Analysis of zz-www.sudokuoftheday.co.uk-20190212-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: ..85...9....81.....5...2....7.428....2...973.....7......7..4.8..63.8.4.7..1...65. initial
Autosolve
position: 7.854..9.9.281.57..5.792...37.428....2...973....37.....97..4.8..6398.4.7..1237659 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A3: 4,6 => SOL * DIS # A3: 1 => CTR => A3: 4,6 * PRF # C6: 4,6 => SOL * DIS # I1: 1,2 => CTR => I1: 6 * PRF # I1: 6 => SOL * PRF # A3: 6 => SOL * DIS # A6: 4,8 => CTR => A6: 1,6 * PRF # B6: 4,8 => SOL * DIS # B6: 1 => CTR => B6: 4,8 * CNT 9 HDP CHAINS / 21 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A3: 4,6 => SOL * STA A3: 4,6 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..85...9....81.....5...2....7.428....2...973.....7......7..4.8..63.8.4.7..1...65. | initial |
| 7.854..9.9.281.57..5.792...37.428....2...973....37.....97..4.8..6398.4.7..1237659 | autosolve |
| 718543296932816574654792813379428165425169738186375942297654381563981427841237659 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (25) B1: 1,3 B2: 3,4 C3: 4,6 F1: 3,6 F2: 3,6 G1: 1,2 I2: 4,6 G3: 3,8 H3: 1,4 I3: 3,8 C5: 4,5 D5: 1,6 E5: 5,6 F6: 1,5 G4: 1,9 H4: 1,6 I4: 1,5 A7: 2,5 A8: 2,5 A9: 4,8 B9: 4,8 D7: 1,6 E7: 5,6 F8: 1,5 H8: 1,2 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,A3: 1.. / B1 = 1 => 0 pairs (*) / A3 = 1 => 0 pairs (X) D5,F6: 1.. / D5 = 1 => 22 pairs (_) / F6 = 1 => 0 pairs (X) D7,F8: 1.. / D7 = 1 => 0 pairs (X) / F8 = 1 => 22 pairs (_) A3,H3: 1.. / A3 = 1 => 0 pairs (X) / H3 = 1 => 0 pairs (_) A5,D5: 1.. / A5 = 1 => 0 pairs (X) / D5 = 1 => 22 pairs (_) F8,H8: 1.. / F8 = 1 => 22 pairs (_) / H8 = 1 => 0 pairs (X) B1,B6: 1.. / B1 = 1 => 0 pairs (*) / B6 = 1 => 0 pairs (X) D5,D7: 1.. / D5 = 1 => 22 pairs (_) / D7 = 1 => 0 pairs (X) F6,F8: 1.. / F6 = 1 => 0 pairs (X) / F8 = 1 => 22 pairs (_) G1,I1: 2.. / G1 = 2 => 27 pairs (_) / I1 = 2 => 0 pairs (X) A7,A8: 2.. / A7 = 2 => 22 pairs (_) / A8 = 2 => 0 pairs (X) A8,H8: 2.. / A8 = 2 => 0 pairs (X) / H8 = 2 => 22 pairs (_) H6,H8: 2.. / H6 = 2 => 0 pairs (X) / H8 = 2 => 22 pairs (_) B1,B2: 3.. / B1 = 3 => 0 pairs (X) / B2 = 3 => 0 pairs (_) F1,F2: 3.. / F1 = 3 => 0 pairs (*) / F2 = 3 => 0 pairs (X) G3,I3: 3.. / G3 = 3 => 17 pairs (_) / I3 = 3 => 25 pairs (_) G7,I7: 3.. / G7 = 3 => 25 pairs (_) / I7 = 3 => 17 pairs (_) B1,F1: 3.. / B1 = 3 => 0 pairs (X) / F1 = 3 => 0 pairs (_) B2,F2: 3.. / B2 = 3 => 0 pairs (*) / F2 = 3 => 0 pairs (X) G3,G7: 3.. / G3 = 3 => 17 pairs (_) / G7 = 3 => 25 pairs (_) I3,I7: 3.. / I3 = 3 => 25 pairs (_) / I7 = 3 => 17 pairs (_) I2,H3: 4.. / I2 = 4 => 0 pairs (*) / H3 = 4 => 0 pairs (X) A9,B9: 4.. / A9 = 4 => 26 pairs (_) / B9 = 4 => 0 pairs (*) B2,I2: 4.. / B2 = 4 => 0 pairs (X) / I2 = 4 => 0 pairs (_) H3,H6: 4.. / H3 = 4 => 0 pairs (X) / H6 = 4 => 0 pairs (_) E5,F6: 