Analysis of zz-www.sudokuoftheday.co.uk-20060713-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006
level: medium
position: ..8.943......3...52....5.986..........4.2........4.27..56.82...1..6...32.3...1.5. initial
Autosolve
position: 5.8.943......3...52.3.65.9862..1......4.2........4.27..56382...1.7659.32.32471.5. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 4,7 => CTR => B2: 1,6,9 * DIS # G2: 4,7 => CTR => G2: 1,6 * DIS # D2: 1,2 => CTR => D2: 7,8 * DIS # F4: 7,8 => CTR => F4: 3 * DIS # D1: 1,7 => CTR => D1: 2 * DIS # D2: 1,7 => CTR => D2: 2,8 * DIS # G3: 1,7 => CTR => G3: 4 * DIS # D4: 5,9 => CTR => D4: 7,8 * DIS # A5: 3,8 => CTR => A5: 7 * PRF # F6: 3,8 => SOL * DIS # G7: 4,9 => CTR => G7: 1,7 * DIS # G7: 1,4 => CTR => G7: 7,9 * DIS # H2: 1,4 => CTR => H2: 2,6 * DIS # G9: 8 => CTR => G9: 6,9 * CNT 14 HDP CHAINS / 43 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B2: 4,7 => CTR => B2: 1,6,9 * DIS B2: 1,6,9 # B3: 1 => CTR => B3: 4,7 * DIS B2: 1,6,9 + B3: 4,7 # G2: 4,7 => CTR => G2: 1,6 * PRF B2: 1,6,9 + B3: 4,7 + G2: 1,6 # B2: 6 => SOL * STA B2: 1,6,9 + B3: 4,7 + G2: 1,6 + B2: 6 * CNT 4 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..8.943......3...52....5.986..........4.2........4.27..56.82...1..6...32.3...1.5. | initial |
| 5.8.943......3...52.3.65.9862..1......4.2........4.27..56382...1.7659.32.32471.5. | autosolve |
| 518294367469837125273165498625713984784926513391548276956382741147659832832471659 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) A2: 4,7 C2: 1,9 F2: 7,8 D3: 1,7 C4: 5,9 A6: 3,8 H4: 4,8 A7: 4,9 B8: 4,8 A9: 8,9 H7: 1,4 G8: 4,8 I9: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,C6: 1.. / C2 = 1 => 17 pairs (_) / C6 = 1 => 14 pairs (_) D1,D2: 2.. / D1 = 2 => 17 pairs (_) / D2 = 2 => 0 pairs (X) H1,H2: 2.. / H1 = 2 => 0 pairs (X) / H2 = 2 => 17 pairs (_) D1,H1: 2.. / D1 = 2 => 17 pairs (_) / H1 = 2 => 0 pairs (X) D2,H2: 2.. / D2 = 2 => 0 pairs (X) / H2 = 2 => 17 pairs (_) A5,A6: 3.. / A5 = 3 => 0 pairs (X) / A6 = 3 => 14 pairs (_) F4,I4: 3.. / F4 = 3 => 15 pairs (_) / I4 = 3 => 0 pairs (X) A7,B8: 4.. / A7 = 4 => 0 pairs (X) / B8 = 4 => 16 pairs (_) B3,G3: 4.. / B3 = 4 => 0 pairs (X) / G3 = 4 => 16 pairs (_) B8,G8: 4.. / B8 = 4 => 16 pairs (_) / G8 = 4 => 0 pairs (X) A2,A7: 4.. / A2 = 4 => 16 pairs (_) / A7 = 4 => 0 pairs (X) I4,I7: 4.. / I4 = 4 => 15 pairs (_) / I7 = 4 => 0 pairs (X) C4,C6: 5.. / C4 = 5 => 15 pairs (_) / C6 = 5 => 18 pairs (_) G4,G5: 5.. / G4 = 5 => 17 pairs (_) / G5 = 5 => 15 pairs (_) D5,G5: 5.. / D5 = 5 => 17 pairs (_) / G5 = 5 => 15 pairs (_) C6,D6: 5.. / C6 = 5 => 18 pairs (_) / D6 = 5 => 15 pairs (_) B1,B2: 6.. / B1 = 6 => 15 pairs (_) / B2 = 6 => 0 pairs (*) F5,F6: 6.. / F5 = 6 => 0 pairs (*) / F6 = 6 => 0 pairs (X) G9,I9: 6.. / G9 = 6 => 18 pairs (_) / I9 = 6 => 15 pairs (_) F6,I6: 6.. / F6 = 6 => 14 pairs (_) / I6 = 6 => 0 pairs (*) A5,B5: 7.. / A5 = 7 => 16 pairs (_) / B5 = 7 => 0 pairs (X) D4,F4: 7.. / D4 = 7 => 16 pairs (_) / F4 = 7 => 0 pairs (X) G7,I7: 7.. / G7 = 7 => 16 pairs (_) / I7 = 7 => 0 pairs (X) A2,A5: 7.. / A2 = 7 => 0 pairs (X) / A5 = 7 => 16 pairs (_) F2,F4: 7.. / F2 = 7 => 16 pairs (_) / F4 = 7 => 0 pairs (X) I1,I7: 7.. / I1 = 7 => 16 pairs (_) / I7 = 7 => 0 pairs (X) D2,F2: 8.. / D2 = 8 => 16 pairs (_) / F2 = 8 => 0 pairs (X) H4,H5: 8.. / H4 = 8 => 14 pairs (_) / H5 = 8 => 0 pairs (X) B8,A9: 8.. / B8 = 8 => 0 pairs (X) / A9 = 8 => 16 pairs (_) G8,G9: 8.. / G8 = 8 => 16 pairs (_) / G9 = 8 => 0 pairs (X) B8,G8: 8.. / B8 = 8 => 0 pairs (X) / G8 = 8 => 16 pairs (_) A9,G9: 8.. / A9 = 8 => 16 pairs (_) / G9 = 8 => 0 pairs (X) B2,C2: 9.. / B2 = 9 => 17 pairs (_) / C2 = 9 => 14 pairs (_) A7,A9: 9.. / A7 = 9 => 16 pairs (_) / A9 = 9 => 0 pairs (X) * DURATION: 0:00:40.080087 START: 00:39:18.004914 END: 00:39:58.085001 2019-05-01 * CP COUNT: (34) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,A7,A9,B8,C2,C4,D3,F2,G8,H4,H7,I9) * 5.8.943......3...52.3.65.9862..1......4.2........4.27..56382...1.7659.32.32471.5. * PAIR A2: 4,7 BLK 1 B2: 4,7,1,6,9 # reduction candidate for 4,7 B2: 4,7 => CTR * 568.943.7479.381652137654986258179437.4.2.5....154.276.56382..4147659832832471659 B2: 1,6,9 # 13 pairs B3: 4,7,1 # reduction candidate for 4,7 B3: 4,7 # 15 pairs * PAIR A2: 4,7 ROW 2 G2: 4,7,1,6 # reduction candidate for 4,7 G2: 4,7 => CTR * 5.8.943.7....38..52.3.65.9862..17..3..4.2........4.27..56382..4147659832832471.5. G2: 1,6 # 14 pairs * PAIR C2: 1,9 BLK 1 B2: 1,9,4,6,7 # reduction candidate for 1,9 B2: 1,9 # 17 pairs B2: 4,6,7 # 14 pairs * PAIR C2: 1,9 COL C C6: 1,9,5 # reduction candidate for 1,9 C6: 5 # 18 pairs C6: 1,9 # 15 pairs * PAIR F2: 7,8 BLK 2 D2: 7,8,1,2 # reduction candidate for 7,8 D2: 1,2 => CTR * 5.8.943.7479.38..5213765498625.179437.4.2358.....4.27..56382..4147659832832471.5. D2: 7,8 # 18 pairs * PAIR F2: 7,8 COL F F4: 7,8,3 # reduction candidate for 7,8 F4: 7,8 => CTR * 5.8.943.74...3.1.52.3.6549862..1..437.4.23.8.381546279956382714147659832832471956 F4: 3 # 15 pairs * PAIR D3: 1,7 BLK 2 D1: 1,7,2 # reduction candidate for 1,7 D1: 1,7 => CTR * 5.8.94327479238..5213765498625.179437.4.2358.....4.27..56382..4147659832832471.5. D1: 2 # 17 pairs D2: 1,7,2,8 # reduction candidate for 1,7 D2: 1,7 => CTR * 518294367469738125273165498625817943794523.8.38..4627.956382714147659832832471.5. D2: 2,8 # 14 pairs * PAIR D3: 1,7 ROW 3 B3: 1,7,4 # reduction candidate for 1,7 B3: 1,7 # 16 pairs G3: 1,7,4 # reduction candidate for 1,7 G3: 1,7 => CTR * 5.8.943..7...38.45243.65.9862..17.8...4.2........4.27.456382.1.187659432932471856 