Analysis of zz-www.sudokuoftheday.co.uk-20060724-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006
level: medium
position: .2..3..6.....8.3.....7.45.....6....9.9...2.58....912...54...81....8436..3......9. initial
Autosolve
position: .2.13596.....8.3.....7.458....658..9.9..72.58....912.6.54...813...8436.53..51..9. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C9: 7,8 => CTR => C9: 2,6 * PRF # F7: 7 => SOL * PRF # H2: 4,7 => SOL * PRF # I9: 4,7 => SOL * PRF # I2: 1,2 => SOL * DIS # B6: 3,4 => CTR => B6: 7,8 * PRF # G4: 1,4 => SOL * DIS # A5: 6 => CTR => A5: 1,4 * DIS # B9: 6,7 => CTR => B9: 8 * DIS # C9: 6,7 => CTR => C9: 2,8 * PRF # F7: 6,7 => SOL * DIS # A2: 6,7 => CTR => A2: 1,4,5 * PRF # A8: 1,7 => SOL * DIS # C8: 1,7 => CTR => C8: 2,9 * PRF # F7: 6,7 => SOL * DIS # B9: 6,7 => CTR => B9: 8 * DIS # C9: 6,7 => CTR => C9: 2,8 * PRF # I9: 4 => SOL * PRF # H2: 4 => SOL * PRF # I9: 4,7 => SOL * PRF # G4: 1 => SOL * CNT 21 HDP CHAINS / 53 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C9: 7,8 => CTR => C9: 2,6 * DIS C9: 2,6 # F7: 6,9 => CTR => F7: 7 * PRF C9: 2,6 + F7: 7 => SOL * STA C9: 2,6 + F7: 7 * CNT 3 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .2..3..6.....8.3.....7.45.....6....9.9...2.58....912...54...81....8436..3......9. | initial |
| .2.13596.....8.3.....7.458....658..9.9..72.58....912.6.54...813...8436.53..51..9. | autosolve |
| 428135967567289341931764582243658179196372458875491236654927813719843625382516794 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) C1: 7,8 D2: 2,9 F2: 6,9 E3: 2,6 I1: 4,7 I3: 1,2 D5: 3,4 D6: 3,4 G5: 1,4 A7: 6,7 B8: 1,7 D7: 2,9 E7: 2,6 F9: 6,7 H8: 2,7 G9: 4,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I2,I3: 1.. / I2 = 1 => 0 pairs (*) / I3 = 1 => 0 pairs (X) G4,G5: 1.. / G4 = 1 => 0 pairs (*) / G5 = 1 => 0 pairs (X) D2,E3: 2.. / D2 = 2 => 0 pairs (*) / E3 = 2 => 0 pairs (X) A4,C4: 2.. / A4 = 2 => 16 pairs (_) / C4 = 2 => 0 pairs (X) D7,E7: 2.. / D7 = 2 => 24 pairs (_) / E7 = 2 => 0 pairs (*) H8,I9: 2.. / H8 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) E3,I3: 2.. / E3 = 2 => 24 pairs (_) / I3 = 2 => 0 pairs (*) C9,I9: 2.. / C9 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) A4,A8: 2.. / A4 = 2 => 16 pairs (_) / A8 = 2 => 0 pairs (X) D2,D7: 2.. / D2 = 2 => 0 pairs (*) / D7 = 2 => 0 pairs (X) E3,E7: 2.. / E3 = 2 => 24 pairs (_) / E7 = 2 => 0 pairs (*) H2,H8: 2.. / H2 = 2 => 24 pairs (_) / H8 = 2 => 0 pairs (*) B3,C3: 3.. / B3 = 3 => 16 pairs (_) / C3 = 3 => 17 pairs (_) D5,D6: 3.. / D5 = 3 => 16 pairs (_) / D6 = 3 => 0 pairs (X) H4,H6: 3.. / H4 = 3 => 17 pairs (_) / H6 = 3 => 17 pairs (_) C5,D5: 3.. / C5 = 3 => 0 pairs (X) / D5 = 3 => 16 pairs (_) D5,D6: 4.. / D5 = 4 => 0 pairs (X) / D6 = 4 => 16 pairs (_) G9,I9: 4.. / G9 = 4 => 21 pairs (_) / I9 = 4 => 0 pairs (*) A1,I1: 4.. / A1 = 4 => 19 pairs (_) / I1 = 4 => 21 pairs (_) A2,C2: 5.. / A2 = 5 => 16 pairs (_) / C2 = 5 => 26 pairs (_) A6,C6: 5.. / A6 = 5 => 26 pairs (_) / C6 = 5 => 16 pairs (_) A2,A6: 5.. / A2 = 5 => 16 pairs (_) / A6 = 5 => 26 pairs (_) C2,C6: 5.. / C2 = 5 => 26 pairs (_) / C6 = 5 => 16 pairs (_) F2,E3: 6.. / F2 = 6 => 24 pairs (_) / E3 = 6 => 0 pairs (*) A5,C5: 6.. / A5 = 6 => 0 pairs (X) / C5 = 6 => 16 pairs (_) E3,E7: 6.. / E3 = 6 => 0 pairs (*) / E7 = 6 => 0 pairs (X) F7,F9: 7.. / F7 = 7 => 0 pairs (*) / F9 = 7 => 0 pairs (X) A7,F7: 7.. / A7 = 7 => 24 pairs (_) / F7 = 7 => 0 pairs (*) G4,G9: 7.. / G4 = 7 => 21 pairs (_) / G9 = 7 => 0 pairs (*) A1,C1: 8.. / A1 = 8 => 21 pairs (_) / C1 = 8 => 18 pairs (_) B9,C9: 8.. / B9 = 8 => 19 pairs (_) / C9 = 8 => 0 pairs (X) A1,A6: 8.. / A1 = 8 => 21 pairs (_) / A6 = 8 => 18 pairs (_) B6,B9: 8.. / B6 = 8 => 0 pairs (X) / B9 = 8 => 19 pairs (_) A3,C3: 9.. / A3 = 9 => 16 pairs (_) / C3 = 9 => 17 pairs (_) D2,F2: 9.. / D2 = 9 => 24 pairs (_) / F2 = 9 => 0 pairs (*) A8,C8: 9.. / A8 = 9 => 17 pairs (_) / C8 = 9 => 16 pairs (_) D7,F7: 9.. / D7 = 9 => 0 pairs (*) / F7 = 9 => 0 pairs (X) A3,A8: 9.. / A3 = 9 => 16 pairs (_) / A8 = 9 => 17 pairs (_) C3,C8: 9.. / C3 = 9 => 17 pairs (_) / C8 = 9 => 16 pairs (_) D2,D7: 9.. / D2 = 9 => 24 pairs (_) / D7 = 9 => 0 pairs (*) F2,F7: 9.. / F2 = 9 => 0 pairs (*) / F7 = 9 => 0 pairs (X) * DURATION: 0:00:49.519497 START: 01:14:52.865423 END: 01:15:42.384920 2019-05-01 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B8,C1,D2,D5,D6,D7,E3,E7,F2,F9,G5,G9,H8,I1,I3) * .2.13596.....8.3.....7.458....658..9.9..72.58....912.6.54...813...8436.53..51..9. * PAIR C1: 7,8 BLK 1 A1: 7,8,4 # reduction candidate for 7,8 A1: 7,8 # 21 pairs A1: 4 # 19 pairs * PAIR C1: 7,8 COL C C6: 7,8,3,5 # reduction candidate for 7,8 C6: 7,8 # 26 pairs C9: 7,8,2,6 # reduction candidate for 7,8 C9: 7,8 => CTR * 827135964...986327.3.724581...6587.9.9..72158....912.6.54269813...843675368517492 C9: 2,6 # 20 pairs * PAIR F2: 6,9 COL F F7: 6,9,7 # reduction candidate for 6,9 F7: 7 => SOLVED * 428135967567289341931764582243658179196372458875491236654927813719843625382516794 F7: 6,9 # 24 pairs * PAIR I1: 4,7 BLK 3 H2: 4,7,2 # reduction candidate for 