Analysis of zz-www.sudokuoftheday.co.uk-20060711-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: ..1..2..574..........5..8.33.......6.6..1...4..7..6.2..........5182.......69.354. initial
Autosolve
position: 831..24.5745......6295..8.33.4.2...6962.1...41.74.6.2.493......5182.....276983541 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E1: 6,7 => CTR => E1: 9 * DIS # H1: 9 => CTR => H1: 6,7 * DIS # D7: 6,7 => CTR => D7: 1 * PRF # F3: 4,7 => SOL * DIS # E8: 4,7 => CTR => E8: 6 * DIS # G2: 2,9 => CTR => G2: 1,6 * DIS # F3: 4 => CTR => F3: 1,7 * DIS # F4: 5,8 => CTR => F4: 7,9 * DIS # F4: 7,8 => CTR => F4: 5,9 * DIS # D5: 7,8 => CTR => D5: 3 * DIS # D5: 8 => CTR => D5: 3,7 * DIS # E6: 3,9 => CTR => E6: 5 * PRF # E6: 5 => SOL * DIS # G8: 6 => CTR => G8: 3,9 * DIS # E8: 4,7 => CTR => E8: 6 * PRF # F3: 4,7 => SOL * DIS # G2: 1,9 => CTR => G2: 2,6 * CNT 17 HDP CHAINS / 36 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E1: 6,7 => CTR => E1: 9 * DIS E1: 9 # D7: 6,7 => CTR => D7: 1 * PRF E1: 9 + D7: 1 => SOL * STA E1: 9 + D7: 1 * CNT 3 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..1..2..574..........5..8.33.......6.6..1...4..7..6.2..........5182.......69.354. | initial |
| 831..24.5745......6295..8.33.4.2...6962.1...41.74.6.2.493......5182.....276983541 | autosolve |
| 831692475745831692629547813354729186962318754187456329493175268518264937276983541 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) D1: 6,7 E3: 4,7 I2: 2,9 H3: 1,7 B4: 5,8 B6: 5,8 D4: 7,8 G5: 3,7 G6: 3,9 I6: 8,9 F8: 4,7 G7: 2,6 H7: 6,8 I8: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G4,H4: 1.. / G4 = 1 => 15 pairs (_) / H4 = 1 => 0 pairs (X) D7,F7: 1.. / D7 = 1 => 17 pairs (_) / F7 = 1 => 0 pairs (X) F3,H3: 1.. / F3 = 1 => 17 pairs (_) / H3 = 1 => 0 pairs (*) D2,D7: 1.. / D2 = 1 => 0 pairs (X) / D7 = 1 => 17 pairs (_) G2,G4: 1.. / G2 = 1 => 0 pairs (X) / G4 = 1 => 15 pairs (_) G2,I2: 2.. / G2 = 2 => 0 pairs (X) / I2 = 2 => 13 pairs (_) G7,I7: 2.. / G7 = 2 => 13 pairs (_) / I7 = 2 => 0 pairs (X) G2,G7: 2.. / G2 = 2 => 0 pairs (X) / G7 = 2 => 13 pairs (_) I2,I7: 2.. / I2 = 2 => 13 pairs (_) / I7 = 2 => 0 pairs (X) D2,E2: 3.. / D2 = 3 => 0 pairs (X) / E2 = 3 => 17 pairs (_) D5,E6: 3.. / D5 = 3 => 17 pairs (_) / E6 = 3 => 0 pairs (X) G8,H8: 3.. / G8 = 3 => 0 pairs (X) / H8 = 3 => 16 pairs (_) E6,G6: 3.. / E6 = 3 => 0 pairs (X) / G6 = 3 => 17 pairs (_) D2,D5: 3.. / D2 = 3 => 0 pairs (X) / D5 = 3 => 17 pairs (_) E2,E6: 3.. / E2 = 3 => 17 pairs (_) / E6 = 3 => 0 pairs (X) H5,H8: 3.. / H5 = 3 => 0 pairs (X) / H8 = 3 => 16 pairs (_) E3,F3: 4.. / E3 = 4 => 14 pairs (_) / F3 = 4 => 0 pairs (X) E8,F8: 4.. / E8 = 4 => 0 pairs (X) / F8 = 4 => 14 pairs (_) E3,E8: 4.. / E3 = 4 => 14 pairs (_) / E8 = 4 => 0 pairs (X) F3,F8: 4.. / F3 = 4 => 0 pairs (X) / F8 = 4 => 14 pairs (_) B4,B6: 5.. / B4 = 5 => 0 pairs (*) / B6 = 5 => 0 pairs (X) H4,H5: 5.. / H4 = 5 => 0 pairs (X) / H5 = 5 => 18 pairs (_) E7,F7: 5.. / E7 = 5 => 0 pairs (X) / F7 = 5 => 0 pairs (_) F5,H5: 5.. / F5 = 5 => 0 pairs (X) / H5 = 5 => 18 pairs (_) B6,E6: 5.. / B6 = 5 => 0 pairs (X) / E6 = 5 => 0 pairs (_) E6,E7: 5.. / E6 = 5 => 0 pairs (*) / E7 = 5 => 0 pairs (X) H1,H3: 7.. / H1 = 7 => 0 pairs (*) / H3 = 7 => 0 pairs (X) G4,G5: 7.. / G4 = 7 => 0 pairs (X) / G5 = 7 => 16 pairs (_) I7,I8: 7.. / I7 = 7 => 0 pairs (X) / I8 = 7 => 21 pairs (_) D2,F2: 8.. / D2 = 8 => 19 pairs (_) / F2 = 8 => 17 pairs (_) B4,B6: 8.. / B4 = 8 => 0 pairs (X) / B6 = 8 => 0 pairs (_) H7,I7: 8.. / H7 = 8 => 0 pairs (X) / I7 = 8 => 0 pairs (_) B6,I6: 8.. / B6 = 8 => 0 pairs (*) / I6 = 8 => 0 pairs (X) I6,I7: 8.. / I6 = 8 => 0 pairs (X) / I7 = 8 => 0 pairs (_) F4,E6: 9.. / F4 = 9 => 17 pairs (_) / E6 = 9 => 0 pairs (X) E1,H1: 9.. / E1 = 9 => 19 pairs (_) / H1 = 9 => 0 pairs (X) F2,F4: 9.. / F2 = 9 => 0 pairs (X) / F4 = 9 => 17 pairs (_) * DURATION: 0:00:46.394921 START: 00:36:34.176218 END: 00:37:20.571139 2019-05-01 * CP COUNT: (37) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B6,D1,D4,E3,F8,G5,G6,G7,H3,H7,I2,I6,I8) * 831..24.5745......6295..8.33.4.2...6962.1...41.74.6.2.493......5182.....276983541 * PAIR D1: 6,7 BLK 2 E1: 6,7,9 # reduction candidate for 6,7 E1: 6,7 => CTR * 831672495745...6126295418733.4.2.1.6962.1.7.4187456.2.4931.72.8518264.37276983541 E1: 9 # 19 pairs * PAIR D1: 6,7 ROW 1 H1: 6,7,9 # reduction candidate for 6,7 H1: 9 => CTR * 831672495745...6126295418733.4.2.1.6962.1.7.4187456.2.4931.72.8518264.37276983541 H1: 6,7 # 19 pairs * PAIR D1: 6,7 COL D D7: 6,7,1 # reduction candidate for 6,7 D7: 6,7 => CTR * 831..24.5745138...6295..8133.4.291.696231.784187456.2.493......5182.....276983541 D7: 1 # 17 pairs * PAIR E3: 4,7 BLK 2 F3: 4,7,1 # reduction candidate for 4,7 F3: 4,7 => SOLVED * 831692475745831692629547813354729186962318754187456329493175268518264937276983541 F3: 1 # 17 pairs * PAIR E3: 4,7 COL E E8: 4,7,6 # reduction candidate for 4,7 E8: 4,7 => CTR * 831..24.5745.....26295..8.338472...6962.1.7.41574.6.28493.512875182....9276983541 E8: 6 # 21 pairs * PAIR I2: 2,9 BLK 3 G2: 2,9,1,6 # reduction candidate for 2,9 G2: 2,9 => CTR * 