Analysis of zz-www.sudokuoftheday.co.uk-20190420-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019
level: medium
position: ..45.28..52..3....9.7.............5....3.6..9..3.8..2..49.71...17..4......29..71. initial
Autosolve
position: ..45.28..52..3....9.7.............5....3.6..9..3.8..2..49.71...17..4......29..714 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I1: 3,6 => CTR => I1: 1,7 * DIS # E1: 1,6 => CTR => E1: 9 * DIS # F2: 4,8 => CTR => F2: 7,9 * DIS # I1: 1,6 => CTR => I1: 3,7 * DIS # I6: 7 => CTR => I6: 1,6 * DIS # D6: 1 => CTR => D6: 4,7 * DIS # G4: 1,4 => CTR => G4: 3 * CNT 7 HDP CHAINS / 41 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I1: 3,6 => CTR => I1: 1,7 * DIS I1: 1,7 # E1: 1,6 => CTR => E1: 9 * DIS I1: 1,7 + E1: 9 # F2: 4,8 => CTR => F2: 7 * DIS I1: 1,7 + E1: 9 + F2: 7 # G2: 1,6 => CTR => G2: 4,9 * DIS I1: 1,7 + E1: 9 + F2: 7 + G2: 4,9 # C2: 1,6 => CTR => C2: 8 * DIS I1: 1,7 + E1: 9 + F2: 7 + G2: 4,9 + C2: 8 # D2: 4 => CTR => D2: 1,6 * PRF I1: 1,7 + E1: 9 + F2: 7 + G2: 4,9 + C2: 8 + D2: 1,6 # A4: 4,7 => SOL * STA I1: 1,7 + E1: 9 + F2: 7 + G2: 4,9 + C2: 8 + D2: 1,6 + A4: 4,7 * CNT 7 HDP CHAINS / 34 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..45.28..52..3....9.7.............5....3.6..9..3.8..2..49.71...17..4......29..71. | initial |
| ..45.28..52..3....9.7.............5....3.6..9..3.8..2..49.71...17..4......29..714 | autosolve |
| 314592867528637941967418235796124358281356479453789126649271583175843692832965714 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) A1: 3,6 E3: 1,6 F3: 4,8 I2: 1,6 G3: 2,5 I3: 2,5 A6: 4,7 B6: 5,9 F6: 5,9 G5: 1,4 C8: 5,6 E9: 5,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G3,I3: 2.. / G3 = 2 => 10 pairs (_) / I3 = 2 => 10 pairs (_) A4,A5: 2.. / A4 = 2 => 20 pairs (_) / A5 = 2 => 23 pairs (_) E4,E5: 2.. / E4 = 2 => 23 pairs (_) / E5 = 2 => 20 pairs (_) D7,D8: 2.. / D7 = 2 => 13 pairs (_) / D8 = 2 => 15 pairs (_) A4,E4: 2.. / A4 = 2 => 20 pairs (_) / E4 = 2 => 23 pairs (_) A5,E5: 2.. / A5 = 2 => 23 pairs (_) / E5 = 2 => 20 pairs (_) G4,I4: 3.. / G4 = 3 => 12 pairs (_) / I4 = 3 => 0 pairs (X) F8,F9: 3.. / F8 = 3 => 15 pairs (_) / F9 = 3 => 17 pairs (_) B3,H3: 3.. / B3 = 3 => 23 pairs (_) / H3 = 3 => 14 pairs (_) G3,I3: 5.. / G3 = 5 => 10 pairs (_) / I3 = 5 => 10 pairs (_) E5,F6: 5.. / E5 = 5 => 