Analysis of zz-www.sudokuoftheday.co.uk-20190401-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: 42.....963.....5.2..9..5...2.3.7............9.67.1.4.5...6....7..4..18....1..8.5. initial
Autosolve
position: 425.8..963.6...5.2..926534.2.3.7......8..6..9967812435..26..917..4..18.3..1..8.54 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B3: 1,8 => CTR => B3: 7 * PRF # D2: 4,9 => SOL * DIS # D2: 1 => CTR => D2: 4,9 * DIS # F2: 4,9 => CTR => F2: 7 * PRF # F2: 7 => SOL * DIS # B3: 1,8 => CTR => B3: 7 * DIS # B5: 1 => CTR => B5: 4,5 * DIS # D4: 9 => CTR => D4: 4,5 * DIS # F2: 4,9 => CTR => F2: 7 * PRF # F2: 7 => SOL * DIS # B7: 3 => CTR => B7: 5,8 * DIS # A8: 5 => CTR => A8: 6,7 * DIS # E7: 5 => CTR => E7: 3,4 * CNT 13 HDP CHAINS / 26 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B3: 1,8 => CTR => B3: 7 * PRF B3: 7 # D2: 4,9 => SOL * STA B3: 7 + D2: 4,9 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 42.....963.....5.2..9..5...2.3.7............9.67.1.4.5...6....7..4..18....1..8.5. | initial |
| 425.8..963.6...5.2..926534.2.3.7......8..6..9967812435..26..917..4..18.3..1..8.54 | autosolve |
| 425183796316497582879265341243579168158346279967812435582634917694751823731928654 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (20) B2: 1,8 D1: 1,3 F1: 3,7 E2: 4,9 G1: 1,7 H2: 7,8 I3: 1,8 B4: 4,5 A5: 1,5 F4: 4,9 G4: 1,6 H4: 6,8 I4: 1,8 G5: 2,7 H5: 2,7 A7: 5,8 A9: 6,7 F7: 3,4 H8: 2,6 G9: 2,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,D2: 1.. / D1 = 1 => 0 pairs (*) / D2 = 1 => 0 pairs (X) G1,I3: 1.. / G1 = 1 => 0 pairs (X) / I3 = 1 => 0 pairs (_) A5,B5: 1.. / A5 = 1 => 23 pairs (_) / B5 = 1 => 0 pairs (X) G4,I4: 1.. / G4 = 1 => 0 pairs (*) / I4 = 1 => 0 pairs (X) D1,G1: 1.. / D1 = 1 => 0 pairs (*) / G1 = 1 => 0 pairs (X) B2,D2: 1.. / B2 = 1 => 0 pairs (*) / D2 = 1 => 0 pairs (X) A3,A5: 1.. / A3 = 1 => 0 pairs (X) / A5 = 1 => 23 pairs (_) G1,G4: 1.. / G1 = 1 => 0 pairs (X) / G4 = 1 => 0 pairs (_) I3,I4: 1.. / I3 = 1 => 0 pairs (*) / I4 = 1 => 0 pairs (X) G5,H5: 2.. / G5 = 2 => 0 pairs (*) / H5 = 2 => 0 pairs (X) E8,E9: 2.. / E8 = 2 => 0 pairs (X) / E9 = 2 => 0 pairs (_) H8,G9: 2.. / H8 = 2 => 0 pairs (*) / G9 = 2 => 0 pairs (X) E8,H8: 2.. / E8 = 2 => 0 pairs (X) / H8 = 2 => 0 pairs (_) E9,G9: 2.. / E9 = 2 => 0 pairs (*) / G9 = 2 => 0 pairs (X) G5,G9: 2.. / G5 = 2 => 0 pairs (*) / G9 = 2 => 0 pairs (X) H5,H8: 2.. / H5 = 2 => 0 pairs (X) / H8 = 2 => 0 pairs (_) D1,F1: 3.. / D1 = 3 => 0 pairs (X) / F1 = 3 => 0 pairs (_) D5,E5: 3.. / D5 = 3 => 0 pairs (*) / E5 = 3 => 0 pairs (X) B7,B9: 3.. / B7 = 3 => 0 pairs (X) / B9 = 3 => 28 pairs (_) F1,F7: 3.. / F1 = 3 => 0 pairs (*) / F7 = 3 => 0 pairs (X) B4,B5: 4.. / B4 = 4 => 23 pairs (_) / B5 = 4 => 24 pairs (_) E7,F7: 4.. / E7 = 4 => 0 pairs (X) / F7 = 4 => 0 pairs (_) B4,D4: 5.. / B4 = 5 => 24 pairs (_) / D4 = 5 => 23 pairs (_) G4,H4: 6.. / G4 = 6 => 0 pairs (X) / H4 = 6 => 0 pairs (_) A8,A9: 6.. / A8 = 6 => 0 pairs (*) / A9 = 6 => 0 pairs (X) H8,G9: 6.. / H8 = 6 => 0 pairs (X) / G9 = 6 => 0 pairs (_) A8,H8: 