SOL * STA A1: 7,8 * CNT 1 HDP CHAINS / 1 HYP OPENED