Analysis of zz-www.sudokuoftheday.co.uk-20190305-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: ....9..34....6..598...3.....9..761...625.3.9.4.7.......1....4..........3..3..9.2. initial
Autosolve
position: ....9..34.3..6..598.9.3.6..39..7614.1625437984.79..36.91.3..4........9.3..3..952. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A1: 2,7 => SOL * DIS # A8: 2,7 => CTR => A8: 5,6 * DIS # D2: 2,4 => CTR => D2: 1,7,8 * DIS # F3: 2,4 => CTR => F3: 5 * DIS # B3: 5 => CTR => B3: 2,4 * DIS # D1: 2,8 => CTR => D1: 1,7 * DIS # D2: 2,8 => CTR => D2: 1,4,7 * DIS # F2: 2,8 => CTR => F2: 1,4,7 * DIS # I9: 6 => CTR => I9: 1,7 * DIS # C8: 5,8 => CTR => C8: 4,6 * DIS # B8: 5,8 => CTR => B8: 2,4,7 * DIS # F6: 2,8 => CTR => F6: 1 * DIS # D1: 2,8 => CTR => D1: 1,7 * DIS # D2: 2,8 => CTR => D2: 1,4,7 * DIS # A8: 6,7 => CTR => A8: 2,5 * DIS # D9: 6,7 => CTR => D9: 1,4,8 * PRF # A1: 6,7 => SOL * DIS # A1: 2,5 => CTR => A1: 6,7 * DIS # D8: 1,8 => CTR => D8: 4,6,7 * DIS # F8: 1,8 => CTR => F8: 4,7 * DIS # D9: 1,8 => CTR => D9: 4,6,7 * DIS # E6: 1,8 => CTR => E6: 2 * DIS # F7: 7,8 => CTR => F7: 2 * CNT 23 HDP CHAINS / 61 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A1: 2,7 => SOL * STA A1: 2,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....9..34....6..598...3.....9..761...625.3.9.4.7.......1....4..........3..3..9.2. | initial |
| ....9..34.3..6..598.9.3.6..39..7614.1625437984.79..36.91.3..4........9.3..3..952. | autosolve |
| 756198234231764859849235617395876142162543798487921365918352476524617983673489521 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) A2: 2,7 C2: 1,4 D3: 2,4 G1: 2,8 G2: 2,8 H3: 1,7 I3: 1,7 C4: 5,8 B6: 5,8 D4: 2,8 I4: 2,5 I6: 2,5 A9: 6,7 E9: 1,8 H7: 7,8 I7: 6,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,C2: 1.. / C1 = 1 => 0 pairs (X) / C2 = 1 => 0 pairs (_) H3,I3: 1.. / H3 = 1 => 23 pairs (_) / I3 = 1 => 19 pairs (_) E6,F6: 1.. / E6 = 1 => 0 pairs (X) / F6 = 1 => 17 pairs (_) H8,I9: 1.. / H8 = 1 => 19 pairs (_) / I9 = 1 => 23 pairs (_) H3,H8: 1.. / H3 = 1 => 23 pairs (_) / H8 = 1 => 19 pairs (_) I3,I9: 1.. / I3 = 1 => 19 pairs (_) / I9 = 1 => 23 pairs (_) G1,G2: 2.. / G1 = 2 => 15 pairs (_) / G2 = 2 => 0 pairs (X) I4,I6: 2.. / I4 = 2 => 14 pairs (_) / I6 = 2 => 0 pairs (X) A8,B8: 2.. / A8 = 2 => 0 pairs (X) / B8 = 2 => 18 pairs (_) E7,F7: 2.. / E7 = 2 => 0 pairs (X) / F7 = 2 => 14 pairs (_) D4,I4: 2.. / D4 = 2 => 0 pairs (X) / I4 = 2 => 14 pairs (_) E6,E7: 2.. / E6 = 2 => 14 pairs (_) / E7 = 2 => 0 pairs (X) C2,B3: 4.. / C2 = 4 => 0 pairs (X) / B3 = 4 => 0 pairs (_) B9,D9: 4.. / B9 = 4 => 0 pairs (X) / D9 = 4 => 0 pairs (_) C2,C8: 4.. / C2 = 4 => 0 pairs (X) / C8 = 4 => 0 pairs (_) F1,F3: 5.. / F1 = 5 => 0 pairs (X) / F3 = 5 => 17 pairs (_) C4,B6: 5.. / C4 = 5 => 14 pairs (_) / B6 = 5 => 0 pairs (X) I4,I6: 5.. / I4 = 5 => 0 pairs (X) / I6 = 5 => 14 pairs (_) E7,E8: 5.. / E7 = 5 => 14 pairs (_) / E8 = 5 => 0 pairs (X) B3,F3: 5.. / B3 = 5 => 0 pairs (X) / F3 = 5 => 17 pairs (_) C4,I4: 5.. / C4 = 5 => 14 pairs (_) / I4 = 5 => 0 pairs (X) B6,I6: 5.. / B6 = 5 => 0 pairs (X) / I6 = 5 => 14 pairs (_) C7,E7: 5.. / C7 = 5 => 0 pairs (X) / E7 = 5 => 14 pairs (_) A1,A8: 5.. / A1 = 5 => 0 pairs (X) / A8 = 5 => 14 pairs (_) A1,C1: 6.. / A1 = 6 => 0 pairs (X) / C1 = 6 => 0 pairs (_) D8,D9: 6.. / D8 = 6 => 16 pairs (_) / D9 = 6 => 0 pairs (X) I7,I9: 6.. / I7 = 6 => 19 pairs (_) / I9 = 6 => 0 pairs (X) C7,I7: 6.. / C7 = 6 => 0 pairs (X) / I7 = 6 => 19 pairs (_) H3,I3: 7.. / H3 = 7 => 19 pairs (_) / I3 = 7 => 23 pairs (_) G1,G2: 8.. / G1 = 8 => 0 pairs (X) / G2 = 8 => 15 pairs (_) C4,B6: 8.. / C4 = 8 => 0 pairs (X) / B6 = 8 => 14 pairs (_) H7,H8: 8.. / H7 = 8 => 19 pairs (_) / H8 = 8 => 14 pairs (_) C4,D4: 8.. / C4 = 8 => 0 pairs (X) / D4 = 8 => 14 pairs (_) * DURATION: 0:00:59.741107 START: 04:14:59.514991 END: 04:15:59.256098 2019-05-01 * CP COUNT: (33) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A9,B6,C2,C4,D3,D4,E9,G1,G2,H3,H7,I3,I4,I6,I7) * ....9..34.3..6..598.9.3.6..39..7614.1625437984.79..36.91.3..4........9.3..3..952. * PAIR A2: 2,7 BLK 1 A1: 2,7,5,6 # reduction candidate for 2,7 A1: 2,7 => SOLVED * 756198234231764859849235617395876142162543798487921365918352476524617983673489521 A1: 5,6 # 17 pairs B1: 2,7,5 # reduction candidate for 2,7 B1: 2,7 # 19 pairs * PAIR A2: 2,7 ROW 2 D2: 2,7,1,4,8 # reduction candidate for 2,7 D2: 2,7 # 17 pairs F2: 2,7,1,4,8 # reduction candidate for 2,7 F2: 2,7 # 17 pairs * PAIR A2: 2,7 COL A A8: 2,7,5,6 # reduction candidate for 2,7 A8: 2,7 => CTR * 526197.34.31.6..598492356..39.8761421625437984879..36591.3..4.6.546..9.3673489521 A8: 5,6 # 20 pairs * PAIR C2: 1,4 ROW 2 D2: 1,4,2,7,8 # reduction candidate for 1,4 D2: 1,4 # 17 pairs F2: 1,4,2,7,8 # reduction candidate for 1,4 F2: 1,4 # 17 pairs * PAIR D3: 2,4 BLK 2 D2: 2,4,1,7,8 # reduction candidate for 2,4 D2: 2,4 => CTR * ....9..34.342618598294356..39587614216254379848791236591.3..4.......49.3.43.8952. D2: 1,7,8 # 16 pairs F2: 2,4,1,7,8 # reduction candidate for 