Analysis of zz-www.sudokuoftheday.co.uk-20190307-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019
level: medium
position: ....6...715...2.....9....8..3..2..54..5......8...39....82..4.634..6958........... initial
Autosolve
position: ...96.5.715...2..9..9.5..8.93..2..54..5...3988..539...582..49634.36958...9.283..5 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A3: 2,3 => SOL * PRF # H1: 2,3 => SOL * DIS # B3: 2,4 => CTR => B3: 6,7 * PRF # H1: 2,4 => SOL * DIS # C2: 4,8 => CTR => C2: 6,7 * PRF # C2: 6,7 => SOL * PRF # F4: 1,8 => SOL * DIS # F4: 6,7 => CTR => F4: 1,8 * DIS # D2: 4,7 => CTR => D2: 3,8 * DIS # D3: 4,7 => CTR => D3: 1,3 * PRF # C2: 4,7 => SOL * DIS # C2: 6,8 => CTR => C2: 4,7 * DIS # D3: 1,7 => CTR => D3: 3,4 * DIS # F4: 1,7 => CTR => F4: 6,8 * DIS # F5: 1,7 => CTR => F5: 6 * DIS # C2: 4,6 => CTR => C2: 7,8 * DIS # H1: 3,4 => CTR => H1: 1,2 * DIS # D2: 3,4 => CTR => D2: 7,8 * DIS # C9: 6 => CTR => C9: 1,7 * DIS # B5: 1,7 => CTR => B5: 2,6 * PRF # B6: 1,7 => SOL * PRF # A5: 6,7 => SOL * DIS # D3: 1,7 => CTR => D3: 3,4 * PRF # D4: 1,7 => SOL * DIS # D4: 8 => CTR => D4: 1,7 * DIS # D5: 1,7 => CTR => D5: 4 * DIS # E5: 4 => CTR => E5: 1,7 * DIS # I6: 1,2 => CTR => I6: 6 * CNT 28 HDP CHAINS / 60 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A3: 2,3 => SOL * STA A3: 2,3 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....6...715...2.....9....8..3..2..54..5......8...39....82..4.634..6958........... | initial |
| ...96.5.715...2..9..9.5..8.93..2..54..5...3988..539...582..49634.36958...9.283..5 | autosolve |
| 348961527157842639269357481936728154725416398814539276582174963473695812691283745 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) A1: 2,3 B1: 2,4 C1: 4,8 F1: 1,8 E2: 4,7 F3: 1,7 G2: 4,6 H2: 3,4 B8: 1,7 A9: 6,7 D7: 1,7 E7: 1,7 I8: 1,2 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B8,C9: 1.. / B8 = 1 => 18 pairs (_) / C9 = 1 => 16 pairs (_) D7,E7: 1.. / D7 = 1 => 13 pairs (_) / E7 = 1 => 14 pairs (_) F1,H1: 1.. / F1 = 1 => 0 pairs (*) / H1 = 1 => 0 pairs (X) E5,E7: 1.. / E5 = 1 => 13 pairs (_) / E7 = 1 => 14 pairs (_) A5,B5: 2.. / A5 = 2 => 15 pairs (_) / B5 = 2 => 0 pairs (*) H8,I8: 2.. / H8 = 2 => 19 pairs (_) / I8 = 2 => 15 pairs (_) G3,G6: 2.. / G3 = 2 => 14 pairs (_) / G6 = 2 => 15 pairs (_) A1,A3: 3.. / A1 = 3 => 14 pairs (_) / A3 = 3 => 0 pairs (X) D2,D3: 3.. / D2 = 3 => 0 pairs (X) / D3 = 3 => 14 pairs (_) H1,H2: 3.. / H1 = 3 => 0 pairs (X) / H2 = 3 => 14 pairs (_) A1,H1: 3.. / A1 = 3 => 14 pairs (_) / H1 = 3 => 0 pairs (X) D2,H2: 3.. / D2 = 3 => 0 pairs (X) / H2 = 3 => 14 pairs (_) A3,D3: 3.. / A3 = 3 => 0 pairs (X) / D3 = 3 => 14 pairs (_) B6,C6: 4.. / B6 = 4 => 0 pairs (X) / C6 = 4 => 0 pairs (_) D5,E5: 4.. / D5 = 4 => 15 pairs (_) / E5 = 4 => 0 pairs (X) G9,H9: 4.. / G9 = 4 => 0 pairs (X) / H9 = 4 => 17 pairs (_) E2,E5: 4.. / E2 = 4 => 15 pairs (_) / E5 = 4 => 0 pairs (X) F4,F5: 6.. / F4 = 6 => 0 pairs (X) / F5 = 6 => 14 pairs (_) A9,C9: 6.. / A9 = 6 => 14 pairs (_) / C9 = 6 => 0 pairs (X) C2,G2: 6.. / C2 = 6 => 0 pairs (X) / G2 = 6 => 14 pairs (_) I3,I6: 6.. / I3 = 6 => 0 pairs (X) / I6 = 6 => 15 pairs (_) D7,E7: 7.. / D7 = 7 => 14 pairs (_) / E7 = 7 => 13 pairs (_) B8,H8: 7.. / B8 = 7 => 16 pairs (_) / H8 = 7 => 18 pairs (_) C1,C2: 8.. / C1 = 8 => 0 pairs (*) / C2 = 8 => 0 pairs (X) F1,D2: 8.. / F1 = 8 => 0 pairs (X) / D2 = 8 => 0 pairs (_) D4,F4: 8.. / D4 = 8 => 0 pairs (X) / F4 = 8 => 0 pairs (_) C1,F1: 8.. / C1 = 8 => 0 pairs (*) / F1 = 8 => 0 pairs (X) C2,D2: 8.. / C2 = 8 => 0 pairs (X) / D2 = 8 => 0 pairs (_) D2,D4: 8.. / D2 = 8 => 0 pairs (*) / D4 = 8 => 0 pairs (X) F1,F4: 8.. / F1 = 8 => 0 pairs (X) / F4 = 8 => 0 pairs (_) * DURATION: 0:00:40.137796 START: 04:18:40.159838 END: 04:19:20.297634 2019-05-01 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A9,B1,B8,C1,D7,E2,E7,F1,F3,G2,H2,I8) * ...96.5.715...2..9..9.5..8.93..2..54..5...3988..539...582..49634.36958...9.283..5 * PAIR A1: 2,3 BLK 1 A3: 2,3,6,7 # reduction candidate for 2,3 A3: 2,3 => SOLVED * 348961527157842639269357481936728154725416398814539276582174963473695812691283745 A3: 6,7 # 15 pairs * PAIR A1: 2,3 ROW 1 H1: 2,3,1,4 # reduction candidate for 2,3 H1: 2,3 => SOLVED * 348961527157842639269357481936728154725416398814539276582174963473695812691283745 H1: 1,4 # 15 pairs * PAIR B1: 2,4 BLK 1 B3: 2,4,6,7 # reduction candidate for 2,4 B3: 2,4 => CTR * 3.89615.715.8.2.39..9357.8.93..286542.54.6398864539...582..49634.36958...9.283..5 B3: 6,7 # 14 pairs * PAIR B1: 2,4 ROW 1 H1: 2,4,1,3 # reduction candidate for 2,4 H1: 2,4 => SOLVED * 348961527157842639269357481936728154725416398814539276582174963473695812691283745 H1: 1,3 # 15 pairs * PAIR C1: 4,8 BLK 1 C2: 4,8,6,7 # reduction candidate for 4,8 C2: 4,8 => CTR * ...968517158..2639..9351482936827154..5..639881.5392.6582..49634.3695821.91283..5 C2: 6,7 => SOLVED * 348961527157842639269357481936728154725416398814539276582174963473695812691283745 * PAIR F1: 1,8 COL F F4: 1,8,6,7 # reduction candidate for 1,8 F4: 1,8 => SOLVED * 