0 pairs (*) / F6 = 5 => 0 pairs (X) C8,B9: 5.. / C8 = 5 => 14 pairs (_) / B9 = 5 => 0 pairs (X) G7,I7: 5.. / G7 = 5 => 10 pairs (_) / I7 = 5 => 10 pairs (_) B6,F6: 5.. / B6 = 5 => 0 pairs (*) / F6 = 5 => 0 pairs (X) C8,F8: 5.. / C8 = 5 => 14 pairs (_) / F8 = 5 => 0 pairs (X) C5,C8: 5.. / C5 = 5 => 0 pairs (X) / C8 = 5 => 14 pairs (_) E5,E9: 5.. / E5 = 5 => 0 pairs (*) / E9 = 5 => 0 pairs (X) G3,G7: 5.. / G3 = 5 => 10 pairs (_) / G7 = 5 => 10 pairs (_) I3,I7: 5.. / I3 = 5 => 10 pairs (_) / I7 = 5 => 10 pairs (_) B4,C4: 6.. / B4 = 6 => 0 pairs (X) / C4 = 6 => 15 pairs (_) G6,I6: 6.. / G6 = 6 => 13 pairs (_) / I6 = 6 => 18 pairs (_) D2,F2: 7.. / D2 = 7 => 18 pairs (_) / F2 = 7 => 14 pairs (_) H1,I1: 7.. / H1 = 7 => 0 pairs (X) / I1 = 7 => 20 pairs (_) A5,H5: 7.. / A5 = 7 => 0 pairs (X) / H5 = 7 => 20 pairs (_) F2,F4: 7.. / F2 = 7 => 14 pairs (_) / F4 = 7 => 18 pairs (_) H1,H5: 7.. / H1 = 7 => 0 pairs (X) / H5 = 7 => 20 pairs (_) C2,B3: 8.. / C2 = 8 => 15 pairs (_) / B3 = 8 => 24 pairs (_) I4,H5: 8.. / I4 = 8 => 14 pairs (_) / H5 = 8 => 0 pairs (X) A7,A9: 8.. / A7 = 8 => 21 pairs (_) / A9 = 8 => 14 pairs (_) A9,F9: 8.. / A9 = 8 => 14 pairs (_) / F9 = 8 => 21 pairs (_) E1,F2: 9.. / E1 = 9 => 13 pairs (_) / F2 = 9 => 0 pairs (X) B4,B6: 9.. / B4 = 9 => 0 pairs (*) / B6 = 9 => 0 pairs (X) G8,H8: 9.. / G8 = 9 => 13 pairs (_) / H8 = 9 => 16 pairs (_) E1,H1: 9.. / E1 = 9 => 13 pairs (_) / H1 = 9 => 0 pairs (X) B6,F6: 9.. / B6 = 9 => 19 pairs (_) / F6 = 9 => 0 pairs (*) E1,E4: 9.. / E1 = 9 => 13 pairs (_) / E4 = 9 => 0 pairs (X) G2,G8: 9.. / G2 = 9 => 16 pairs (_) / G8 = 9 => 13 pairs (_) * DURATION: 0:00:39.870026 START: 05:28:12.190540 END: 05:28:52.060566 2019-05-01 * CP COUNT: (37) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B6,C8,E3,E9,F3,F6,G3,G5,I2,I3) * ..45.28..52..3....9.7.............5....3.6..9..3.8..2..49.71...17..4......29..714 * PAIR A1: 3,6 BLK 1 B1: 3,6,1 # reduction candidate for 3,6 B1: 3,6 # 19 pairs B3: 3,6,1,8 # reduction candidate for 3,6 B3: 3,6 # 17 pairs * PAIR A1: 3,6 ROW 1 H1: 3,6,7,9 # reduction candidate for 3,6 H1: 3,6 # 22 pairs I1: 3,6,1,7 # reduction candidate for 3,6 I1: 3,6 => CTR * 3145928765268379419.7164.3.2..419357751326489493785.2..49.71.6.17564..9..32958714 I1: 1,7 # 14 pairs * PAIR A1: 3,6 COL A A7: 3,6,8 # reduction candidate for 3,6 