G3: 4 # 16 pairs * PAIR C4: 5,9 BLK 4 C6: 5,9,1 # reduction candidate for 5,9 C6: 5,9 # 17 pairs C6: 1 # 14 pairs * PAIR C4: 5,9 ROW 4 D4: 5,9,7,8 # reduction candidate for 5,9 D4: 5,9 => CTR * 5.8.943.74...38..52.3.6549862..17.837.4.23...3...4627.956382714147659832832471.5. D4: 7,8 # 16 pairs G4: 5,9,4 # reduction candidate for 5,9 G4: 5,9 # 18 pairs * PAIR A6: 3,8 BLK 4 A5: 3,8,7 # reduction candidate for 3,8 A5: 3,8 => CTR * 5.8.943..7...38..52.3.65.9862..17..3.74.2........4.27.456382.1.187659432932471856 A5: 7 # 16 pairs * PAIR A6: 3,8 ROW 6 F6: 3,8,6 # reduction candidate for 3,8 F6: 3,8 => SOLVED * 518294367469837125273165498625713984784926513391548276956382741147659832832471659 F6: 6 # 14 pairs * PAIR A7: 4,9 ROW 7 G7: 4,9,1,7 # reduction candidate for 4,9 G7: 4,9 => CTR * 5687943217..238.45243.65.9862..13.84..4.2..6.....4627.456382917187659432932471856 G7: 1,7 # 14 pairs I7: 4,9,1,7 # reduction candidate for 4,9 I7: 4,9 # 18 pairs * PAIR A9: 8,9 ROW 9 G9: 8,9,6 # reduction candidate for 8,9 G9: 6 # 18 pairs G9: 8,9 # 15 pairs * PAIR H7: 1,4 BLK 9 G7: 1,4,7,9 # reduction candidate for 1,4 G7: 1,4 => CTR * 5.8.943..4...376.5273.6549862..13.847.4.2...33...4.27.956382147147659832832471.5. G7: 7,9 # 14 pairs I7: 1,4,7,9 # reduction candidate for 1,4 I7: 1,4 # 19 pairs * PAIR H7: 1,4 COL H H2: 1,4,2,6 # reduction candidate for 1,4 H2: 1,4 => CTR * 5.8.943274792386152.3.65.9862..17..3..4.2..6.....4627..56382..4147659832832471.5. H2: 2,6 # 17 pairs * PAIR I9: 6,9 BLK 9 G9: 6,9,8 # reduction candidate for 6,9 G9: 8 => CTR * 5.8.9432.7..238.45243.65.9862..1..84..4.2........4627.456382.1.187659432932471856 G9: 6,9 # 16 pairs * PAIR I9: 6,9 COL I I5: 6,9,1,3 # reduction candidate for 6,9 I5: 6,9 # 18 pairs I6: 6,9,1,3 # reduction candidate for 6,9 I6: 6,9 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060713-absurd-base-pr-000.dot * REASONING * DIS # B2: 4,7 => CTR => B2: 1,6,9 * DIS # G2: 4,7 => CTR => G2: 1,6 * DIS # D2: 1,2 => CTR => D2: 7,8 * DIS # F4: 7,8 => CTR => F4: 3 * DIS # D1: 1,7 => CTR => D1: 2 * DIS # D2: 1,7 => CTR => D2: 2,8 * DIS # G3: 1,7 => CTR => G3: 4 * DIS # D4: 5,9 => CTR => D4: 7,8 * DIS # A5: 3,8 => CTR => A5: 7 * PRF # F6: 3,8 => SOL * DIS # G7: 4,9 => CTR => G7: 1,7 * DIS # G7: 1,4 => CTR => G7: 7,9 * DIS # H2: 1,4 => CTR => H2: 2,6 * DIS # G9: 8 => CTR => G9: 6,9 * CNT 14 HDP CHAINS / 43 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,A7,A9,B8,C2,C4,D3,F2,G8,H4,H7,I9) * 5.8.943......3...52.3.65.9862..1......4.2........4.27..56382...1.7659.32.32471.5. * PAIR A2: 4,7 BLK 1 B2: 4,7,1,6,9 # reduction candidate for 4,7 B2: 4,7 => CTR * 568.943.7479.381652137654986258179437.4.2.5....154.276.56382..4147659832832471659 B3: 4,7,1 # reduction