348961527157842639269357481936728154725416398814539276582174963473695812691283745 F4: 6,7 => CTR * ...968517158..2639..935148293.82..54..5...3988..539276582..4963473695821691283..5 * PAIR E2: 4,7 BLK 2 D2: 4,7,3,8 # reduction candidate for 4,7 D2: 4,7 => CTR * ...968517158..2639..935148293.82..54..5...3988..539276582..4963473695821691283..5 D2: 3,8 # 14 pairs D3: 4,7,1,3 # reduction candidate for 4,7 D3: 4,7 => CTR * 24896153715.372.493.945..8.93.82..54..5.4.3988..539...582.149634.36958...9.2834.5 D3: 1,3 # 14 pairs * PAIR E2: 4,7 ROW 2 C2: 4,7,6,8 # reduction candidate for 4,7 C2: 4,7 => SOLVED * 348961527157842639269357481936728154725416398814539276582174963473695812691283745 C2: 6,8 => CTR * ...968517158..2639..935148293.82..54..5...3988..539276582..4963473695821691283..5 * PAIR E2: 4,7 COL E E5: 4,7,1 # reduction candidate for 4,7 E5: 4,7 # 14 pairs E5: 1 # 13 pairs * PAIR F3: 1,7 BLK 2 D3: 1,7,3,4 # reduction candidate for 1,7 D3: 1,7 => CTR * ...96.5.715.342..9..9.5..8.93..2..54..5...3988..539...582..49634.36958...9.283..5 D3: 3,4 # 15 pairs * PAIR F3: 1,7 COL F F4: 1,7,6,8 # reduction candidate for 1,7 F4: 1,7 => CTR * ...968517158..2639..9351482936827154..5..63988..539276582..49634736958...9.283..5 F4: 6,8 # 14 pairs F5: 1,7,6 # reduction candidate for 1,7 F5: 1,7 => CTR * ...968517158..2639..935148293.826.54..5..73988..539276582..496347369582169.283..5 F5: 6 # 14 pairs * PAIR G2: 4,6 BLK 3 G3: 4,6,1,2 # reduction candidate for 4,6 G3: 4,6 # 17 pairs G3: 1,2 # 14 pairs * PAIR G2: 4,6 ROW 2 C2: 4,6,7,8 # reduction candidate for 4,6 C2: 4,6 => CTR * ..89615.715.872..9..9.5..8.93..2..54..5...3988..539...582..49634.36958...9.283..5 C2: 7,8 # 15 pairs * PAIR H2: 3,4 BLK 3 H1: 3,4,1,2 # reduction candidate for 3,4 H1: 3,4 => CTR * 328961547157842639649357.8.936.28.542.54.63988.4539..6582..49634.36958..791283..5 H1: 1,2 # 17 pairs * PAIR H2: 3,4 ROW 2 D2: 3,4,7,8 # reduction candidate for 3,4 D2: 3,4 => CTR * ...968517158.72639..935148293.82..54..5.4.3988..539276582714963473695821691283..5 D2: 7,8 # 15 pairs * PAIR B8: 1,7 BLK 7 C9: 1,7,6 # reduction candidate for 1,7 C9: 6 => CTR * ...96.5.715...26.9..9.5..8193..26.54..5...3988..539..6582..4963413695872796283..5 C9: 1,7 # 14 pairs * PAIR B8: 1,7 ROW 8 H8: 1,7,2 # reduction candidate for 1,7 H8: 2 # 19 pairs H8: 1,7 # 15 pairs * PAIR B8: 1,7 COL B B5: 1,7,2,6 # reduction candidate for 1,7 B5: 1,7 => CTR * 3..96.5.715...2639769351482936.27154275..63988..539276582..49634.36958..69.283..5 B5: 2,6 # 15 pairs B6: 