Analysis of zz-www.sudokuoftheday.co.uk-20190208-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: .5.1....69..54.7.8...9......3542..89..8..92.........348.....4.........2.6...5.... initial
Autosolve
position: .5.1823969..5437183819..542.3542..89..8..92572..8.5.348....14655......2.6...5..7. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # E6: 6,7 => SOL * DIS # E6: 1 => CTR => E6: 6,7 * PRF # E6: 6,7 => SOL * DIS # E6: 1 => CTR => E6: 6,7 * DIS # E5: 3,6 => CTR => E5: 1 * PRF # E5: 1 => SOL * DIS # D8: 7 => CTR => D8: 3,6 * PRF # E6: 1,6 => SOL * DIS # E6: 7 => CTR => E6: 1,6 * DIS # E8: 6 => CTR => E8: 3,9 * DIS # D7: 2,3 => CTR => D7: 7 * CNT 11 HDP CHAINS / 20 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # E6: 6,7 => SOL * STA E6: 6,7 * CNT 1 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .5.1....69..54.7.8...9......3542..89..8..92.........348.....4.........2.6...5.... | initial |
| .5.1823969..5437183819..542.3542..89..8..92572..8.5.348....14655......2.6...5..7. | autosolve |
| 754182396926543718381976542135427689468319257279865134892731465517694823643258971 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (21) A1: 4,7 C1: 4,7 B2: 2,6 C2: 2,6 E3: 6,7 F3: 6,7 A4: 1,7 A5: 1,4 B5: 4,6 F4: 6,7 D5: 3,6 G4: 1,6 G6: 1,6 E7: 3,9 F8: 4,8 D9: 2,3 F9: 4,8 G8: 8,9 I8: 1,3 G9: 8,9 I9: 1,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A4,A5: 1.. / A4 = 1 => 0 pairs (*) / A5 = 1 => 0 pairs (X) E5,E6: 1.. / E5 = 1 => 0 pairs (*) / E6 = 1 => 0 pairs (X) G4,G6: 1.. / G4 = 1 => 0 pairs (X) / G6 = 1 => 0 pairs (_) B8,B9: 1.. / B8 = 1 => 21 pairs (_) / B9 = 1 => 20 pairs (_) I8,I9: 1.. / I8 = 1 => 20 pairs (_) / I9 = 1 => 21 pairs (_) A4,G4: 1.. / A4 = 1 => 0 pairs (*) / G4 = 1 => 0 pairs (X) A5,E5: 1.. / A5 = 1 => 0 pairs (X) / E5 = 1 => 0 pairs (_) E6,G6: 1.. / E6 = 1 => 0 pairs (X) / G6 = 1 => 0 pairs (_) B8,I8: 1.. / B8 = 1 => 21 pairs (_) / I8 = 1 => 20 pairs (_) B9,I9: 1.. / B9 = 1 => 20 pairs (_) / I9 = 1 => 21 pairs (_) B2,C2: 2.. / B2 = 2 => 21 pairs (_) / C2 = 2 => 0 pairs (X) D7,D9: 2.. / D7 = 2 => 0 pairs (X) / D9 = 2 => 21 pairs (_) D5,E5: 3.. / D5 = 3 => 22 pairs (_) / E5 = 3 => 0 pairs (X) I8,I9: 3.. / I8 = 3 => 21 pairs (_) / I9 = 3 => 20 pairs (_) A1,C1: 4.. / A1 = 4 => 0 pairs (X) / C1 = 4 => 0 pairs (_) A5,B5: 4.. / A5 = 4 => 0 pairs (*) / B5 = 4 => 0 pairs (X) F8,F9: 4.. / F8 = 4 => 17 pairs (_) / F9 = 4 => 18 pairs (_) A1,A5: 4.. / A1 = 4 => 0 pairs (X) / A5 = 4 => 0 pairs (_) B2,C2: 6.. / B2 = 6 => 0 pairs (X) / C2 = 6 => 21 pairs (_) E3,F3: 6.. / E3 = 6 => 0 pairs (X) / F3 = 6 => 0 pairs (_) G4,G6: 6.. / G4 = 6 => 0 pairs (*) / G6 = 6 => 0 pairs (X) D8,E8: 6.. / D8 = 6 => 22 pairs (_) / E8 = 6 => 0 pairs (X) F4,G4: 6.. / F4 = 6 => 0 pairs (X) / G4 = 6 => 0 pairs (_) C2,C6: 6.. / C2 = 6 => 21 pairs (_) / C6 = 6 => 0 pairs (X) D5,D8: 6.. / D5 = 6 => 0 pairs (X) / D8 = 6 => 22 pairs (_) F3,F4: 6.. / F3 = 6 => 0 pairs (*) / F4 = 6 => 0 pairs (X) A1,C1: 7.. / A1 = 7 => 0 pairs (*) / C1 = 7 => 0 pairs (X) E3,F3: 7.. / E3 = 7 => 0 pairs (*) / F3 = 7 => 0 pairs (X) F4,E6: 7.. / F4 = 7 => 0 pairs (*) / E6 = 7 => 0 pairs (X) D7,D8: 7.. / D7 = 7 => 22 pairs (_) / D8 = 7 => 0 pairs (X) A4,F4: 7.. / A4 = 7 => 0 pairs (X) / F4 = 7 => 0 pairs (_) A1,A4: 7.. / A1 = 7 => 0 pairs (*) / A4 = 7 => 0 pairs (X) E3,E6: 7.. / E3 = 7 => 0 pairs (*) / E6 = 7 => 0 pairs (X) F3,F4: 7.. / F3 = 7 => 0 pairs (X) / F4 = 7 => 0 pairs (_) F8,F9: 8.. / F8 = 8 => 18 pairs (_) / F9 = 8 => 17 pairs (_) G8,G9: 8.. / G8 = 8 => 17 pairs (_) / G9 = 8 => 18 pairs (_) F8,G8: 8.. / F8 = 8 => 18 pairs (_) / G8 = 8 => 17 pairs (_) F9,G9: 8.. / F9 = 8 => 17 pairs (_) / G9 = 8 => 18 pairs (_) B6,C6: 9.. / B6 = 9 => 23 pairs (_) / C6 = 9 => 21 pairs (_) E7,E8: 9.. / E7 = 9 => 22 pairs (_) / E8 = 9 => 21 pairs (_) G8,G9: 9.. / G8 = 9 => 18 pairs (_) / G9 = 9 => 17 pairs (_) * DURATION: 0:00:48.957580 START: 03:34:42.895936 END: 03:35:31.853516 2019-05-01 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,A5,B2,B5,C1,C2,D5,D9,E3,E7,F3,F4,F8,F9,G4,G6,G8,G9,I8,I9) * .5.1823969..5437183819..542.3542..89..8..92572..8.5.348....14655......2.6...5..7. * PAIR C1: 4,7 COL C C8: 4,7,3,9 # reduction candidate for 4,7 C8: 4,7 # 23 pairs C8: 3,9 # 22 pairs * PAIR E3: 6,7 COL E E6: 6,7,1 # reduction candidate for 6,7 E6: 6,7 => SOLVED * 754182396926543718381976542135427689468319257279865134892731465517694823643258971 E6: 1 => CTR * .5.1823969..543718381976542.35427689..8..92572..815.348....14655......2.6...5..7. * PAIR F4: 6,7 BLK 5 E6: 6,7,1 # reduction candidate for 6,7 E6: 6,7 => SOLVED * 754182396926543718381976542135427689468319257279865134892731465517694823643258971 E6: 1 => CTR * .5.1823969..543718381976542.35427689..8..92572..815.348....14655......2.6...5..7. * PAIR D5: 3,6 BLK 5 E5: 3,6,1 # reduction candidate for 3,6 E5: 3,6 => CTR * .5.1823969..5437183819..542.3542..89148..92572..8156348....14655......2.6...5..7. E5: 1 => SOLVED * 754182396926543718381976542135427689468319257279865134892731465517694823643258971 * PAIR D5: 3,6 COL D D8: 3,6,7 # reduction candidate for 3,6 D8: 7 => CTR * .5.1823969..5437183819..542.3542..89..86392572..8156348....14655......2.6...5..7. D8: 3,6 # 22 pairs * PAIR G6: 1,6 ROW 6 E6: 1,6,7 # reduction candidate for 1,6 E6: 1,6 => SOLVED * 754182396926543718381976542135427689468319257279865134892731465517694823643258971 E6: 7 => CTR * .5.1823969..5437183819..542.3542..89..8.192572..8751348....14655......2.6...5..7. * PAIR E7: 3,9 BLK 8 E8: 3,9,6 # reduction candidate for 3,9 E8: 6 => CTR * .5.1823969..543718381976542.35427689..86392572..815.348...914655...6..2.6...5..7. E8: 3,9 # 22 pairs * PAIR E7: 3,9 ROW 7 C7: 3,9,2,7 # reduction candidate for 3,9 C7: 3,9 # 24 pairs C7: 2,7 # 24 pairs * PAIR D9: 2,3 BLK 8 D7: 2,3,7 # reduction candidate for 2,3 D7: 2,3 => CTR * .5.1823969..543718381976542.35427689..86392572..815.348....14655..76..2.6...5..7. D7: 7 # 22 pairs * PAIR D9: 2,3 ROW 9 C9: 2,3,4,9 # reduction candidate for 2,3 C9: 2,3 # 23 pairs C9: 4,9 # 22 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190208-absurd-base-pr-000.dot * REASONING * PRF # E6: 6,7 => SOL * DIS # E6: 1 => CTR => E6: 6,7 * PRF # E6: 6,7 => SOL * DIS # E6: 1 => CTR => E6: 6,7 * DIS # E5: 3,6 => CTR => E5: 1 * PRF # E5: 1 => SOL * DIS # D8: 7 => CTR => D8: 3,6 * PRF # E6: 1,6 => SOL * DIS # E6: 7 => CTR => E6: 1,6 * DIS # E8: 6 => CTR => E8: 3,9 * DIS # D7: 2,3 => CTR => D7: 7 * CNT 11 HDP CHAINS / 20 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,A5,B2,B5,C1,C2,D5,D9,E3,E7,F3,F4,F8,F9,G4,G6,G8,G9,I8,I9) * .5.1823969..5437183819..542.3542..89..8..92572..8.5.348....14655......2.6...5..7. * PAIR C1: 4,7 COL C C8: 4,7,3,9 # reduction candidate for 4,7 C8: 4,7 # 23 pairs C8: 3,9 # 22 pairs * PAIR E3: 6,7 COL E E6: 6,7,1 # reduction candidate for 6,7 E6: 6,7 => SOLVED * 754182396926543718381976542135427689468319257279865134892731465517694823643258971 * DURATION: 0:00:02.994695 START: 03:35:46.304900 END: 03:35:49.299595 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190208-absurd-base-pr-001.dot * REASONING * PRF # E6: 6,7 => SOL * STA E6: 6,7 * CNT 1 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190208, absurd
Solution
position: 754182396926543718381976542135427689468319257279865134892731465517694823643258971 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 # C8: 4,7 => UNS * INC # C8: 3,9 => UNS * PRF # E6: 6,7 => SOL * DIS # E6: 1 => CTR => E6: 6,7 * PRF # E6: 6,7 => SOL * DIS # E6: 1 => CTR => E6: 6,7 * DIS # E5: 3,6 => CTR => E5: 1 * PRF # E5: 1 => SOL * INC # D8: 3,6 => UNS * DIS # D8: 7 => CTR => D8: 3,6 * PRF # E6: 1,6 => SOL * DIS # E6: 7 => CTR => E6: 1,6 * INC # E8: 3,9 => UNS * DIS # E8: 6 => CTR => E8: 3,9 * INC # C7: 3,9 => UNS * INC # C7: 2,7 => UNS * DIS # D7: 2,3 => CTR => D7: 7 * INC # D7: 7 => UNS * INC # C9: 2,3 => UNS * INC # C9: 4,9 => UNS * CNT 20 HDP CHAINS / 20 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C8: 4,7 => UNS * INC # C8: 3,9 => UNS * PRF # E6: 6,7 => SOL * STA E6: 6,7 * CNT 3 HDP CHAINS / 3 HYP OPENED