A7: 3,6 # 14 pairs A9: 3,6,8 # reduction candidate for 3,6 A9: 3,6 # 21 pairs * PAIR E3: 1,6 BLK 2 E1: 1,6,9 # reduction candidate for 1,6 E1: 1,6 => CTR * ..45.289752.739.4.9.7..4.3.2...97.58458326179793185426.49.71...175.4.9....295.714 E1: 9 # 13 pairs D2: 1,6,4,7,8 # reduction candidate for 1,6 D2: 1,6 # 23 pairs D3: 1,6,4,8 # reduction candidate for 1,6 D3: 1,6 # 16 pairs * PAIR E3: 1,6 ROW 3 B3: 1,6,3,8 # reduction candidate for 1,6 B3: 1,6 # 20 pairs B3: 3,8 # 14 pairs * PAIR F3: 4,8 BLK 2 D2: 4,8,1,6,7 # reduction candidate for 4,8 D2: 4,8 # 18 pairs F2: 4,8,7,9 # reduction candidate for 4,8 F2: 4,8 => CTR * 3645928..52.73....9.761.....96.273582..356.79753.89.2.649.71...175.43...832965714 F2: 7,9 # 13 pairs D3: 4,8,1,6 # reduction candidate for 4,8 D3: 4,8 # 18 pairs * PAIR I2: 1,6 BLK 3 I1: 1,6,3,7 # reduction candidate for 1,6 I1: 1,6 => CTR * ..459287.52..3794.9.7.64.3.2..41935.751326489493785.2..49.71.6.17564..9...295.714 I1: 3,7 # 15 pairs G2: 1,6,4,9 # reduction candidate for 1,6 G2: 1,6 # 25 pairs * PAIR I2: 1,6 ROW 2 C2: 1,6,8 # reduction candidate for 1,6 C2: 1,6 # 24 pairs D2: 1,6,4,7,8 # reduction candidate for 1,6 D2: 1,6 # 23 pairs * PAIR I2: 1,6 COL I I6: 1,6,7 # reduction candidate for 1,6 I6: 7 => CTR * ..459287.52..3....9.7.............5.7..326..94.3185627.49.71...175.4......295.714 I6: 1,6 # 18 pairs * PAIR G3: 2,5 COL G G7: 2,5,3,6 # reduction candidate for 2,5 G7: 3,6 # 16 pairs G7: 2,5 # 13 pairs * PAIR I3: 2,5 COL I I7: 2,5,3,6,8 # reduction candidate for 2,5 I7: 2,5 # 13 pairs I7: 3,6,8 # 11 pairs * PAIR A6: 4,7 BLK 4 A4: 4,7,2 # reduction candidate for 4,7 A4: 4,7 # 23 pairs A5: 4,7,2 # reduction candidate for 4,7 A5: 4,7 # 20 pairs * PAIR A6: 4,7 ROW 6 D6: 4,7,1 # reduction candidate for 4,7 D6: 1 => CTR * ..45.289752.739.419.7..4.3.2..497.58458326179793185426.49.71...175.4.9....295.714 D6: 4,7 # 20 pairs * PAIR G5: 1,4 BLK 6 G4: 1,4,3 # reduction candidate for 1,4 G4: 1,4 => CTR * ..459287.52..3....9.7....3........537..3264894.3185627.49.71.6.17564..9...295.714 G4: 3 # 12 pairs G6: 1,4,6 # reduction candidate for 1,4 G6: 1,4 # 18 pairs * PAIR G5: 1,4 COL G G2: 1,4,6,9 # reduction candidate for 1,4 G2: 1,4 # 16 pairs G2: 6,9 # 15 pairs * PAIR C8: 5,6 BLK 7 B9: 5,6,3 # reduction candidate for 5,6 B9: 3 # 19 pairs B9: 5,6 # 18 pairs * PAIR E9: 5,6 