Analysis of zz-www.sudokuoftheday.co.uk-20190404-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: 512.7...6.......4..3...8.......1.....64.8..2.1....6..5.96.3...8...9.........679.. initial
Autosolve
position: 512.7...66......4.43.6.8.......1.....64.8..2.1....6..5.96.3...8...9........8679.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F1: 9 => CTR => F1: 3,4 * DIS # H1: 3,8 => CTR => H1: 9 * DIS # G7: 2,7 => CTR => G7: 1,4,5 * CNT 3 HDP CHAINS / 29 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F1: 9 => CTR => F1: 3,4 * DIS F1: 3,4 # I9: 1 => CTR => I9: 2,3 * DIS F1: 3,4 + I9: 2,3 # B4: 5 => CTR => B4: 7,8 * PRF F1: 3,4 + I9: 2,3 + B4: 7,8 # C6: 7,8 => SOL * STA F1: 3,4 + I9: 2,3 + B4: 7,8 + C6: 7,8 * CNT 4 HDP CHAINS / 16 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 512.7...6.......4..3...8.......1.....64.8..2.1....6..5.96.3...8...9.........679.. | initial |
| 512.7...66......4.43.6.8.......1.....64.8..2.1....6..5.96.3...8...9........8679.. | autosolve |
| 512374896687159342439628571975213684364785129128496735796532418853941267241867953 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) B2: 7,8 C3: 7,9 D1: 3,4 G1: 3,8 A7: 2,7 A9: 2,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D2,F2: 1.. / D2 = 1 => 6 pairs (_) / F2 = 1 => 7 pairs (_) G5,I5: 1.. / G5 = 1 => 6 pairs (_) / I5 = 1 => 7 pairs (_) C8,C9: 1.. / C8 = 1 => 8 pairs (_) / C9 = 1 => 7 pairs (_) D2,D7: 1.. / D2 = 1 => 6 pairs (_) / D7 = 1 => 7 pairs (_) D1,F1: 4.. / D1 = 4 => 6 pairs (_) / F1 = 4 => 15 pairs (_) B8,B9: 4.. / B8 = 4 => 0 pairs (X) / B9 = 4 => 6 pairs (_) B9,I9: 4.. / B9 = 4 => 6 pairs (_) / I9 = 4 => 0 pairs (X) E6,E8: 4.. / E6 = 4 => 0 pairs (X) / E8 = 4 => 15 pairs (_) B4,C4: 5.. / B4 = 5 => 10 pairs (_) / C4 = 5 => 9 pairs (_) D5,F5: 5.. / D5 = 5 => 7 pairs (_) / F5 = 5 => 10 pairs (_) G4,H4: 6.. / G4 = 6 => 6 pairs (_) / H4 = 6 => 6 pairs (_) G8,H8: 6.. / G8 = 6 => 6 pairs (_) / H8 = 6 => 6 pairs (_) G4,G8: 6.. / G4 = 6 => 6 pairs (_) / G8 = 6 => 6 pairs (_) H4,H8: 6.. / H4 = 6 => 6 pairs (_) / H8 = 6 => 6 pairs (_) B2,C2: 8.. / B2 = 8 => 8 pairs (_) / C2 = 8 => 7 pairs (_) G1,H1: 8.. / G1 = 8 => 6 pairs (_) / H1 = 8 => 0 pairs (X) A4,A8: 8.. / A4 = 8 => 11 pairs (_) / A8 = 8 => 6 pairs (_) C2,C3: 9.. / C2 = 9 => 7 pairs (_) / C3 = 9 => 7 pairs (_) A4,A5: 9.. / A4 = 9 => 8 pairs (_) / A5 = 9 => 7 pairs (_) F1,H1: 9.. / F1 = 9 => 0 pairs (X) / H1 = 9 => 15 pairs (_) E6,H6: 9.. / E6 = 9 => 15 pairs (_) / H6 = 9 => 0 pairs (X) * DURATION: 0:00:16.552530 START: 05:03:44.355224 END: 05:04:00.907754 2019-05-01 * CP COUNT: (21) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A9,B2,C3,D1,G1) * 512.7...66......4.43.6.8.......1.....64.8..2.1....6..5.96.3...8...9........8679.. * PAIR B2: 7,8 BLK 1 C2: 7,8,9 # reduction candidate