2,4 F2: 2,4 # 18 pairs F3: 2,4,5 # reduction candidate for 2,4 F3: 2,4 => CTR * .7..9583423..6..59859.3.6..3958761421625437984879..36591.3524..52....9.3.43.8952. F3: 5 # 17 pairs * PAIR D3: 2,4 ROW 3 B3: 2,4,5 # reduction candidate for 2,4 B3: 5 => CTR * .71295834234.6..59859.3.6..3958761421625437984879..36591.3524..52....9.3.43.8952. B3: 2,4 # 17 pairs * PAIR G1: 2,8 ROW 1 D1: 2,8,1,7 # reduction candidate for 2,8 D1: 2,8 => CTR * 671.95.342341678598594326..39..7614.1625437984.79..36.91.3..4..52..149.3743689521 D1: 1,7 # 17 pairs F1: 2,8,1,5,7 # reduction candidate for 2,8 F1: 2,8 # 20 pairs * PAIR G2: 2,8 ROW 2 D2: 2,8,1,4,7 # reduction candidate for 2,8 D2: 2,8 => CTR * ..6.9..34731.64.598.9.3.6..39..7614.1625437984.79..36.91.3..4........9.3..3..952. D2: 1,4,7 # 16 pairs F2: 2,8,1,4,7 # reduction candidate for 2,8 F2: 2,8 => CTR * ..6.9..3473146..598492356..39.8761421625437984879..36591.3..4.6..46..9.36731.952. F2: 1,4,7 # 16 pairs * PAIR H3: 1,7 COL H H8: 1,7,8 # reduction candidate for 1,7 H8: 1,7 # 19 pairs H8: 8 # 14 pairs * PAIR I3: 1,7 COL I I9: 1,7,6 # reduction candidate for 1,7 I9: 6 => CTR * ....9..34.3..6..598.9.3.67139..7614.1625437984.79..36.916352487...68.913783419526 I9: 1,7 # 19 pairs * PAIR C4: 5,8 COL C C7: 5,8,6 # reduction candidate for 5,8 C7: 5,8 # 19 pairs C8: 5,8,4,6 # reduction candidate for 5,8 C8: 5,8 => CTR * 671.95.3423476185985923467139587614.1625437984.79..36.916352487...6..9137.3..9526 C8: 4,6 # 17 pairs * PAIR B6: 5,8 COL B B8: 5,8,2,4,7 # reduction candidate for 5,8 B8: 5,8 => CTR * 5.6.9..34731.6..598492356..39.8761421625437984879..36591.3..4.62546..9.36734.952. B8: 2,4,7 # 16 pairs * PAIR D4: 2,8 BLK 5 E6: 2,8,1 # reduction candidate for 2,8 E6: 2,8 # 17 pairs F6: 2,8,1 # reduction candidate for 2,8 F6: 2,8 => CTR * 5.6.9..34.31.6..598492356..39.8761421625437984.791.36.91.32.4......5.9.3..3.8952. F6: 1 # 17 pairs * PAIR D4: 2,8 COL D D1: 2,8,1,7 # reduction candidate for 2,8 D1: 2,8 => CTR * 671.95.342341678598594326..39..7614.1625437984.79..36.91.3..4..52..149.3743689521 D1: 1,7 # 17 pairs D2: 2,8,1,4,7 # reduction candidate for 2,8 D2: 2,8 => CTR * ..6.9..34731.64.598.9.3.6..39..7614.1625437984.79..36.91.3..4........9.3..3..952. D2: 1,4,7 # 16 pairs * PAIR A9: 6,7 BLK 7 A8: 6,7,2,5 # reduction candidate for 6,7 A8: 6,7 => CTR * 5.6.9..34231.6.8598492356..39.8761421625437984879..36591.3..4.6......9.3..3..952. A8: 2,5 # 17 pairs * PAIR A9: 6,7 ROW 9 D9: 6,7,1,4,8 # reduction candidate for 6,7 D9: 6,7 => CTR * 671.95.34234.6.859859.3.6173958761421625437984879..365918352476526.1.983743689521 D9: 1,4,8 # 16 pairs I9: 6,7,1 # reduction candidate for 6,7 I9: 6,7 # 19 pairs * PAIR A9: 6,7 COL A A1: 6,7,2,5 # reduction candidate for 6,7 A1: 6,7 => SOLVED * 756198234231764859849235617395876142162543798487921365918352476524617983673489521 A1: 2,5 => CTR * ..6.9..34731.6..598492356..39.8761421625437984879..36591.3..4.6..4...9.3.73489521 * PAIR E9: 1,8 BLK 8 D8: 1,8,4,6,7 # reduction candidate for 1,8 D8: 1,8 => CTR * .7..9..34234761859859432617395.7614.1625437984.79..36.91.3..4.6.....49.3743689521 D8: 4,6,7 # 16 pairs E8: 1,8,5 # reduction candidate for 1,8 E8: 1,8 # 14 pairs F8: 1,8,4,7 # reduction candidate for 1,8 F8: 1,8 => CTR * ....9..34.3..6..598.923.6..3958761421625437984879..36591.3524......1.9.3..3.8952. F8: 4,7 # 17 pairs D9: 1,8,4,6,7 # reduction candidate for 1,8 D9: 1,8 => CTR * ....9..34.34.6..598.943.6..39..7614.1625437984.79..36.91.3.7486...6.49.3643..9527 D9: 4,6,7 # 16 pairs * PAIR E9: 1,8 COL E E6: 1,8,2 # reduction candidate for 1,8 E6: 1,8 => CTR * 5.6.9..34.31.6..598492356..39.8761421625437984.79..36.91.32.4......5.9.3..3..952. E6: 2 # 14 pairs * PAIR H7: 7,8 BLK 9 H8: 7,8,1 # reduction candidate for 7,8 H8: 7,8 # 23 pairs H8: 1 # 19 pairs * PAIR H7: 7,8 ROW 7 F7: 7,8,2 # reduction candidate for 7,8 F7: 7,8 => CTR * 5.6.9..34.31.6..598492356..39.8761421625437984.79..36.91.32.4......5.9.3..3..952. F7: 2 # 14 pairs * PAIR I7: 6,7 BLK 9 I9: 6,7,1 # reduction candidate for 6,7 I9: 1 # 23 pairs I9: 6,7 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190305-absurd-base-pr-000.dot * REASONING * PRF # A1: 2,7 => SOL * DIS # A8: 2,7 => CTR => A8: 5,6 * DIS # D2: 2,4 => CTR => D2: 1,7,8 * DIS # F3: 2,4 => CTR => F3: 5 * DIS # B3: 5 => CTR => B3: 2,4 * DIS # D1: 2,8 => CTR => D1: 1,7 * DIS # D2: 2,8 => CTR => D2: 1,4,7 * DIS # F2: 2,8 => CTR => F2: 1,4,7 * DIS # I9: 6 => CTR => I9: 1,7 * DIS # C8: 5,8 => CTR => C8: 4,6 * DIS # B8: 5,8 => CTR => B8: 2,4,7 * DIS # F6: 2,8 => CTR => F6: 1 * DIS # D1: 2,8 => CTR => D1: 1,7 * DIS # D2: 2,8 => CTR => D2: 1,4,7 * DIS # A8: 6,7 => CTR => A8: 2,5 * DIS # D9: 6,7 => CTR => D9: 1,4,8 * PRF # A1: 6,7 => SOL * DIS # A1: 2,5 => CTR => A1: 6,7 * DIS # D8: 1,8 => CTR => D8: 4,6,7 * DIS # F8: 1,8 => CTR => F8: 4,7 * DIS # D9: 1,8 => CTR => D9: 4,6,7 * DIS # E6: 1,8 => CTR => E6: 2 * DIS # F7: 7,8 => CTR => F7: 2 * CNT 23 HDP CHAINS / 61 