5.. / E5 = 5 => 0 pairs (X) / F6 = 5 => 22 pairs (_) A7,A8: 5.. / A7 = 5 => 0 pairs (X) / A8 = 5 => 22 pairs (_) E7,F8: 5.. / E7 = 5 => 22 pairs (_) / F8 = 5 => 0 pairs (X) C4,I4: 5.. / C4 = 5 => 28 pairs (_) / I4 = 5 => 26 pairs (_) A7,E7: 5.. / A7 = 5 => 0 pairs (X) / E7 = 5 => 22 pairs (_) A8,F8: 5.. / A8 = 5 => 22 pairs (_) / F8 = 5 => 0 pairs (X) E5,E7: 5.. / E5 = 5 => 0 pairs (X) / E7 = 5 => 22 pairs (_) F6,F8: 5.. / F6 = 5 => 22 pairs (_) / F8 = 5 => 0 pairs (X) A3,C3: 6.. / A3 = 6 => 0 pairs (*) / C3 = 6 => 0 pairs (X) F1,F2: 6.. / F1 = 6 => 0 pairs (X) / F2 = 6 => 0 pairs (_) I1,I2: 6.. / I1 = 6 => 0 pairs (*) / I2 = 6 => 0 pairs (X) D5,E5: 6.. / D5 = 6 => 0 pairs (X) / E5 = 6 => 22 pairs (_) H4,H6: 6.. / H4 = 6 => 26 pairs (_) / H6 = 6 => 0 pairs (X) D7,E7: 6.. / D7 = 6 => 22 pairs (_) / E7 = 6 => 0 pairs (X) F1,I1: 6.. / F1 = 6 => 0 pairs (X) / I1 = 6 => 0 pairs (_) F2,I2: 6.. / F2 = 6 => 0 pairs (*) / I2 = 6 => 0 pairs (X) C4,H4: 6.. / C4 = 6 => 0 pairs (X) / H4 = 6 => 26 pairs (_) A3,A6: 6.. / A3 = 6 => 0 pairs (*) / A6 = 6 => 0 pairs (X) D5,D7: 6.. / D5 = 6 => 0 pairs (X) / D7 = 6 => 22 pairs (_) E5,E7: 6.. / E5 = 6 => 22 pairs (_) / E7 = 6 => 0 pairs (X) G3,I3: 8.. / G3 = 8 => 25 pairs (_) / I3 = 8 => 17 pairs (_) A9,B9: 8.. / A9 = 8 => 0 pairs (*) / B9 = 8 => 0 pairs (X) A5,I5: 8.. / A5 = 8 => 23 pairs (_) / I5 = 8 => 27 pairs (_) B6,B9: 8.. / B6 = 8 => 0 pairs (*) / B9 = 8 => 0 pairs (X) G3,G6: 8.. / G3 = 8 => 25 pairs (_) / G6 = 8 => 17 pairs (_) C4,C6: 9.. / C4 = 9 => 23 pairs (_) / C6 = 9 => 26 pairs (_) G4,G6: 9.. / G4 = 9 => 26 pairs (_) / G6 = 9 => 23 pairs (_) C4,G4: 9.. / C4 = 9 => 23 pairs (_) / G4 = 9 => 26 pairs (_) C6,G6: 9.. / C6 = 9 => 26 pairs (_) / G6 = 9 => 23 pairs (_) * DURATION: 0:01:13.101747 START: 03:40:30.118935 END: 03:41:43.220682 2019-05-01 * CP COUNT: (54) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A8,A9,B1,B2,B9,C3,C5,D5,D7,E5,E7,F1,F2,F6,F8,G1,G3,G4,H3,H4,H8,I2,I3,I4) * 7.854..9.9.281.57..5.792...37.428....2...973....37.....97..4.8..6398.4.7..1237659 * PAIR C3: 4,6 BLK 1 A3: 4,6,1 # reduction candidate for 4,6 A3: 4,6 => SOLVED * 718543296932816574654792813379428165425169738186375942297654381563981427841237659 A3: 1 => CTR * 7.854..9.9.281.57.156792.4.37.428.6..2.16973.61.375.2..97654.8..6398.4.7..1237659 * PAIR C3: 4,6 COL C C6: 4,6,5,9 # reduction candidate for 4,6 C6: 4,6 => SOLVED * 718543296932816574654792813379428165425169738186375942297654381563981427841237659 C6: 5,9 # 26 pairs * PAIR G1: 1,2 BLK 3 I1: 1,2,6 # reduction candidate for 1,2 I1: 1,2 => CTR * 738546.9.942813576156792.4.37.428.6..2.16973.61.375.2..97654.8..6398.4.7..1237659 I1: 6 => SOLVED * 718543296932816574654792813379428165425169738186375942297654381563981427841237659 * PAIR G1: 1,2 COL G G7: 1,2,3 # reduction candidate for 1,2 G7: 3 # 25 pairs G7: 