ROW 9 B9: 5,6,3 # reduction candidate for 5,6 B9: 3 # 19 pairs B9: 5,6 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190420-absurd-base-pr-000.dot * REASONING * DIS # I1: 3,6 => CTR => I1: 1,7 * DIS # E1: 1,6 => CTR => E1: 9 * DIS # F2: 4,8 => CTR => F2: 7,9 * DIS # I1: 1,6 => CTR => I1: 3,7 * DIS # I6: 7 => CTR => I6: 1,6 * DIS # D6: 1 => CTR => D6: 4,7 * DIS # G4: 1,4 => CTR => G4: 3 * CNT 7 HDP CHAINS / 41 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B6,C8,E3,E9,F3,F6,G3,G5,I2,I3) * ..45.28..52..3....9.7.............5....3.6..9..3.8..2..49.71...17..4......29..714 * PAIR A1: 3,6 BLK 1 B1: 3,6,1 # reduction candidate for 3,6 B1: 3,6 # 19 pairs B3: 3,6,1,8 # reduction candidate for 3,6 B3: 3,6 # 17 pairs * PAIR A1: 3,6 ROW 1 H1: 3,6,7,9 # reduction candidate for 3,6 H1: 3,6 # 22 pairs I1: 3,6,1,7 # reduction candidate for 3,6 I1: 3,6 => CTR * 3145928765268379419.7164.3.2..419357751326489493785.2..49.71.6.17564..9..32958714 * RESTART * PAIR A1: 3,6 ROW 1 H1: 3,6,7,9 # reduction candidate for 3,6 H1: 3,6 # 22 pairs H1: 7,9 # 16 pairs * PAIR A1: 3,6 COL A A7: 3,6,8 # reduction candidate for 3,6 A7: 3,6 # 16 pairs A9: 3,6,8 # reduction candidate for 3,6 A9: 3,6 # 24 pairs * PAIR RESTART * PAIR A1: 3,6 BLK 1 B1: 3,6,1 # reduction candidate for 3,6 B1: 3,6 # 19 pairs B3: 3,6,1,8 # reduction candidate for 3,6 B3: 3,6 # 21 pairs * PAIR A1: 3,6 ROW 1 H1: 3,6,7,9 # reduction candidate for 3,6 H1: 3,6 # 22 pairs H1: 7,9 # 16 pairs * PAIR A1: 3,6 COL A A7: 3,6,8 # reduction candidate for 3,6 A7: 3,6 # 16 pairs A9: 3,6,8 # reduction candidate for 3,6 A9: 3,6 # 24 pairs * PAIR E3: 1,6 BLK 2 E1: 1,6,9 # reduction candidate for 1,6 E1: 1,6 => CTR * ..45.289752.739.4.9.7..4.3.2...97.58458326179793185426.49.71...175.4.9....295.714 D2: 1,6,4,7,8 # reduction candidate for 1,6 D2: 1,6 # 25 pairs D3: 1,6,4,8 # reduction candidate for 1,6 D3: 1,6 # 18 pairs * PAIR E3: 1,6 ROW 3 B3: 1,6,3,8 # reduction candidate for 1,6 B3: 1,6 # 26 pairs B3: 3,8 # 16 pairs * PAIR F3: 4,8 BLK 2 D2: 4,8,1,6,7 # reduction candidate for 4,8 D2: 4,8 # 20 pairs F2: 4,8,7 # reduction candidate for 4,8 F2: 4,8 => CTR * 3645928..52.73....9.761.....96.273582..356.79753.89.2.649.71.83175843...832965714 D3: 4,8,1,6 # reduction candidate for 4,8 D3: 4,8 # 25 pairs * PAIR RESTART * PAIR F3: 4,8 BLK 2 D2: 4,8,1,6 # reduction candidate for 4,8 D2: 4,8 # 20 pairs D3: 4,8,1,6 # reduction candidate for 4,8 D3: 4,8 # 25 pairs * PAIR I2: 1,6 BLK 3 G2: 1,6,4,9 # reduction candidate for 1,6 G2: 1,6 => CTR * ..459283752.437.9.937..8.4..96..4.58.81356479453789.2..49.71...175.439....29..714 * PAIR I2: 1,6 ROW 2 C2: 1,6,8 # reduction candidate for 1,6 C2: 1,6 => CTR * .145928.7526837941987164.3..6...9358.58316479.93.85126.49.71...175.4..9.632958714 D2: 1,6,4 # reduction candidate for 1,6 D2: 1,6 # 25 pairs * RESTART * PAIR I2: 1,6 ROW 2 D2: 1,6,4 # reduction candidate for 1,6 D2: 4 => CTR * .14592837528437961937..8.4..96..4.58.81356479453789126349271.8.17.84..9.8.29..714 * PAIR RESTART * PAIR G3: 2,5 COL G G7: 2,5,3,6 # reduction candidate for 2,5 G7: 3,6 # 27 pairs G7: 2,5 # 26 pairs * PAIR I3: 2,5 COL I I7: 2,5,3,6,8 # reduction candidate for 2,5 I7: 2,5 # 28 pairs I7: 3,6,8 # 26 pairs * PAIR A6: 4,7 BLK 4 A4: 4,7,2 # reduction candidate for 4,7 A4: 4,7 => SOLVED * 314592867528637941967418235796124358281356479453789126649271583175843692832965714 * DURATION: 0:00:24.359808 START: 05:29:16.504282 END: 05:29:40.864090 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190420-absurd-base-pr-001.dot * REASONING * DIS # I1: 3,6 => CTR => I1: 1,7 * DIS I1: 1,7 # E1: 1,6 => CTR => E1: 9 * DIS I1: 1,7 + E1: 9 # F2: 4,8 => CTR => F2: 7 * DIS I1: 1,7 + E1: 9 + F2: 7 # G2: 1,6 => CTR => G2: 4,9 * DIS I1: 1,7 + E1: 9 + F2: 7 + G2: 4,9 # C2: 1,6 => CTR => C2: 8 * DIS I1: 1,7 + E1: 9 + F2: 7 + G2: 4,9 + C2: 8 # D2: 4 => CTR => D2: 1,6 * PRF I1: 1,7 + E1: 9 + F2: 7 + G2: 4,9 + C2: 8 + D2: 1,6 # A4: 4,7 => SOL * STA I1: 1,7 + E1: 9 + F2: 7 + G2: 4,9 + C2: 8 + D2: 1,6 + A4: 4,7 * CNT 7 HDP CHAINS / 34 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190420, absurd
Solution
position: 314592867528637941967418235796124358281356479453789126649271583175843692832965714 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 # B1: 3,6 => UNS * INC # B3: 3,6 => UNS * INC # H1: 3,6 => UNS * DIS # I1: 3,6 => CTR => I1: 1,7 * INC # I1: 1,7 => UNS * INC # A7: 3,6 => UNS * INC # A9: 3,6 => UNS * DIS # E1: 1,6 => CTR => E1: 9 * INC # E1: 9 => UNS * INC # D2: 1,6 => UNS * INC # D3: 1,6 => UNS * INC # B3: 1,6 => UNS * INC # B3: 3,8 => UNS * INC # D2: 4,8 => UNS * DIS # F2: 4,8 => CTR => F2: 7,9 * INC # F2: 7,9 => UNS * INC # D3: 4,8 => UNS * DIS # I1: 1,6 => CTR => I1: 3,7 * INC # I1: 3,7 => UNS * INC # G2: 1,6 => UNS * INC # C2: 1,6 => UNS * INC # D2: 1,6 => UNS * INC # I6: 1,6 => UNS * DIS # I6: 7 => CTR => I6: 1,6 * INC # G7: 2,5 => UNS * INC # G7: 3,6 => UNS * INC # I7: 2,5 => UNS * INC # I7: 3,6,8 => UNS * INC # A4: 4,7 => UNS * INC # A5: 4,7 => UNS * INC # D6: 4,7 => UNS * DIS # D6: 1 => CTR => D6: 4,7 * DIS # G4: 1,4 => CTR => G4: 3 * INC # G4: 3 => UNS * INC # G6: 1,4 => UNS * INC # G2: 1,4 => UNS * INC # G2: 6,9 => UNS * INC # B9: 5,6 => UNS * INC # B9: 3 => UNS * INC # B9: 5,6 => UNS * INC # B9: 3 => UNS * CNT 41 HDP CHAINS / 41 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 3,6 => UNS * INC # B3: 3,6 => UNS * INC # H1: 3,6 => UNS * DIS # I1: 3,6 => CTR => I1: 1,7 * INC I1: 1,7 # H1: 3,6 => UNS * INC I1: 1,7 # H1: 7,9 => UNS * INC I1: 1,7 # A7: 3,6 => UNS * INC I1: 1,7 # A9: 3,6 => UNS * INC I1: 1,7 # B1: 3,6 => UNS * INC I1: 1,7 # B3: 3,6 => UNS * INC I1: 1,7 # H1: 3,6 => UNS * INC I1: 1,7 # H1: 7,9 => UNS * INC I1: 1,7 # A7: 3,6 => UNS * INC I1: 1,7 # A9: 3,6 => UNS * DIS I1: 1,7 # E1: 1,6 => CTR => E1: 9 * INC I1: 1,7 + E1: 9 # D2: 1,6 => UNS * INC I1: 1,7 + E1: 9 # D3: 1,6 => UNS * INC I1: 1,7 + E1: 9 # B3: 1,6 => UNS * INC I1: 1,7 + E1: 9 # B3: 3,8 => UNS * INC I1: 1,7 + E1: 9 # D2: 4,8 => UNS * DIS I1: 1,7 + E1: 9 # F2: 4,8 => CTR => F2: 7 * INC I1: 1,7 + E1: 9 + F2: 7 # D3: 4,8 => UNS * INC I1: 1,7 + E1: 9 + F2: 7 # D2: 4,8 => UNS * INC I1: 1,7 + E1: 9 + F2: 7 # D3: 4,8 => UNS * DIS I1: 1,7 + E1: 9 + F2: 7 # G2: 1,6 => CTR => G2: 4,9 * DIS I1: 1,7 + E1: 9 + F2: 7 + G2: 4,9 # C2: 1,6 => CTR => C2: 8 * INC I1: 1,7 + E1: 9 + F2: 7 + G2: 4,9 + C2: 8 # D2: 1,6 => UNS * INC I1: 1,7 + E1: 9 + F2: 7 + G2: 4,9 + C2: 8 # D2: 1,6 => UNS * DIS I1: 1,7 + E1: 9 + F2: 7 + G2: 4,9 + C2: 8 # D2: 4 => CTR => D2: 1,6 * INC I1: 1,7 + E1: 9 + F2: 7 + G2: 4,9 + C2: 8 + D2: 1,6 # G7: 2,5 => UNS * INC I1: 1,7 + E1: 9 + F2: 7 + G2: 4,9 + C2: 8 + D2: 1,6 # G7: 3,6 => UNS * INC I1: 1,7 + E1: 9 + F2: 7 + G2: 4,9 + C2: 8 + D2: 1,6 # I7: 2,5 => UNS * INC I1: 1,7 + E1: 9 + F2: 7 + G2: 4,9 + C2: 8 + D2: 1,6 # I7: 3,6,8 => UNS * PRF I1: 1,7 + E1: 9 + F2: 7 + G2: 4,9 + C2: 8 + D2: 1,6 # A4: 4,7 => SOL * STA I1: 1,7 + E1: 9 + F2: 7 + G2: 4,9 + C2: 8 + D2: 1,6 + A4: 4,7 * CNT 34 HDP CHAINS / 34 HYP OPENED