Analysis of zz-www.sudokuoftheday.co.uk-20060910-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Sep&YEAR=2006
level: medium
position: ........1.......6.....819..25...8.7.8.437.2..3...9.........9..663..4...8..72..3.. initial
Autosolve
position: ........1.......6.....819..259..8.738.437.2.937..92......839726632.47.989872..3.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E1: 6 => CTR => E1: 2,5 * DIS # D6: 1,6 => CTR => D6: 4,5 * DIS # D6: 1,6 => CTR => D6: 4,5 * DIS # E9: 5 => CTR => E9: 1,6 * DIS # D6: 5,6 => CTR => D6: 1,4 * DIS # G6: 1,5 => CTR => G6: 4,6,8 * DIS # H6: 1,5 => CTR => H6: 4,8 * DIS # H9: 4 => CTR => H9: 1,5 * DIS # G6: 4,5 => CTR => G6: 1,6,8 * DIS # H6: 4,5 => CTR => H6: 1,8 * DIS # D6: 1,6 => CTR => D6: 4,5 * DIS # A7: 5 => CTR => A7: 1,4 * DIS # B2: 1,4 => CTR => B2: 2,9 * DIS # C2: 1,5 => CTR => C2: 3,8 * DIS # E9: 6 => CTR => E9: 1,5 * DIS # E9: 5,6 => CTR => E9: 1 * DIS # H9: 4 => CTR => H9: 1,5 * DIS # G6: 1,5 => CTR => G6: 4,6,8 * DIS # H9: 1 => CTR => H9: 4,5 * CNT 19 HDP CHAINS / 48 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 => CTR => E1: 2,5 * DIS E1: 2,5 # G6: 4,5,8 => CTR => G6: 1,6 * DIS E1: 2,5 + G6: 1,6 # H9: 4 => CTR => H9: 1,5 * DIS E1: 2,5 + G6: 1,6 + H9: 1,5 # B2: 1,4 => CTR => B2: 2,9 * PRF E1: 2,5 + G6: 1,6 + H9: 1,5 + B2: 2,9 => SOL * STA E1: 2,5 + G6: 1,6 + H9: 1,5 + B2: 2,9 * CNT 5 HDP CHAINS / 9 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ........1.......6.....819..25...8.7.8.437.2..3...9.........9..663..4...8..72..3.. | initial |
| ........1.......6.....819..259..8.738.437.2.937..92......839726632.47.989872..3.. | autosolve |
| 798623541123954867546781932259168473864375219371492685415839726632547198987216354 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) F1: 3,4 E2: 2,5 F2: 3,4 I2: 2,7 I3: 2,7 B5: 1,6 C6: 1,6 E4: 1,6 F5: 5,6 H5: 1,5 I6: 4,5 B7: 1,4 C7: 1,5 D8: 1,5 F9: 5,6 G8: 1,5 I9: 4,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B5,C6: 1.. / B5 = 1 => 0 pairs (X) / C6 = 1 => 21 pairs (_) D8,E9: 1.. / D8 = 1 => 0 pairs (X) / E9 = 1 => 21 pairs (_) G8,H9: 1.. / G8 = 1 => 21 pairs (_) / H9 = 1 => 0 pairs (X) B5,H5: 1.. / B5 = 1 => 0 pairs (X) / H5 = 1 => 21 pairs (_) D8,G8: 1.. / D8 = 1 => 0 pairs (X) / G8 = 1 => 21 pairs (_) E9,H9: 1.. / E9 = 1 => 21 pairs (_) / H9 = 1 => 0 pairs (X) A2,A7: 1.. / A2 = 1 => 18 pairs (_) / A7 = 1 => 17 pairs (_) E4,E9: 1.. / E4 = 1 => 0 pairs (X) / E9 = 1 => 21 pairs (_) E1,E2: 2.. / E1 = 2 => 21 pairs (_) / E2 = 2 => 0 pairs (X) I2,I3: 2.. / I2 = 2 => 21 pairs (_) / I3 = 2 => 23 pairs (_) B1,E1: 2.. / B1 = 2 => 0 pairs (X) / E1 = 2 => 21 pairs (_) B3,I3: 