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A9,B6,C2,C4,D3,D4,E9,G1,G2,H3,H7,I3,I4,I6,I7) * ....9..34.3..6..598.9.3.6..39..7614.1625437984.79..36.91.3..4........9.3..3..952. * PAIR A2: 2,7 BLK 1 A1: 2,7,5,6 # reduction candidate for 2,7 A1: 2,7 => SOLVED * 756198234231764859849235617395876142162543798487921365918352476524617983673489521 * DURATION: 0:00:02.076354 START: 04:16:53.421210 END: 04:16:55.497564 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190305-absurd-base-pr-001.dot * REASONING * PRF # A1: 2,7 => SOL * STA A1: 2,7 * 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, 20190305, absurd
Solution
position: 756198234231764859849235617395876142162543798487921365918352476524617983673489521 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 # A1: 2,7 => SOL * INC # A1: 5,6 => UNS * INC # B1: 2,7 => UNS * INC # D2: 2,7 => UNS * INC # F2: 2,7 => UNS * DIS # A8: 2,7 => CTR => A8: 5,6 * INC # A8: 5,6 => UNS * INC # D2: 1,4 => UNS * INC # F2: 1,4 => UNS * DIS # D2: 2,4 => CTR => D2: 1,7,8 * INC # D2: 1,7,8 => UNS * INC # F2: 2,4 => UNS * DIS # F3: 2,4 => CTR => F3: 5 * INC # F3: 5 => UNS * INC # B3: 2,4 => UNS * DIS # B3: 5 => CTR => B3: 2,4 * DIS # D1: 2,8 => CTR => D1: 1,7 * INC # D1: 1,7 => UNS * INC # F1: 2,8 => UNS * DIS # D2: 2,8 => CTR => D2: 1,4,7 * INC # D2: 1,4,7 => UNS * DIS # F2: 2,8 => CTR => F2: 1,4,7 * INC # F2: 1,4,7 => UNS * INC # H8: 1,7 => UNS * INC # H8: 8 => UNS * INC # I9: 1,7 => UNS * DIS # I9: 6 => CTR => I9: 1,7 * INC # C7: 5,8 => UNS * DIS # C8: 5,8 => CTR => C8: 4,6 * INC # C8: 4,6 => UNS * DIS # B8: 5,8 => CTR => B8: 2,4,7 * INC # B8: 2,4,7 => UNS * INC # E6: 2,8 => UNS * DIS # F6: 2,8 => CTR => F6: 1 * INC # F6: 1 => UNS * DIS # D1: 2,8 => CTR => D1: 1,7 * INC # D1: 1,7 => UNS * DIS # D2: 2,8 => CTR => D2: 1,4,7 * INC # D2: 1,4,7 => UNS * DIS # A8: 6,7 => CTR => A8: 2,5 * INC # A8: 2,5 => UNS * DIS # D9: 6,7 => CTR => D9: 1,4,8 * INC # D9: 1,4,8 => UNS * INC # I9: 6,7 => UNS * PRF # A1: 6,7 => SOL * DIS # A1: 2,5 => CTR => A1: 6,7 * DIS # D8: 1,8 => CTR => D8: 4,6,7 * INC # D8: 4,6,7 => UNS * INC # E8: 1,8 => UNS * DIS # F8: 1,8 => CTR => F8: 4,7 * INC # F8: 4,7 => UNS * DIS # D9: 1,8 => CTR => D9: 4,6,7 * INC # D9: 4,6,7 => UNS * DIS # E6: 1,8 => CTR => E6: 2 * INC # E6: 2 => UNS * INC # H8: 7,8 => UNS * INC # H8: 1 => UNS * DIS # F7: 7,8 => CTR => F7: 2 * INC # F7: 2 => UNS * INC # I9: 6,7 => UNS * INC # I9: 1 => UNS * CNT 61 HDP CHAINS / 61 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A1: 2,7 => SOL * STA A1: 2,7 * CNT 1 HDP CHAINS / 1 HYP OPENED