1,2 # 17 pairs * PAIR H3: 1,4 ROW 3 A3: 1,4,6 # reduction candidate for 1,4 A3: 6 => SOLVED * 718543296932816574654792813379428165425169738186375942297654381563981427841237659 A3: 1,4 # 28 pairs * PAIR C5: 4,5 BLK 4 C6: 4,5,6,9 # reduction candidate for 4,5 C6: 6,9 # 26 pairs C6: 4,5 # 26 pairs * PAIR C5: 4,5 ROW 5 I5: 4,5,8 # reduction candidate for 4,5 I5: 8 # 27 pairs I5: 4,5 # 23 pairs * PAIR A9: 4,8 COL A A5: 4,8,1 # reduction candidate for 4,8 A5: 4,8 # 22 pairs A6: 4,8,1,6 # reduction candidate for 4,8 A6: 4,8 => CTR * 7.854..9.9.281.57.654792.1.37.428.6.125..973....37.....97..4.8..6398.4.7..1237659 A6: 1,6 # 26 pairs * PAIR B9: 4,8 COL B B6: 4,8,1 # reduction candidate for 4,8 B6: 4,8 => SOLVED * 718543296932816574654792813379428165425169738186375942297654381563981427841237659 B6: 1 => CTR * 738546.9.942813576156792.4.37.428....2...973..1.375....97.54.8.563981427.81237659 * PAIR H8: 1,2 BLK 9 G7: 1,2,3 # reduction candidate for 1,2 G7: 1,2 # 17 pairs I7: 1,2,3 # reduction candidate for 1,2 I7: 1,2 # 25 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190212-absurd-base-pr-000.dot * REASONING * PRF # A3: 4,6 => SOL * DIS # A3: 1 => CTR => A3: 4,6 * PRF # C6: 4,6 => SOL * DIS # I1: 1,2 => CTR => I1: 6 * PRF # I1: 6 => SOL * PRF # A3: 6 => SOL * DIS # A6: 4,8 => CTR => A6: 1,6 * PRF # B6: 4,8 => SOL * DIS # B6: 1 => CTR => B6: 4,8 * CNT 9 HDP CHAINS / 21 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A8,A9,B1,B2,B9,C3,C5,D5,D7,E5,E7,F1,F2,F6,F8,G1,G3,G4,H3,H4,H8,I2,I3,I4) * 7.854..9.9.281.57..5.792...37.428....2...973....37.....97..4.8..6398.4.7..1237659 * PAIR C3: 4,6 BLK 1 A3: 4,6,1 # reduction candidate for 4,6 A3: 4,6 => SOLVED * 718543296932816574654792813379428165425169738186375942297654381563981427841237659 * DURATION: 0:00:01.673786 START: 03:42:00.809520 END: 03:42:02.483306 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190212-absurd-base-pr-001.dot * REASONING * PRF # A3: 4,6 => SOL * STA A3: 4,6 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190212, absurd
Solution
position: 718543296932816574654792813379428165425169738186375942297654381563981427841237659 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: 4,6 => SOL * DIS # A3: 1 => CTR => A3: 4,6 * PRF # C6: 4,6 => SOL * INC # C6: 5,9 => UNS * DIS # I1: 1,2 => CTR => I1: 6 * PRF # I1: 6 => SOL * INC # G7: 1,2 => UNS * INC # G7: 3 => UNS * INC # A3: 1,4 => UNS * PRF # A3: 6 => SOL * INC # C6: 4,5 => UNS * INC # C6: 6,9 => UNS * INC # I5: 4,5 => UNS * INC # I5: 8 => UNS * INC # A5: 4,8 => UNS * DIS # A6: 4,8 => CTR => A6: 1,6 * INC # A6: 1,6 => UNS * PRF # B6: 4,8 => SOL * DIS # B6: 1 => CTR => B6: 4,8 * INC # G7: 1,2 => UNS * INC # I7: 1,2 => UNS * CNT 21 HDP CHAINS / 21 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A3: 4,6 => SOL * STA A3: 4,6 * CNT 1 HDP CHAINS / 1 HYP OPENED