for 7,8 C2: 9 # 7 pairs C2: 7,8 # 7 pairs * PAIR B2: 7,8 COL B B4: 7,8,2,5 # reduction candidate for 7,8 B4: 7,8 # 11 pairs B6: 7,8,2 # reduction candidate for 7,8 B6: 7,8 # 8 pairs B8: 7,8,2,4,5 # reduction candidate for 7,8 B8: 7,8 # 11 pairs * PAIR C3: 7,9 BLK 1 C2: 7,9,8 # reduction candidate for 7,9 C2: 7,9 # 8 pairs C2: 8 # 7 pairs * PAIR C3: 7,9 ROW 3 H3: 7,9,1,5 # reduction candidate for 7,9 H3: 7,9 # 9 pairs I3: 7,9,1,2 # reduction candidate for 7,9 I3: 7,9 # 9 pairs * PAIR D1: 3,4 BLK 2 F1: 3,4,9 # reduction candidate for 3,4 F1: 9 => CTR * 512479..66......4.43.6.8.......1.....64.8..2.1...964.5.96.34..8...9........8679.. F1: 3,4 # 15 pairs * PAIR D1: 3,4 COL D D4: 3,4,2,7 # reduction candidate for 3,4 D4: 3,4 # 9 pairs D6: 3,4,2,7 # reduction candidate for 3,4 D6: 3,4 # 9 pairs * PAIR G1: 3,8 BLK 3 H1: 3,8,9 # reduction candidate for 3,8 H1: 3,8 => CTR * 512479..66......4.43.6.8.......14....64.8..2.1...964.5.96.3...8...94.....4.8679.. H1: 9 # 15 pairs * PAIR G1: 3,8 COL G G4: 3,8,4,6,7 # reduction candidate for 3,8 G4: 3,8 # 9 pairs G6: 3,8,4,7 # reduction candidate for 3,8 G6: 3,8 # 8 pairs * PAIR A7: 2,7 BLK 7 A8: 2,7,3,8 # reduction candidate for 2,7 A8: 2,7 # 12 pairs B8: 2,7,4,5,8 # reduction candidate for 2,7 B8: 2,7 # 10 pairs * PAIR A7: 2,7 ROW 7 G7: 2,7,1,4,5 # reduction candidate for 2,7 G7: 2,7 => CTR * 512.79..66......4.43.6.8...9...1.....64.8..2.1...46.95.96.34..88..9........8679.. G7: 1,4,5 # 6 pairs * PAIR A7: 2,7 COL A A4: 2,7,3,8,9 # reduction candidate for 2,7 A4: 2,7 # 11 pairs A4: 3,8,9 # 7 pairs * PAIR A9: 2,3 BLK 7 A8: 2,3,7,8 # reduction candidate for 2,3 A8: 2,3 # 12 pairs A8: 7,8 # 7 pairs * PAIR A9: 2,3 ROW 9 I9: 2,3,1,4 # reduction candidate for 2,3 I9: 2,3 # 9 pairs I9: 1,4 # 9 pairs * PAIR A9: 2,3 COL A A4: 2,3,7,8,9 # reduction candidate for 2,3 A4: 2,3 # 8 pairs A4: 7,8,9 # 7 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190404-absurd-base-pr-000.dot * REASONING * DIS # F1: 9 => CTR => F1: 3,4 * DIS # H1: 3,8 => CTR => H1: 9 * DIS # G7: 2,7 => CTR => G7: 1,4,5 * CNT 3 HDP CHAINS / 29 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A9,B2,C3,D1,G1) * 512.7...66......4.43.6.8.......1.....64.8..2.1....6..5.96.3...8...9........8679.. * PAIR B2: 7,8 BLK 1 C2: 7,8,9 # reduction candidate for 7,8 C2: 9 # 7 pairs C2: 7,8 # 7 pairs * PAIR B2: 7,8 COL B B4: 7,8,2,5 # reduction candidate for 7,8 B4: 7,8 # 11 pairs B6: 7,8,2 # reduction candidate for 7,8 B6: 7,8 # 8 pairs B8: 7,8,2,4,5 # reduction candidate for 7,8 B8: 7,8 # 11 pairs * PAIR C3: 7,9 BLK 1 C2: 7,9,8 # reduction candidate for 7,9 C2: 7,9 # 8 pairs C2: 8 # 7 pairs * PAIR C3: 7,9 ROW 3 H3: 7,9,1,5 # reduction candidate for 7,9 H3: 7,9 # 9 pairs I3: 7,9,1,2 # reduction candidate for 7,9 I3: 7,9 # 9 pairs * PAIR D1: 3,4 BLK 2 F1: 