1,7,4,6 # reduction candidate for 1,7 B6: 1,7 => SOLVED * 348961527157842639269357481936728154725416398814539276582174963473695812691283745 B6: 4,6 # 14 pairs * PAIR A9: 6,7 BLK 7 C9: 6,7,1 # reduction candidate for 6,7 C9: 6,7 # 18 pairs C9: 1 # 16 pairs * PAIR A9: 6,7 COL A A3: 6,7,2,3 # reduction candidate for 6,7 A3: 6,7 # 15 pairs A5: 6,7,2 # reduction candidate for 6,7 A5: 6,7 => SOLVED * 348961527157842639269357481936728154725416398814539276582174963473695812691283745 A5: 2 # 15 pairs * PAIR D7: 1,7 COL D D3: 1,7,3,4 # reduction candidate for 1,7 D3: 1,7 => CTR * ...96.5.715.342..9..9.5..8.93..2..54..5...3988..539...582..49634.36958...9.283..5 D3: 3,4 # 15 pairs D4: 1,7,8 # reduction candidate for 1,7 D4: 1,7 => SOLVED * 348961527157842639269357481936728154725416398814539276582174963473695812691283745 D4: 8 => CTR * ...968517158..2639..935148293.82..54..5...3988..539276582..4963473695821691283..5 D5: 1,7,4 # reduction candidate for 1,7 D5: 1,7 => CTR * ...968517158.72639..935148293.82..54..514.3988..539276582714963473695821691283..5 D5: 4 # 15 pairs * PAIR E7: 1,7 COL E E5: 1,7,4 # reduction candidate for 1,7 E5: 4 => CTR * ...968517158.72639..935148293.82..54..514.3988..539276582714963473695821691283..5 E5: 1,7 # 15 pairs * PAIR I8: 1,2 BLK 9 H8: 1,2,7 # reduction candidate for 1,2 H8: 7 # 18 pairs H8: 1,2 # 16 pairs * PAIR I8: 1,2 COL I I3: 1,2,6 # reduction candidate for 1,2 I3: 1,2 # 15 pairs I6: 1,2,6 # reduction candidate for 1,2 I6: 1,2 => CTR * ...96.5.7156872439..9.5..8693..2..54..5...3988..539...582..49634.36958...9.283..5 I6: 6 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190307-absurd-base-pr-000.dot * REASONING * PRF # A3: 2,3 => SOL * PRF # H1: 2,3 => SOL * DIS # B3: 2,4 => CTR => B3: 6,7 * PRF # H1: 2,4 => SOL * DIS # C2: 4,8 => CTR => C2: 6,7 * PRF # C2: 6,7 => SOL * PRF # F4: 1,8 => SOL * DIS # F4: 6,7 => CTR => F4: 1,8 * DIS # D2: 4,7 => CTR => D2: 3,8 * DIS # D3: 4,7 => CTR => D3: 1,3 * PRF # C2: 4,7 => SOL * DIS # C2: 6,8 => CTR => C2: 4,7 * DIS # D3: 1,7 => CTR => D3: 3,4 * DIS # F4: 1,7 => CTR => F4: 6,8 * DIS # F5: 1,7 => CTR => F5: 6 * DIS # C2: 4,6 => CTR => C2: 7,8 * DIS # H1: 3,4 => CTR => H1: 1,2 * DIS # D2: 3,4 => CTR => D2: 7,8 * DIS # C9: 6 => CTR => C9: 1,7 * DIS # B5: 1,7 => CTR => B5: 2,6 * PRF # B6: 1,7 => SOL * PRF # A5: 6,7 => SOL * DIS # D3: 1,7 => CTR => D3: 3,4 * PRF # D4: 1,7 => SOL * DIS # D4: 8 => CTR => D4: 1,7 * DIS # D5: 1,7 => CTR => D5: 4 * DIS # E5: 4 => CTR => E5: 1,7 * DIS # I6: 1,2 => CTR => I6: 6 * CNT 28 HDP CHAINS / 60 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A9,B1,B8,C1,D7,E2,E7,F1,F3,G2,H2,I8) * ...96.5.715...2..9..9.5..8.93..2..54..5...3988..539...582..49634.36958...9.283..5 * PAIR A1: 2,3 BLK 1 A3: 2,3,6,7 # reduction candidate for 2,3 A3: 2,3 => SOLVED * 348961527157842639269357481936728154725416398814539276582174963473695812691283745 * DURATION: 0:00:01.907118 START: 04:20:06.777415 END: 04:20:08.684533 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190307-absurd-base-pr-001.dot * REASONING * PRF # A3: 2,3 => SOL * STA A3: 2,3 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190307, absurd
Solution
position: 348961527157842639269357481936728154725416398814539276582174963473695812691283745 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 # A3: 2,3 => SOL * INC # A3: 6,7 => UNS * PRF # H1: 2,3 => SOL * INC # H1: 1,4 => UNS * DIS # B3: 2,4 => CTR => B3: 6,7 * INC # B3: 6,7 => UNS * PRF # H1: 2,4 => SOL * INC # H1: 1,3 => UNS * DIS # C2: 4,8 => CTR => C2: 6,7 * PRF # C2: 6,7 => SOL * PRF # F4: 1,8 => SOL * DIS # F4: 6,7 => CTR => F4: 1,8 * DIS # D2: 4,7 => CTR => D2: 3,8 * INC # D2: 3,8 => UNS * DIS # D3: 4,7 => CTR => D3: 1,3 * INC # D3: 1,3 => UNS * PRF # C2: 4,7 => SOL * DIS # C2: 6,8 => CTR => C2: 4,7 * INC # E5: 4,7 => UNS * INC # E5: 1 => UNS * DIS # D3: 1,7 => CTR => D3: 3,4 * INC # D3: 3,4 => UNS * DIS # F4: 1,7 => CTR => F4: 6,8 * INC # F4: 6,8 => UNS * DIS # F5: 1,7 => CTR => F5: 6 * INC # F5: 6 => UNS * INC # G3: 4,6 => UNS * INC # G3: 1,2 => UNS * DIS # C2: 4,6 => CTR => C2: 7,8 * INC # C2: 7,8 => UNS * DIS # H1: 3,4 => CTR => H1: 1,2 * INC # H1: 1,2 => UNS * DIS # D2: 3,4 => CTR => D2: 7,8 * INC # D2: 7,8 => UNS * INC # C9: 1,7 => UNS * DIS # C9: 6 => CTR => C9: 1,7 * INC # H8: 1,7 => UNS * INC # H8: 2 => UNS * DIS # B5: 1,7 => CTR => B5: 2,6 * INC # B5: 2,6 => UNS * PRF # B6: 1,7 => SOL * INC # B6: 4,6 => UNS * INC # C9: 6,7 => UNS * INC # C9: 1 => UNS * INC # A3: 6,7 => UNS * PRF # A5: 6,7 => SOL * INC # A5: 2 => UNS * DIS # D3: 1,7 => CTR => D3: 3,4 * INC # D3: 3,4 => UNS * PRF # D4: 1,7 => SOL * DIS # D4: 8 => CTR => D4: 1,7 * DIS # D5: 1,7 => CTR => D5: 4 * INC # D5: 4 => UNS * INC # E5: 1,7 => UNS * DIS # E5: 4 => CTR => E5: 1,7 * INC # H8: 1,2 => UNS * INC # H8: 7 => UNS * INC # I3: 1,2 => UNS * DIS # I6: 1,2 => CTR => I6: 6 * INC # I6: 6 => UNS * CNT 60 HDP CHAINS / 60 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A3: 2,3 => SOL * STA A3: 2,3 * CNT 1 HDP CHAINS / 1 HYP OPENED