4,7 H2: 4,7 => SOLVED * 428135967567289341931764582243658179196372458875491236654927813719843625382516794 H2: 2 # 24 pairs I2: 4,7,1,2 # reduction candidate for 4,7 I2: 4,7 # 24 pairs * PAIR I1: 4,7 ROW 1 A1: 4,7,8 # reduction candidate for 4,7 A1: 8 # 21 pairs A1: 4,7 # 18 pairs * PAIR I1: 4,7 COL I I9: 4,7,2 # reduction candidate for 4,7 I9: 4,7 => SOLVED * 428135967567289341931764582243658179196372458875491236654927813719843625382516794 I9: 2 # 24 pairs * PAIR I3: 1,2 BLK 3 I2: 1,2,4,7 # reduction candidate for 1,2 I2: 1,2 => SOLVED * 428135967567289341931764582243658179196372458875491236654927813719843625382516794 I2: 4,7 # 24 pairs * PAIR D6: 3,4 ROW 6 B6: 3,4,7,8 # reduction candidate for 3,4 B6: 3,4 => CTR * 428135967567289341.1.7645822..658.39.96372458835491276654927813...843625382516794 B6: 7,8 # 17 pairs H6: 3,4,7 # reduction candidate for 3,4 H6: 3,4 # 18 pairs * PAIR G5: 1,4 BLK 6 G4: 1,4,7 # reduction candidate for 1,4 G4: 1,4 => SOLVED * 428135967567289341931764582243658179196372458875491236654927813719843625382516794 G4: 7 # 21 pairs * PAIR G5: 1,4 ROW 5 A5: 1,4,6 # reduction candidate for 1,4 A5: 6 => CTR * .2.13596....98632.936724581.42658739693472158...391246754269813219843675368517492 A5: 1,4 # 16 pairs * PAIR A7: 6,7 BLK 7 B9: 6,7,8 # reduction candidate for 6,7 B9: 6,7 => CTR * 827135964...986327.3.724581.7.6581.9.9..72.58.8..912.6.54269813...843675368517492 B9: 8 # 19 pairs C9: 6,7,2,8 # reduction candidate for 6,7 C9: 6,7 => CTR * .2.13596....98632..63724581...6587.9691.72.58....912.6.54269813...843675386517492 C9: 2,8 # 17 pairs * PAIR A7: 6,7 ROW 7 F7: 6,7,9 # reduction candidate for 6,7 F7: 6,7 => SOLVED * 428135967567289341931764582243658179196372458875491236654927813719843625382516794 F7: 9 # 24 pairs * PAIR A7: 6,7 COL A A2: 6,7,1,4,5 # reduction candidate for 6,7 A2: 6,7 => CTR * 827135964645.893.1...764582...658..9.96372.585..4912.6754926813.1.8436.53..51..9. A2: 1,4,5 # 16 pairs * PAIR B8: 1,7 BLK 7 A8: 1,7,2,9 # reduction candidate for 1,7 A8: 1,7 => SOLVED * 428135967567289341931764582243658179196372458875491236654927813719843625382516794 A8: 2,9 # 17 pairs C8: 1,7,2,9 # reduction candidate for 1,7 C8: 1,7 => CTR * .2.13596..6.2893.113976458224.658..9.96372158...4912.66549278139..843625382516.9. C8: 2,9 # 17 pairs * PAIR B8: 1,7 COL B B2: 1,7,4,6 # reduction candidate for 1,7 B2: 1,7 # 24 pairs B4: 1,7,3,4 # reduction candidate for 1,7 B4: 1,7 # 20 pairs * PAIR F9: 6,7 BLK 8 F7: 6,7,9 # reduction candidate for 6,7 F7: 6,7 => SOLVED * 