Analysis of zz-www.sudokuoftheday.co.uk-20060811-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006
level: medium
position: 46.7....99.5..3............2....9..8.7.3..9..3...72.5.....1.4..8.4...5..6.3.24..1 initial
Autosolve
position: 46.7....99.5..3..7.3..9...52....9..8.7.3..9..3...72.5.....1.4.3814.375..6.3.24..1 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C3: 2,8 => CTR => C3: 1,7 * DIS # C3: 2,8 => CTR => C3: 1,7 * DIS # C6: 1,6 => CTR => C6: 8,9 * PRF # H5: 1,6 => SOL * DIS # C6: 1,6 => CTR => C6: 8,9 * PRF # D6: 1,6 => SOL * PRF # I5: 2 => SOL * PRF # B7: 5,9 => SOL * PRF # H8: 2 => SOL * PRF # I5: 2,6 => SOL * CNT 10 HDP CHAINS / 46 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C3: 2,8 => CTR => C3: 1,7 * DIS C3: 1,7 # D2: 2,8 => CTR => D2: 1,4,6 * PRF C3: 1,7 + D2: 1,4,6 # G2: 1,6 => SOL * STA C3: 1,7 + D2: 1,4,6 + G2: 1,6 * CNT 3 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 46.7....99.5..3............2....9..8.7.3..9..3...72.5.....1.4..8.4...5..6.3.24..1 | initial |
| 46.7....99.5..3..7.3..9...52....9..8.7.3..9..3...72.5.....1.4.3814.375..6.3.24..1 | autosolve |
| 468751239925483167137296845241569378576348912389172654792615483814937526653824791 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) B2: 2,8 A3: 1,7 E1: 5,8 B4: 4,5 C4: 1,6 A5: 1,5 G4: 3,7 H4: 3,7 G6: 1,6 I6: 4,6 A7: 5,7 B9: 5,9 D8: 6,9 I8: 2,6 G9: 7,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H5,G6: 1.. / H5 = 1 => 0 pairs (*) / G6 = 1 => 0 pairs (X) C4,D4: 1.. / C4 = 1 => 24 pairs (_) / D4 = 1 => 18 pairs (_) A3,A5: 1.. / A3 = 1 => 16 pairs (_) / A5 = 1 => 0 pairs (X) D2,D3: 2.. / D2 = 2 => 22 pairs (_) / D3 = 2 => 15 pairs (_) H5,I5: 2.. / H5 = 2 => 15 pairs (_) / I5 = 2 => 0 pairs (*) B7,C7: 2.. / B7 = 2 => 18 pairs (_) / C7 = 2 => 0 pairs (*) H8,I8: 2.. / H8 = 2 => 0 pairs (*) / I8 = 2 => 0 pairs (X) C1,G1: 2.. / C1 = 2 => 19 pairs (_) / G1 = 2 => 17 pairs (_) B2,B7: 2.. / B2 = 2 => 0 pairs (*) / B7 = 2 => 0 pairs (X) H5,H8: 2.. / H5 = 2 => 15 pairs (_) / H8 = 2 => 0 pairs (*) I5,I8: 2.. / I5 = 2 => 0 pairs (*) / I8 = 2 => 0 pairs (X) G1,H1: 3.. / G1 = 3 => 20 pairs (_) / H1 = 3 => 13 pairs (_) G4,H4: 3.. / G4 = 3 => 13 pairs (_) / H4 = 3 => 20 pairs (_) G1,G4: 3.. / G1 = 3 => 20 pairs (_) / G4 = 3 => 13 pairs (_) H1,H4: 3.. / H1 = 3 => 13 pairs (_) / H4 = 3 => 20 pairs (_) H2,H3: 4.. / H2 = 4 => 0 pairs (X) / H3 = 4 => 15 pairs (_) B4,B6: 4.. / B4 = 4 => 16 pairs (_) / B6 = 4 => 0 pairs (X) I5,I6: 4.. / I5 = 4 => 15 pairs (_) / I6 = 4 => 0 pairs (*) D3,H3: 4.. / D3 = 4 => 0 pairs (X) / H3 = 4 => 15 pairs (_) E5,I5: 