3,4,9 # reduction candidate for 3,4 F1: 9 => CTR * 512479..66......4.43.6.8.......1.....64.8..2.1...964.5.96.34..8...9........8679.. * PAIR A9: 2,3 ROW 9 I9: 2,3,1 # reduction candidate for 2,3 I9: 1 => CTR * 5123748966..1.9.4.4396.8.1.9...1...436478512912.496..579653.4.88..94....24.8679.1 * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A5,A7,A9,B2,B8,C2,C9,D4,D5,D7,E2,E3,F4,F5,G3,G6,H3,H6,H8,H9,I2,I3,I8,I9) * 5123748966..1.9.4.4396.8...9...1...4.64.8.12912.496..5.96.3.4.88..94.....4.8679.. * PAIR B2: 7,8 COL B B4: 7,8,5 # reduction candidate for 7,8 B4: 5 => CTR * 5123748966871.9.4.4396.8...95..1...476458312912.4967.5296.3.4.88..94.....4.8679.. * PAIR RESTART * PAIR C2: 7,8 COL C C6: 7,8,3 # reduction candidate for 7,8 C6: 7,8 => SOLVED * 512374896687159342439628571975213684364785129128496735796532418853941267241867953 * DURATION: 0:00:09.999560 START: 05:04:13.961756 END: 05:04:23.961316 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190404-absurd-base-pr-001.dot * REASONING * DIS # F1: 9 => CTR => F1: 3,4 * DIS F1: 3,4 # I9: 1 => CTR => I9: 2,3 * DIS F1: 3,4 + I9: 2,3 # B4: 5 => CTR => B4: 7,8 * PRF F1: 3,4 + I9: 2,3 + B4: 7,8 # C6: 7,8 => SOL * STA F1: 3,4 + I9: 2,3 + B4: 7,8 + C6: 7,8 * CNT 4 HDP CHAINS / 16 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190404, absurd
Solution
position: 512374896687159342439628571975213684364785129128496735796532418853941267241867953 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 # C2: 7,8 => UNS * INC # C2: 9 => UNS * INC # B4: 7,8 => UNS * INC # B6: 7,8 => UNS * INC # B8: 7,8 => UNS * INC # C2: 7,9 => UNS * INC # C2: 8 => UNS * INC # H3: 7,9 => UNS * INC # I3: 7,9 => UNS * INC # F1: 3,4 => UNS * DIS # F1: 9 => CTR => F1: 3,4 * INC # D4: 3,4 => UNS * INC # D6: 3,4 => UNS * DIS # H1: 3,8 => CTR => H1: 9 * INC # H1: 9 => UNS * INC # G4: 3,8 => UNS * INC # G6: 3,8 => UNS * INC # A8: 2,7 => UNS * INC # B8: 2,7 => UNS * DIS # G7: 2,7 => CTR => G7: 1,4,5 * INC # G7: 1,4,5 => UNS * INC # A4: 2,7 => UNS * INC # A4: 3,8,9 => UNS * INC # A8: 2,3 => UNS * INC # A8: 7,8 => UNS * INC # I9: 2,3 => UNS * INC # I9: 1,4 => UNS * INC # A4: 2,3 => UNS * INC # A4: 7,8,9 => UNS * CNT 29 HDP CHAINS / 29 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C2: 7,8 => UNS * INC # C2: 9 => UNS * INC # B4: 7,8 => UNS * INC # B6: 7,8 => UNS * INC # B8: 7,8 => UNS * INC # C2: 7,9 => UNS * INC # C2: 8 => UNS * INC # H3: 7,9 => UNS * INC # I3: 7,9 => UNS * INC # F1: 3,4 => UNS * DIS # F1: 9 => CTR => F1: 3,4 * INC F1: 3,4 # I9: 2,3 => UNS * DIS F1: 3,4 # I9: 1 => CTR => I9: 2,3 * INC F1: 3,4 + I9: 2,3 # B4: 7,8 => UNS * DIS F1: 3,4 + I9: 2,3 # B4: 5 => CTR => B4: 7,8 * PRF F1: 3,4 + I9: 2,3 + B4: 7,8 # C6: 7,8 => SOL * STA F1: 3,4 + I9: 2,3 + B4: 7,8 + C6: 7,8 * CNT 16 HDP CHAINS / 16 HYP OPENED