428135967567289341931764582243658179196372458875491236654927813719843625382516794 F7: 9 # 24 pairs * PAIR F9: 6,7 ROW 9 B9: 6,7,8 # reduction candidate for 6,7 B9: 6,7 => CTR * 827135964...986327.3.724581.7.6581.9.9..72.58.8..912.6.54269813...843675368517492 B9: 8 # 19 pairs C9: 6,7,2,8 # reduction candidate for 6,7 C9: 6,7 => CTR * .2.13596....98632..63724581...6587.9691.72.58....912.6.54269813...843675386517492 C9: 2,8 # 17 pairs * PAIR H8: 2,7 BLK 9 I9: 2,7,4 # reduction candidate for 2,7 I9: 4 => SOLVED * 428135967567289341931764582243658179196372458875491236654927813719843625382516794 I9: 2,7 # 21 pairs * PAIR H8: 2,7 ROW 8 A8: 2,7,1,9 # reduction candidate for 2,7 A8: 2,7 # 17 pairs C8: 2,7,1,9 # reduction candidate for 2,7 C8: 2,7 # 18 pairs * PAIR H8: 2,7 COL H H2: 2,7,4 # reduction candidate for 2,7 H2: 4 => SOLVED * 428135967567289341931764582243658179196372458875491236654927813719843625382516794 H2: 2,7 # 21 pairs * PAIR G9: 4,7 BLK 9 I9: 4,7,2 # reduction candidate for 4,7 I9: 4,7 => SOLVED * 428135967567289341931764582243658179196372458875491236654927813719843625382516794 I9: 2 # 24 pairs * PAIR G9: 4,7 COL G G4: 4,7,1 # reduction candidate for 4,7 G4: 1 => SOLVED * 428135967567289341931764582243658179196372458875491236654927813719843625382516794 G4: 4,7 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060724-absurd-base-pr-000.dot * REASONING * DIS # C9: 7,8 => CTR => C9: 2,6 * PRF # F7: 7 => SOL * PRF # H2: 4,7 => SOL * PRF # I9: 4,7 => SOL * PRF # I2: 1,2 => SOL * DIS # B6: 3,4 => CTR => B6: 7,8 * PRF # G4: 1,4 => SOL * DIS # A5: 6 => CTR => A5: 1,4 * DIS # B9: 6,7 => CTR => B9: 8 * DIS # C9: 6,7 => CTR => C9: 2,8 * PRF # F7: 6,7 => SOL * DIS # A2: 6,7 => CTR => A2: 1,4,5 * PRF # A8: 1,7 => SOL * DIS # C8: 1,7 => CTR => C8: 2,9 * PRF # F7: 6,7 => SOL * DIS # B9: 6,7 => CTR => B9: 8 * DIS # C9: 6,7 => CTR => C9: 2,8 * PRF # I9: 4 => SOL * PRF # H2: 4 => SOL * PRF # I9: 4,7 => SOL * PRF # G4: 1 => SOL * CNT 21 HDP CHAINS / 53 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B8,C1,D2,D5,D6,D7,E3,E7,F2,F9,G5,G9,H8,I1,I3) * .2.13596.....8.3.....7.458....658..9.9..72.58....912.6.54...813...8436.53..51..9. * PAIR C1: 7,8 BLK 1 A1: 7,8,4 # reduction candidate for 7,8 A1: 7,8 # 21 pairs A1: 4 # 19 pairs * PAIR C1: 7,8 COL C C6: 7,8,3,5 # reduction candidate for 7,8 C6: 7,8 # 26 pairs C9: 7,8,2,6 # reduction candidate for 7,8 C9: 7,8 => CTR * 827135964...986327.3.724581...6587.9.9..72158....912.6.54269813...843675368517492 * RESTART * PAIR RESTART * PAIR C1: 