2.. / B3 = 2 => 21 pairs (_) / I3 = 2 => 23 pairs (_) F1,F2: 3.. / F1 = 3 => 22 pairs (_) / F2 = 3 => 17 pairs (_) H1,H3: 3.. / H1 = 3 => 18 pairs (_) / H3 = 3 => 25 pairs (_) C2,F2: 3.. / C2 = 3 => 22 pairs (_) / F2 = 3 => 17 pairs (_) C3,H3: 3.. / C3 = 3 => 18 pairs (_) / H3 = 3 => 25 pairs (_) F1,F2: 4.. / F1 = 4 => 17 pairs (_) / F2 = 4 => 22 pairs (_) D4,D6: 4.. / D4 = 4 => 18 pairs (_) / D6 = 4 => 21 pairs (_) A7,B7: 4.. / A7 = 4 => 18 pairs (_) / B7 = 4 => 18 pairs (_) H9,I9: 4.. / H9 = 4 => 0 pairs (X) / I9 = 4 => 21 pairs (_) D4,G4: 4.. / D4 = 4 => 18 pairs (_) / G4 = 4 => 21 pairs (_) I6,I9: 4.. / I6 = 4 => 0 pairs (X) / I9 = 4 => 21 pairs (_) F5,D6: 5.. / F5 = 5 => 21 pairs (_) / D6 = 5 => 0 pairs (X) A7,C7: 5.. / A7 = 5 => 0 pairs (X) / C7 = 5 => 18 pairs (_) F5,H5: 5.. / F5 = 5 => 21 pairs (_) / H5 = 5 => 0 pairs (X) D8,G8: 5.. / D8 = 5 => 21 pairs (_) / G8 = 5 => 0 pairs (X) F5,F9: 5.. / F5 = 5 => 21 pairs (_) / F9 = 5 => 0 pairs (X) I6,I9: 5.. / I6 = 5 => 21 pairs (_) / I9 = 5 => 0 pairs (X) B5,C6: 6.. / B5 = 6 => 21 pairs (_) / C6 = 6 => 0 pairs (X) G4,G6: 6.. / G4 = 6 => 0 pairs (X) / G6 = 6 => 21 pairs (_) E9,F9: 6.. / E9 = 6 => 0 pairs (X) / F9 = 6 => 21 pairs (_) B5,F5: 6.. / B5 = 6 => 21 pairs (_) / F5 = 6 => 0 pairs (X) F5,F9: 6.. / F5 = 6 => 0 pairs (X) / F9 = 6 => 21 pairs (_) I2,I3: 7.. / I2 = 7 => 23 pairs (_) / I3 = 7 => 21 pairs (_) A1,D1: 7.. / A1 = 7 => 18 pairs (_) / D1 = 7 => 0 pairs (X) C1,C2: 8.. / C1 = 8 => 22 pairs (_) / C2 = 8 => 18 pairs (_) G6,H6: 8.. / G6 = 8 => 0 pairs (X) / H6 = 8 => 17 pairs (_) C2,G2: 8.. / C2 = 8 => 18 pairs (_) / G2 = 8 => 22 pairs (_) H1,H6: 8.. / H1 = 8 => 0 pairs (X) / H6 = 8 => 17 pairs (_) B1,B2: 9.. / B1 = 9 => 21 pairs (_) / B2 = 9 => 23 pairs (_) D1,D2: 9.. / D1 = 9 => 23 pairs (_) / D2 = 9 => 21 pairs (_) B1,D1: 9.. / B1 = 9 => 21 pairs (_) / D1 = 9 => 23 pairs (_) B2,D2: 9.. / B2 = 9 => 23 pairs (_) / D2 = 9 => 21 pairs (_) * DURATION: 0:00:51.596881 START: 02:31:59.835726 END: 02:32:51.432607 2019-05-01 * CP COUNT: (43) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,B7,C6,C7,D8,E2,E4,F1,F2,F5,F9,G8,H5,I2,I3,I6,I9) * ........1.......6.....819..259..8.738.437.2.937..92......839726632.47.989872..3.. * PAIR F1: 3,4 ROW 1 H1: 3,4,5,8 # reduction candidate for 3,4 H1: 5,8 # 27 pairs H1: 3,4 # 20 pairs * PAIR E2: 2,5 BLK 2 E1: 2,5,6 # reduction candidate for 2,5 E1: 6 => CTR * .2.96...1.9..2..67...7819.2259.18.738.437.2.937..92......839726632147598987256314 E1: 2,5 # 22 pairs * PAIR C6: 1,6 ROW 6 D6: 1,6,4,5 # reduction candidate for 1,6 D6: 1,6 => CTR * ........1.......6.....819..2594.8.738.4375219371692.....583972663214759898725634. D6: 4,5 # 20 pairs G6: 1,6,4,5,8 # reduction candidate for 1,6 G6: 1,6 # 20 pairs * PAIR E4: 1,6 BLK 5 D4: 1,6,4 # reduction candidate for 1,6 D4: 1,6 # 21 pairs D6: 1,6,4,5 # reduction candidate for 1,6 D6: 1,6 => CTR * ........1.......6.....819..2594.8.738.4375219371692.....583972663214759898725634. D6: 4,5 # 20 pairs * PAIR E4: 1,6 ROW 4 G4: 1,6,4 # reduction candidate for 1,6 G4: 4 # 21 pairs G4: 1,6 # 18 pairs * PAIR E4: 1,6 COL E E9: 1,6,5 # reduction candidate for 1,6 E9: 5 => CTR * ........1.......6.....819..259.18.738.437.2.937..92......839726632147598987256314 E9: 1,6 # 22 pairs * PAIR F5: 5,6 BLK 5 D6: 5,6,1,4 # reduction candidate for 5,6 D6: 5,6 => CTR * ........1.......6.....819..2594186738.437.2.937..92......8397266321475989872..314 D6: 1,4 # 21 pairs * PAIR H5: 1,5 BLK 6 G6: 1,5,4,6,8 # reduction candidate for 1,5 G6: 1,5 => CTR * ........1.......6.....819..2594186738.4375219371692.84...839726632.47.989872..345 G6: 4,6,8 # 17 pairs H6: 1,5,4,8 # reduction candidate for 1,5 H6: 1,5 => CTR * ..3..4581..8.5346.....8193.2594.86738.43752193716928.....839726632.47.989872..345 H6: 4,8 # 18 pairs * PAIR H5: 1,5 COL H H9: 1,5,4 # reduction candidate for 1,5 H9: 4 => CTR * ........1.......6.....819..2591684738.437.2.937..92......839726632.47198987216345 H9: 1,5 # 21 pairs * PAIR I6: 4,5 BLK 6 G6: 4,5,1,6,8 # reduction candidate for 4,5 G6: 4,5 => CTR * ........1.......6.....819..259..86738.437.2.937..92.8....839726632.4719898721.3.. G6: 1,6,8 # 17 pairs H6: 4,5,1,8 # reduction candidate for 4,5 H6: 4,5 => CTR * ..3..4581..8..346.....8193.2594.86738.437.2193716928.....839726632.47.989872..3.. H6: 1,8 # 18 pairs * PAIR I6: 4,5 ROW 6 D6: 4,5,1,6 # reduction candidate for 4,5 D6: 1,6 => CTR * ........1.......6.....819..2594.8.738.4375219371692.....583972663214759898725634. D6: 4,5 # 20 pairs * PAIR B7: 1,4 BLK 7 A7: 1,4,5 # reduction candidate for 1,4 A7: 5 => CTR * ........11......6.....819..259..8.73814376259376592..45418397266321475989872..3.. A7: 1,4 # 18 pairs * PAIR B7: 1,4 COL B B2: 1,4,2,9 # reduction candidate for 1,4 B2: 1,4 => CTR * .9672...171.95..62.2.6819.7259168473864375219371492685145839726632547198987216354 B2: 2,9 # 22 pairs * PAIR C7: 1,5 BLK 7 A7: 1,5,4 # reduction candidate for 1,5 A7: 4 # 18 pairs A7: 1,5 # 18 pairs * PAIR C7: 1,5 COL C C2: 1,5,3,8 # reduction candidate for 1,5 C2: 1,5 => CTR * ..8..4531.....386...3.8194.259..8673814376259376.92.8....839726632.47.989872..3.. C2: 3,8 # 18 pairs * PAIR D8: 1,5 BLK 8 E9: 1,5,6 # reduction candidate for 1,5 E9: 6 => CTR * ........1.......6.....819..259.18.738.437.2.937..92......839726632147598987265314 E9: 1,5 # 21 pairs * PAIR D8: 1,5 COL D D6: 1,5,4,6 # reduction candidate for 1,5 D6: 1,5 # 23 pairs D6: 4,6 # 21 pairs * PAIR F9: 5,6 BLK 8 E9: 5,6,1 # reduction candidate for 5,6 E9: 5,6 => CTR * ........1.......6.....819..259.18.738.437.2.937..92......8397266321475989872..314 E9: 1 # 21 pairs * PAIR G8: 1,5 BLK 9 H9: 1,5,4 # reduction candidate for 1,5 H9: 4 => CTR * ........1.......6.....819..2591684738.437.2.937..92......839726632.47198987216345 H9: 1,5 # 21 pairs * PAIR G8: 1,5 COL G G6: 1,5,4,6,8 # reduction candidate for 1,5 G6: 1,5 => CTR * ........1.......6.....819..2594186738.4375219371692.84...839726632.47.989872..345 G6: 4,6,8 # 17 pairs * PAIR I9: 4,5 BLK 9 H9: 4,5,1 # reduction candidate for 4,5 H9: 1 => CTR * ........1.......6.....819..259..8.738.437.2.937..92......839726632.47.989872..314 H9: 4,5 # 21 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060910-absurd-base-pr-000.dot * REASONING * DIS # E1: 6 => CTR => E1: 2,5 * DIS # D6: 1,6 => CTR => D6: 4,5 * DIS # D6: 1,6 => CTR => D6: 4,5 * DIS # E9: 5 => CTR => E9: 1,6 * DIS # D6: 5,6 => CTR => D6: 1,4 * DIS # G6: 1,5 => CTR => G6: 4,6,8 * DIS # H6: 1,5 => CTR => H6: 4,8 * DIS # H9: 4 => CTR => H9: 1,5 * DIS # G6: 4,5 => CTR => G6: 1,6,8 * DIS # H6: 4,5 => CTR => H6: 1,8 * DIS # D6: 1,6 => CTR => D6: 4,5 * DIS # A7: 5 => CTR => A7: 1,4 * DIS # B2: 1,4 => CTR => B2: 2,9 * DIS # C2: 1,5 => CTR => C2: 3,8 * DIS # E9: 6 => CTR => E9: 1,5 * DIS # E9: 5,6 => CTR => E9: 1 * DIS # H9: 4 => CTR => H9: 1,5 * DIS # G6: 1,5 => CTR => G6: 4,6,8 * DIS # H9: 1 => CTR => H9: 4,5 * CNT 19 HDP CHAINS / 48 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,B7,C6,C7,D8,E2,E4,F1,F2,F5,F9,G8,H5,I2,I3,I6,I9) * ........1.......6.....819..259..8.738.437.2.937..92......839726632.47.989872..3.. * PAIR F1: 3,4 ROW 1 H1: 3,4,5,8 # reduction candidate for 3,4 H1: 5,8 # 27 pairs H1: 3,4 # 20 pairs * PAIR E2: 2,5 BLK 2 E1: 2,5,6 # reduction candidate for 2,5 E1: 6 => CTR * .2.96...1.9..2..67...7819.2259.18.738.437.2.937..92......839726632147598987256314 * PAIR C6: 1,6 ROW 6 G6: 1,6,4,5,8 # reduction candidate for 1,6 G6: 4,5,8 => CTR * ........1.......6.....819..259..86738.4376259376592.14...839726632147.989872..3.. * PAIR RESTART * PAIR H5: 1,5 COL H H9: 1,5,4 # reduction candidate for 1,5 H9: 4 => CTR * ........1.......6.....819..259..8.738.437.219371.92685..5839726632547.989872..3.. * PAIR RESTART * PAIR B7: 1,4 COL B B2: 1,4,2,9 # reduction candidate for 1,4 B2: 1,4 => CTR * 79.62.5.1...95..6.5...819..259168473864375219371492685..5839726632547198987216354 B2: 2,9 => SOLVED * 