candidate for 4,7 B3: 4,7 # 15 pairs * RESTART * PAIR A2: 4,7 BLK 1 B3: 4,7,1 # reduction candidate for 4,7 B3: 1 => CTR * 578.943614...3...521376549862..17..37.4.23...3.1546279956382..4147659832832471956 * PAIR A2: 4,7 ROW 2 G2: 4,7,1,6 # reduction candidate for 4,7 G2: 4,7 => CTR * 5.8.943.7....38..52.3.65.9862..17..3..4.2........4.27..56382..4147659832832471.5. * PAIR RESTART * PAIR C2: 1,9 BLK 1 B2: 1,9,6 # reduction candidate for 1,9 B2: 6 => SOLVED * 518294367469837125273165498625713984784926513391548276956382741147659832832471659 * DURATION: 0:00:06.465839 START: 00:40:25.489372 END: 00:40:31.955211 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060713-absurd-base-pr-001.dot * REASONING * DIS # B2: 4,7 => CTR => B2: 1,6,9 * DIS B2: 1,6,9 # B3: 1 => CTR => B3: 4,7 * DIS B2: 1,6,9 + B3: 4,7 # G2: 4,7 => CTR => G2: 1,6 * PRF B2: 1,6,9 + B3: 4,7 + G2: 1,6 # B2: 6 => SOL * STA B2: 1,6,9 + B3: 4,7 + G2: 1,6 + B2: 6 * CNT 4 HDP CHAINS / 7 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060713, absurd
Solution
position: 518294367469837125273165498625713984784926513391548276956382741147659832832471659 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:
* DIS # B2: 4,7 => CTR => B2: 1,6,9 * INC # B2: 1,6,9 => UNS * INC # B3: 4,7 => UNS * DIS # G2: 4,7 => CTR => G2: 1,6 * INC # G2: 1,6 => UNS * INC # B2: 1,9 => UNS * INC # B2: 4,6,7 => UNS * INC # C6: 1,9 => UNS * INC # C6: 5 => UNS * INC # D2: 7,8 => UNS * DIS # D2: 1,2 => CTR => D2: 7,8 * DIS # F4: 7,8 => CTR => F4: 3 * INC # F4: 3 => UNS * DIS # D1: 1,7 => CTR => D1: 2 * INC # D1: 2 => UNS * DIS # D2: 1,7 => CTR => D2: 2,8 * INC # D2: 2,8 => UNS * INC # B3: 1,7 => UNS * DIS # G3: 1,7 => CTR => G3: 4 * INC # G3: 4 => UNS * INC # C6: 5,9 => UNS * INC # C6: 1 => UNS * DIS # D4: 5,9 => CTR => D4: 7,8 * INC # D4: 7,8 => UNS * INC # G4: 5,9 => UNS * DIS # A5: 3,8 => CTR => A5: 7 * INC # A5: 7 => UNS * PRF # F6: 3,8 => SOL * INC # F6: 6 => UNS * DIS # G7: 4,9 => CTR => G7: 1,7 * INC # G7: 1,7 => UNS * INC # I7: 4,9 => UNS * INC # G9: 8,9 => UNS * INC # G9: 6 => UNS * DIS # G7: 1,4 => CTR => G7: 7,9 * INC # G7: 7,9 => UNS * INC # I7: 1,4 => UNS * DIS # H2: 1,4 => CTR => H2: 2,6 * INC # H2: 2,6 => UNS * INC # G9: 6,9 => UNS * DIS # G9: 8 => CTR => G9: 6,9 * INC # I5: 6,9 => UNS * INC # I6: 6,9 => UNS * CNT 43 HDP CHAINS / 43 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B2: 4,7 => CTR => B2: 1,6,9 * INC B2: 1,6,9 # B3: 4,7 => UNS * INC B2: 1,6,9 # B3: 4,7 => UNS * DIS B2: 1,6,9 # B3: 1 => CTR => B3: 4,7 * DIS B2: 1,6,9 + B3: 4,7 # G2: 4,7 => CTR => G2: 1,6 * INC B2: 1,6,9 + B3: 4,7 + G2: 1,6 # B2: 1,9 => UNS * PRF B2: 1,6,9 + B3: 4,7 + G2: 1,6 # B2: 6 => SOL * STA B2: 1,6,9 + B3: 4,7 + G2: 1,6 + B2: 6 * CNT 7 HDP CHAINS / 7 HYP OPENED