7,8 BLK 1 A1: 7,8,4 # reduction candidate for 7,8 A1: 7,8 # 29 pairs A1: 4 # 20 pairs * PAIR F2: 6,9 COL F F7: 6,9,7 # reduction candidate for 6,9 F7: 6,9 => CTR * .2.13596....98632.963724581...6587.969.472158.7.391246754269813.1.843675386517492 F7: 7 => SOLVED * 428135967567289341931764582243658179196372458875491236654927813719843625382516794 * DURATION: 0:00:06.498091 START: 01:16:19.664482 END: 01:16:26.162573 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060724-absurd-base-pr-001.dot * REASONING * DIS # C9: 7,8 => CTR => C9: 2,6 * DIS C9: 2,6 # F7: 6,9 => CTR => F7: 7 * PRF C9: 2,6 + F7: 7 => SOL * STA C9: 2,6 + F7: 7 * CNT 3 HDP CHAINS / 7 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060724, absurd
Solution
position: 428135967567289341931764582243658179196372458875491236654927813719843625382516794 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 # A1: 7,8 => UNS * INC # A1: 4 => UNS * INC # C6: 7,8 => UNS * DIS # C9: 7,8 => CTR => C9: 2,6 * INC # C9: 2,6 => UNS * INC # F7: 6,9 => UNS * PRF # F7: 7 => SOL * PRF # H2: 4,7 => SOL * INC # H2: 2 => UNS * INC # I2: 4,7 => UNS * INC # A1: 4,7 => UNS * INC # A1: 8 => UNS * PRF # I9: 4,7 => SOL * INC # I9: 2 => UNS * PRF # I2: 1,2 => SOL * INC # I2: 4,7 => UNS * DIS # B6: 3,4 => CTR => B6: 7,8 * INC # B6: 7,8 => UNS * INC # H6: 3,4 => UNS * PRF # G4: 1,4 => SOL * INC # G4: 7 => UNS * INC # A5: 1,4 => UNS * DIS # A5: 6 => CTR => A5: 1,4 * DIS # B9: 6,7 => CTR => B9: 8 * INC # B9: 8 => UNS * DIS # C9: 6,7 => CTR => C9: 2,8 * INC # C9: 2,8 => UNS * PRF # F7: 6,7 => SOL * INC # F7: 9 => UNS * DIS # A2: 6,7 => CTR => A2: 1,4,5 * INC # A2: 1,4,5 => UNS * PRF # A8: 1,7 => SOL * INC # A8: 2,9 => UNS * DIS # C8: 1,7 => CTR => C8: 2,9 * INC # C8: 2,9 => UNS * INC # B2: 1,7 => UNS * INC # B4: 1,7 => UNS * PRF # F7: 6,7 => SOL * INC # F7: 9 => UNS * DIS # B9: 6,7 => CTR => B9: 8 * INC # B9: 8 => UNS * DIS # C9: 6,7 => CTR => C9: 2,8 * INC # C9: 2,8 => UNS * INC # I9: 2,7 => UNS * PRF # I9: 4 => SOL * INC # A8: 2,7 => UNS * INC # C8: 2,7 => UNS * INC # H2: 2,7 => UNS * PRF # H2: 4 => SOL * PRF # I9: 4,7 => SOL * INC # I9: 2 => UNS * INC # G4: 4,7 => UNS * PRF # G4: 1 => SOL * CNT 53 HDP CHAINS / 53 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 7,8 => UNS * INC # A1: 4 => UNS * INC # C6: 7,8 => UNS * DIS # C9: 7,8 => CTR => C9: 2,6 * INC C9: 2,6 # A1: 7,8 => UNS * INC C9: 2,6 # A1: 4 => UNS * DIS C9: 2,6 # F7: 6,9 => CTR => F7: 7 * PRF C9: 2,6 + F7: 7 => SOL * STA C9: 2,6 + F7: 7 * CNT 8 HDP CHAINS / 7 HYP OPENED