4.. / E5 = 4 => 0 pairs (*) / I5 = 4 => 0 pairs (X) E1,F1: 5.. / E1 = 5 => 16 pairs (_) / F1 = 5 => 19 pairs (_) B4,A5: 5.. / B4 = 5 => 0 pairs (X) / A5 = 5 => 16 pairs (_) B9,D9: 5.. / B9 = 5 => 18 pairs (_) / D9 = 5 => 20 pairs (_) A5,A7: 5.. / A5 = 5 => 16 pairs (_) / A7 = 5 => 0 pairs (X) A3,C3: 7.. / A3 = 7 => 0 pairs (X) / C3 = 7 => 16 pairs (_) G4,H4: 7.. / G4 = 7 => 20 pairs (_) / H4 = 7 => 13 pairs (_) A7,C7: 7.. / A7 = 7 => 16 pairs (_) / C7 = 7 => 0 pairs (X) G9,H9: 7.. / G9 = 7 => 13 pairs (_) / H9 = 7 => 20 pairs (_) A3,A7: 7.. / A3 = 7 => 0 pairs (X) / A7 = 7 => 16 pairs (_) C3,C7: 7.. / C3 = 7 => 16 pairs (_) / C7 = 7 => 0 pairs (X) G4,G9: 7.. / G4 = 7 => 20 pairs (_) / G9 = 7 => 13 pairs (_) H4,H9: 7.. / H4 = 7 => 13 pairs (_) / H9 = 7 => 20 pairs (_) B2,B6: 8.. / B2 = 8 => 18 pairs (_) / B6 = 8 => 0 pairs (*) B6,C6: 9.. / B6 = 9 => 14 pairs (_) / C6 = 9 => 17 pairs (_) D8,H8: 9.. / D8 = 9 => 17 pairs (_) / H8 = 9 => 17 pairs (_) C6,C7: 9.. / C6 = 9 => 17 pairs (_) / C7 = 9 => 14 pairs (_) * DURATION: 0:00:43.720613 START: 01:42:55.119686 END: 01:43:38.840299 2019-05-01 * CP COUNT: (36) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,A7,B2,B4,B9,C4,D8,E1,G4,G6,G9,H4,I6,I8) * 46.7....99.5..3..7.3..9...52....9..8.7.3..9..3...72.5.....1.4.3814.375..6.3.24..1 * PAIR B2: 2,8 BLK 1 C1: 2,8,1 # reduction candidate for 2,8 C1: 2,8 # 18 pairs C3: 2,8,1,7 # reduction candidate for 2,8 C3: 2,8 => CTR * 461785239985263..7732.91..52561493781783..9.4349872156527.184.3814.375.2693524781 C3: 1,7 # 18 pairs * PAIR B2: 2,8 ROW 2 D2: 2,8,1,4,6 # reduction candidate for 2,8 D2: 2,8 # 21 pairs G2: 2,8,1,6 # reduction candidate for 2,8 G2: 2,8 # 18 pairs * PAIR A3: 1,7 BLK 1 C3: 1,7,2,8 # reduction candidate for 1,7 C3: 2,8 => CTR * 461785239985263..7732.91..52561493781783..9.4349872156527.184.3814.375.2693524781 C3: 1,7 # 18 pairs * PAIR E1: 5,8 BLK 2 F1: 5,8,1 # reduction candidate for 5,8 F1: 5,8 # 20 pairs F1: 1 # 19 pairs * PAIR E1: 5,8 COL E E5: 5,8,4,6 # reduction candidate for 5,8 E5: 5,8 # 18 pairs E5: 4,6 # 18 pairs * PAIR B4: 4,5 ROW 4 D4: 4,5,1,6 # reduction candidate for 4,5 D4: 4,5 # 27 pairs E4: 4,5,6 # reduction candidate for 4,5 E4: 4,5 # 18 pairs * PAIR C4: 1,6 BLK 4 C5: 1,6,8 # reduction candidate for 1,6 C5: 1,6 # 18 pairs C6: 1,6,8,9 # reduction candidate for 1,6 C6: 1,6 => CTR * 46.7....9985..3..7.37.9...524...9..857834.926396872154729518463814637592653924..1 C6: 8,9 # 16 pairs * PAIR C4: 1,6 ROW 4 D4: 1,6,4,5 # reduction candidate for 1,6 D4: 4,5 # 27 pairs D4: 1,6 # 18 pairs * PAIR A5: 1,5 ROW 5 F5: 1,5,6,8 # reduction candidate for 1,5 F5: 6,8 # 17 pairs F5: 1,5 # 17 pairs * PAIR G6: 1,6 BLK 6 H5: 1,6,2 # reduction candidate for 1,6 H5: 1,6 => SOLVED * 468751239925483167137296845241569378576348912389172654792615483814937526653824791 H5: 2 # 15 pairs * PAIR G6: 1,6 ROW 6 C6: 1,6,8,9 # reduction candidate for 1,6 C6: 1,6 => CTR * 46.7....9985..3..7.37.9...524...9..857834.926396872154729518463814637592653924..1 C6: 8,9 # 16 pairs D6: 1,6,4,8 # reduction candidate for 1,6 D6: 1,6 => SOLVED * 468751239925483167137296845241569378576348912389172654792615483814937526653824791 D6: 4,8 # 16 pairs * PAIR G6: 1,6 COL G G2: 1,6,2,8 # reduction candidate for 1,6 G2: 1,6 # 17 pairs G3: 1,6,2,8 # reduction candidate for 1,6 G3: 1,6 # 20 pairs * PAIR I6: 4,6 BLK 6 I5: 4,6,2 # reduction candidate for 4,6 I5: 2 => SOLVED * 468751239925483167137296845241569378576348912389172654792615483814937526653824791 I5: 4,6 # 15 pairs * PAIR I6: 4,6 ROW 6 D6: 4,6,1,8 # reduction candidate for 4,6 D6: 4,6 # 20 pairs D6: 1,8 # 16 pairs * PAIR B9: 5,9 BLK 7 B7: 5,9,2 # reduction candidate for 5,9 B7: 5,9 => SOLVED * 468751239925483167137296845241569378576348912389172654792615483814937526653824791 B7: 2 # 18 pairs * PAIR B9: 5,9 ROW 9 D9: 5,9,8 # reduction candidate for 5,9 D9: 8 # 18 pairs D9: 5,9 # 18 pairs * PAIR D8: 6,9 BLK 8 D7: 6,9,5,8 # reduction candidate for 6,9 D7: 6,9 # 18 pairs D7: 5,8 # 16 pairs * PAIR D8: 6,9 ROW 8 H8: 6,9,2 # reduction candidate for 6,9 H8: 2 => SOLVED * 468751239925483167137296845241569378576348912389172654792615483814937526653824791 H8: 6,9 # 15 pairs * PAIR I8: 2,6 BLK 9 H8: 2,6,9 # reduction candidate for 2,6 H8: 9 # 17 pairs H8: 2,6 # 17 pairs * PAIR I8: 2,6 COL I I5: 2,6,4 # reduction candidate for 2,6 I5: 2,6 => SOLVED * 468751239925483167137296845241569378576348912389172654792615483814937526653824791 I5: 4 # 15 pairs * PAIR G9: 7,8 BLK 9 H9: 7,8,9 # reduction candidate for 7,8 H9: 9 # 18 pairs H9: 7,8 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060811-absurd-base-pr-000.dot * REASONING * DIS # C3: 2,8 => CTR => C3: 1,7 * DIS # C3: 2,8 => CTR => C3: 1,7 * DIS # C6: 1,6 => CTR => C6: 8,9 * PRF # H5: 1,6 => SOL * DIS # C6: 1,6 => CTR => C6: 8,9 * PRF # D6: 1,6 => SOL * PRF # I5: 2 => SOL * PRF # B7: 5,9 => SOL * PRF # H8: 2 => SOL * PRF # I5: 2,6 => SOL * CNT 10 HDP CHAINS / 46 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,A7,B2,B4,B9,C4,D8,E1,G4,G6,G9,H4,I6,I8) * 46.7....99.5..3..7.3..9...52....9..8.7.3..9..3...72.5.....1.4.3814.375..6.3.24..1 * PAIR B2: 2,8 BLK 1 C1: 2,8,1 # reduction candidate for 2,8 C1: 2,8 # 18 pairs C3: 2,8,1,7 # reduction candidate for 2,8 C3: 2,8 => CTR * 461785239985263..7732.91..52561493781783..9.4349872156527.184.3814.375.2693524781 * RESTART * PAIR B2: 2,8 ROW 2 D2: 2,8,1,4,6 # reduction candidate for 2,8 D2: 2,8 => CTR * 46.751..99.5..3617.3..9..452...69..8.763859243...721565.7.1.4.3814.375.2693524..1 G2: 2,8,1,6 # reduction candidate for 2,8 G2: 2,8 # 22 pairs * RESTART * PAIR B2: 2,8 ROW 2 G2: 2,8,1,6 # reduction candidate for 2,8 G2: 1,6 => SOLVED * 468751239925483167137296845241569378576348912389172654792615483814937526653824791 * DURATION: 0:00:05.177607 START: 01:44:10.286785 END: 01:44:15.464392 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060811-absurd-base-pr-001.dot * REASONING * DIS # C3: 2,8 => CTR => C3: 1,7 * DIS C3: 1,7 # D2: 2,8 => CTR => D2: 1,4,6 * PRF C3: 1,7 + D2: 1,4,6 # G2: 1,6 => SOL * STA C3: 1,7 + D2: 1,4,6 + G2: 1,6 * CNT 3 HDP CHAINS / 6 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060811, absurd
Solution
position: 468751239925483167137296845241569378576348912389172654792615483814937526653824791 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 # C1: 2,8 => UNS * DIS # C3: 2,8 => CTR => C3: 1,7 * INC # C3: 1,7 => UNS * INC # D2: 2,8 => UNS * INC # G2: 2,8 => UNS * INC # C3: 1,7 => UNS * DIS # C3: 2,8 => CTR => C3: 1,7 * INC # F1: 5,8 => UNS * INC # F1: 1 => UNS * INC # E5: 5,8 => UNS * INC # E5: 4,6 => UNS * INC # D4: 4,5 => UNS * INC # E4: 4,5 => UNS * INC # C5: 1,6 => UNS * DIS # C6: 1,6 => CTR => C6: 8,9 * INC # C6: 8,9 => UNS * INC # D4: 1,6 => UNS * INC # D4: 4,5 => UNS * INC # F5: 1,5 => UNS * INC # F5: 6,8 => UNS * PRF # H5: 1,6 => SOL * INC # H5: 2 => UNS * DIS # C6: 1,6 => CTR => C6: 8,9 * INC # C6: 8,9 => UNS * PRF # D6: 1,6 => SOL * INC # D6: 4,8 => UNS * INC # G2: 1,6 => UNS * INC # G3: 1,6 => UNS * INC # I5: 4,6 => UNS * PRF # I5: 2 => SOL * INC # D6: 4,6 => UNS * INC # D6: 1,8 => UNS * PRF # B7: 5,9 => SOL * INC # B7: 2 => UNS * INC # D9: 5,9 => UNS * INC # D9: 8 => UNS * INC # D7: 6,9 => UNS * INC # D7: 5,8 => UNS * INC # H8: 6,9 => UNS * PRF # H8: 2 => SOL * INC # H8: 2,6 => UNS * INC # H8: 9 => UNS * PRF # I5: 2,6 => SOL * INC # I5: 4 => UNS * INC # H9: 7,8 => UNS * INC # H9: 9 => UNS * CNT 46 HDP CHAINS / 46 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 2,8 => UNS * DIS # C3: 2,8 => CTR => C3: 1,7 * DIS C3: 1,7 # D2: 2,8 => CTR => D2: 1,4,6 * INC C3: 1,7 + D2: 1,4,6 # G2: 2,8 => UNS * INC C3: 1,7 + D2: 1,4,6 # G2: 2,8 => UNS * PRF C3: 1,7 + D2: 1,4,6 # G2: 1,6 => SOL * STA C3: 1,7 + D2: 1,4,6 + G2: 1,6 * CNT 6 HDP CHAINS / 6 HYP OPENED