8316.24.5745....6.6295..81338472.1.6962.1.7.41574.6.28493157682518264...276983541 G2: 1,6 # 15 pairs * PAIR H3: 1,7 ROW 3 F3: 1,7,4 # reduction candidate for 1,7 F3: 4 => CTR * 831692475745.3...2629574813384729156962.1.7.41.74.6.28493...287518247..9276983541 F3: 1,7 # 14 pairs * PAIR B4: 5,8 ROW 4 F4: 5,8,7,9 # reduction candidate for 5,8 F4: 5,8 => CTR * 831..2495745839.626295.18.33.4.2...6962.1...41.7496328493.5.2875182...39276983541 F4: 7,9 # 15 pairs H4: 5,8,1,9 # reduction candidate for 5,8 H4: 5,8 # 22 pairs * PAIR D4: 7,8 BLK 5 F4: 7,8,5,9 # reduction candidate for 7,8 F4: 7,8 => CTR * 831..2495745839.626295.18.33.4.2...6962.1...41.7496328493.5.2875182...39276983541 F4: 5,9 # 15 pairs D5: 7,8,3 # reduction candidate for 7,8 D5: 7,8 => CTR * 831..24.57453.8...6295.18733.4.29..6962.1...41.7436928493157.82518264397276983541 D5: 3 # 17 pairs F5: 7,8,5 # reduction candidate for 7,8 F5: 7,8 # 18 pairs * PAIR G5: 3,7 ROW 5 D5: 3,7,8 # reduction candidate for 3,7 D5: 8 => CTR * 831..24.57453.8...6295.18733.4.29..696281...41.7436928493157.82518264397276983541 D5: 3,7 # 18 pairs * PAIR G6: 3,9 ROW 6 E6: 3,9,5 # reduction candidate for 3,9 E6: 3,9 => CTR * 8316.24.5745...2696295418.338472...6962.1.7.41574.6.28493157682518264..7276983541 E6: 5 => SOLVED * 831692475745831692629547813354729186962318754187456329493175268518264937276983541 * PAIR G6: 3,9 COL G G8: 3,9,6 # reduction candidate for 3,9 G8: 6 => CTR * 831..24.5745.....26295..8.338472...6962.1.7541574.6328493.512875182..639276983541 G8: 3,9 # 17 pairs * PAIR I6: 8,9 BLK 6 H4: 8,9,1,5 # reduction candidate for 8,9 H4: 8,9 # 18 pairs H4: 1,5 # 15 pairs * PAIR F8: 4,7 BLK 8 E8: 4,7,6 # reduction candidate for 4,7 E8: 4,7 => CTR * 831..24.5745.....26295..8.338472...6962.1.7.41574.6.28493.512875182....9276983541 E8: 6 # 21 pairs * PAIR F8: 4,7 COL F F3: 4,7,1 # reduction candidate for 4,7 F3: 4,7 => SOLVED * 831692475745831692629547813354729186962318754187456329493175268518264937276983541 F3: 1 # 17 pairs * PAIR G7: 2,6 COL G G2: 2,6,1,9 # reduction candidate for 2,6 G2: 1,9 => CTR * 831..24.5745.....26295..8.338472...6962.1.7541574.6328493.512875182..639276983541 G2: 2,6 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060711-absurd-base-pr-000.dot * REASONING * DIS # E1: 6,7 => CTR => E1: 9 * DIS # H1: 9 => CTR => H1: 6,7 * DIS # D7: 6,7 => CTR => D7: 1 * PRF # F3: 4,7 => SOL * DIS # E8: 4,7 => CTR => E8: 6 * DIS # G2: 2,9 => CTR => G2: 1,6 * DIS # F3: 4 => CTR => F3: 1,7 * DIS # F4: 5,8 => CTR => F4: 7,9 * DIS # F4: 7,8 => CTR => F4: 5,9 * DIS # D5: 7,8 => CTR => D5: 3 * DIS # D5: 8 => CTR => D5: 3,7 * DIS # E6: 3,9 => CTR => E6: 5 * PRF # E6: 5 => SOL * DIS # G8: 6 => CTR => G8: 3,9 * DIS # E8: 4,7 => CTR => E8: 6 * PRF # F3: 4,7 => SOL * DIS # G2: 1,9 => CTR => G2: 2,6 * CNT 17 HDP CHAINS / 36 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B6,D1,D4,E3,F8,G5,G6,G7,H3,H7,I2,I6,I8) * 831..24.5745......6295..8.33.4.2...6962.1...41.74.6.2.493......5182.....276983541 * PAIR D1: 6,7 BLK 2 E1: 6,7,9 # reduction candidate for 6,7 E1: 6,7 => CTR * 831672495745...6126295418733.4.2.1.6962.1.7.4187456.2.4931.72.8518264.37276983541 * PAIR D1: 6,7 COL D D7: 6,7,1 # reduction candidate for 6,7 D7: 6,7 => CTR * 831.924.5745138...6295..8133.4.291.696231.784187456.2.493......5182.....276983541 D7: 1 => SOLVED * 831692475745831692629547813354729186962318754187456329493175268518264937276983541 * DURATION: 0:00:03.686184 START: 00:37:45.302344 END: 00:37:48.988528 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060711-absurd-base-pr-001.dot * REASONING * DIS # E1: 6,7 => CTR => E1: 9 * DIS E1: 9 # D7: 6,7 => CTR => D7: 1 * PRF E1: 9 + D7: 1 => SOL * STA E1: 9 + D7: 1 * CNT 3 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060711, absurd
Solution
position: 831692475745831692629547813354729186962318754187456329493175268518264937276983541 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 # E1: 6,7 => CTR => E1: 9 * INC # E1: 9 => UNS * INC # H1: 6,7 => UNS * DIS # H1: 9 => CTR => H1: 6,7 * DIS # D7: 6,7 => CTR => D7: 1 * INC # D7: 1 => UNS * PRF # F3: 4,7 => SOL * INC # F3: 1 => UNS * DIS # E8: 4,7 => CTR => E8: 6 * INC # E8: 6 => UNS * DIS # G2: 2,9 => CTR => G2: 1,6 * INC # G2: 1,6 => UNS * INC # F3: 1,7 => UNS * DIS # F3: 4 => CTR => F3: 1,7 * DIS # F4: 5,8 => CTR => F4: 7,9 * INC # F4: 7,9 => UNS * INC # H4: 5,8 => UNS * DIS # F4: 7,8 => CTR => F4: 5,9 * INC # F4: 5,9 => UNS * DIS # D5: 7,8 => CTR => D5: 3 * INC # D5: 3 => UNS * INC # F5: 7,8 => UNS * INC # D5: 3,7 => UNS * DIS # D5: 8 => CTR => D5: 3,7 * DIS # E6: 3,9 => CTR => E6: 5 * PRF # E6: 5 => SOL * INC # G8: 3,9 => UNS * DIS # G8: 6 => CTR => G8: 3,9 * INC # H4: 8,9 => UNS * INC # H4: 1,5 => UNS * DIS # E8: 4,7 => CTR => E8: 6 * INC # E8: 6 => UNS * PRF # F3: 4,7 => SOL * INC # F3: 1 => UNS * INC # G2: 2,6 => UNS * DIS # G2: 1,9 => CTR => G2: 2,6 * CNT 36 HDP CHAINS / 36 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # E1: 6,7 => CTR => E1: 9 * DIS E1: 9 # D7: 6,7 => CTR => D7: 1 * PRF E1: 9 + D7: 1 => SOL * STA E1: 9 + D7: 1 * CNT 3 HDP CHAINS / 2 HYP OPENED