798623541123954867546781932259168473864375219371492685415839726632547198987216354 * DURATION: 0:00:08.546588 START: 02:33:21.835232 END: 02:33:30.381820 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060910-absurd-base-pr-001.dot * REASONING * DIS # E1: 6 => CTR => E1: 2,5 * DIS E1: 2,5 # G6: 4,5,8 => CTR => G6: 1,6 * DIS E1: 2,5 + G6: 1,6 # H9: 4 => CTR => H9: 1,5 * DIS E1: 2,5 + G6: 1,6 + H9: 1,5 # B2: 1,4 => CTR => B2: 2,9 * PRF E1: 2,5 + G6: 1,6 + H9: 1,5 + B2: 2,9 => SOL * STA E1: 2,5 + G6: 1,6 + H9: 1,5 + B2: 2,9 * CNT 5 HDP CHAINS / 9 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Sep&YEAR=2006, 20060910, absurd
Solution
position: 798623541123954867546781932259168473864375219371492685415839726632547198987216354 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 # H1: 3,4 => UNS * INC # H1: 5,8 => UNS * INC # E1: 2,5 => UNS * DIS # E1: 6 => CTR => E1: 2,5 * DIS # D6: 1,6 => CTR => D6: 4,5 * INC # D6: 4,5 => UNS * INC # G6: 1,6 => UNS * INC # D4: 1,6 => UNS * DIS # D6: 1,6 => CTR => D6: 4,5 * INC # D6: 4,5 => UNS * INC # G4: 1,6 => UNS * INC # G4: 4 => UNS * INC # E9: 1,6 => UNS * DIS # E9: 5 => CTR => E9: 1,6 * DIS # D6: 5,6 => CTR => D6: 1,4 * INC # D6: 1,4 => UNS * DIS # G6: 1,5 => CTR => G6: 4,6,8 * INC # G6: 4,6,8 => UNS * DIS # H6: 1,5 => CTR => H6: 4,8 * INC # H6: 4,8 => UNS * INC # H9: 1,5 => UNS * DIS # H9: 4 => CTR => H9: 1,5 * DIS # G6: 4,5 => CTR => G6: 1,6,8 * INC # G6: 1,6,8 => UNS * DIS # H6: 4,5 => CTR => H6: 1,8 * INC # H6: 1,8 => UNS * INC # D6: 4,5 => UNS * DIS # D6: 1,6 => CTR => D6: 4,5 * INC # A7: 1,4 => UNS * DIS # A7: 5 => CTR => A7: 1,4 * DIS # B2: 1,4 => CTR => B2: 2,9 * INC # B2: 2,9 => UNS * INC # A7: 1,5 => UNS * INC # A7: 4 => UNS * DIS # C2: 1,5 => CTR => C2: 3,8 * INC # C2: 3,8 => UNS * INC # E9: 1,5 => UNS * DIS # E9: 6 => CTR => E9: 1,5 * INC # D6: 1,5 => UNS * INC # D6: 4,6 => UNS * DIS # E9: 5,6 => CTR => E9: 1 * INC # E9: 1 => UNS * INC # H9: 1,5 => UNS * DIS # H9: 4 => CTR => H9: 1,5 * DIS # G6: 1,5 => CTR => G6: 4,6,8 * INC # G6: 4,6,8 => UNS * INC # H9: 4,5 => UNS * DIS # H9: 1 => CTR => H9: 4,5 * CNT 48 HDP CHAINS / 48 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # H1: 3,4 => UNS * INC # H1: 5,8 => UNS * INC # E1: 2,5 => UNS * DIS # E1: 6 => CTR => E1: 2,5 * INC E1: 2,5 # G6: 1,6 => UNS * DIS E1: 2,5 # G6: 4,5,8 => CTR => G6: 1,6 * INC E1: 2,5 + G6: 1,6 # H9: 1,5 => UNS * DIS E1: 2,5 + G6: 1,6 # H9: 4 => CTR => H9: 1,5 * DIS E1: 2,5 + G6: 1,6 + H9: 1,5 # B2: 1,4 => CTR => B2: 2,9 * PRF E1: 2,5 + G6: 1,6 + H9: 1,5 + B2: 2,9 => SOL * STA E1: 2,5 + G6: 1,6 + H9: 1,5 + B2: 2,9 * CNT 10 HDP CHAINS / 9 HYP OPENED