6.. / A8 = 6 => 0 pairs (*) / H8 = 6 => 0 pairs (X) A9,G9: 6.. / A9 = 6 => 0 pairs (X) / G9 = 6 => 0 pairs (_) G4,G9: 6.. / G4 = 6 => 0 pairs (X) / G9 = 6 => 0 pairs (_) H4,H8: 6.. / H4 = 6 => 0 pairs (*) / H8 = 6 => 0 pairs (X) A3,B3: 7.. / A3 = 7 => 0 pairs (X) / B3 = 7 => 24 pairs (_) F1,F2: 7.. / F1 = 7 => 0 pairs (X) / F2 = 7 => 0 pairs (_) G1,H2: 7.. / G1 = 7 => 0 pairs (*) / H2 = 7 => 0 pairs (X) G5,H5: 7.. / G5 = 7 => 0 pairs (X) / H5 = 7 => 0 pairs (_) D8,D9: 7.. / D8 = 7 => 24 pairs (_) / D9 = 7 => 0 pairs (X) F1,G1: 7.. / F1 = 7 => 0 pairs (X) / G1 = 7 => 0 pairs (_) F2,H2: 7.. / F2 = 7 => 0 pairs (*) / H2 = 7 => 0 pairs (X) G1,G5: 7.. / G1 = 7 => 0 pairs (*) / G5 = 7 => 0 pairs (X) H2,H5: 7.. / H2 = 7 => 0 pairs (X) / H5 = 7 => 0 pairs (_) H2,I3: 8.. / H2 = 8 => 0 pairs (*) / I3 = 8 => 0 pairs (X) H4,I4: 8.. / H4 = 8 => 0 pairs (X) / I4 = 8 => 0 pairs (_) A7,B7: 8.. / A7 = 8 => 21 pairs (_) / B7 = 8 => 0 pairs (*) B2,H2: 8.. / B2 = 8 => 0 pairs (X) / H2 = 8 => 0 pairs (_) A3,A7: 8.. / A3 = 8 => 0 pairs (*) / A7 = 8 => 0 pairs (X) H2,H4: 8.. / H2 = 8 => 0 pairs (*) / H4 = 8 => 0 pairs (X) I3,I4: 8.. / I3 = 8 => 0 pairs (X) / I4 = 8 => 0 pairs (_) D4,F4: 9.. / D4 = 9 => 0 pairs (X) / F4 = 9 => 21 pairs (_) B8,B9: 9.. / B8 = 9 => 23 pairs (_) / B9 = 9 => 0 pairs (X) F2,F4: 9.. / F2 = 9 => 0 pairs (X) / F4 = 9 => 21 pairs (_) * DURATION: 0:01:02.196208 START: 04:58:37.136677 END: 04:59:39.332885 2019-05-01 * CP COUNT: (49) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A7,A9,B2,B4,D1,E2,F1,F4,F7,G1,G4,G5,G9,H2,H4,H5,H8,I3,I4) * 425.8..963.6...5.2..926534.2.3.7......8..6..9967812435..26..917..4..18.3..1..8.54 * PAIR B2: 1,8 BLK 1 A3: 1,8,7 # reduction candidate for 1,8 A3: 1,8 # 24 pairs B3: 1,8,7 # reduction candidate for 1,8 B3: 1,8 => CTR * 425.8..963.6...5.27.926534.2.3.7.6811.8..67299678124358326549175.4..18636.1..8254 B3: 7 # 24 pairs * PAIR E2: 4,9 BLK 2 D2: 4,9,1 # reduction candidate for 4,9 D2: 4,9 => SOLVED * 425183796316497582879265341243579168158346279967812435582634917694751823731928654 D2: 1 => CTR * 4253871963861..572..92653482.3.7.681..8.367299678124358.26.3917..4.218636317.8.54 F2: 4,9,7 # reduction candidate for 4,9 F2: 4,9 => CTR * 425387196386149572..92653482.3974681.485.67299678124358.26.3917..4.21863631798254 F2: 7 => SOLVED * 425183796316497582879265341243579168158346279967812435582634917694751823731928654 * PAIR I3: 1,8 ROW 3 A3: 1,8,7 # reduction candidate for 1,8 A3: 1,8 # 24 pairs B3: 1,8,7 # reduction candidate for 1,8 B3: 1,8 => CTR * 425.8..963.6...5.27.926534.2.3.7.6811.8..67299678124358326549175.4..18636.1..8254 B3: 7 # 24 pairs * PAIR B4: 4,5 BLK 4 B5: 4,5,1 # reduction candidate for 4,5 B5: 1 => CTR * 425.8..96386194572179265348243579.815184367299678124358.2643917..4..18.3..1..8.54 B5: 4,5 # 23 pairs * PAIR B4: 4,5 ROW 4 D4: 4,5,9 # reduction candidate for 4,5 D4: 9 => CTR * 425.8..963.6...5.2..926534.253974...148..6..9967812435..2643917..4..18.3.31798.54 D4: 4,5 # 21 pairs * PAIR A5: 1,5 BLK 4 B5: 1,5,4 # reduction candidate for 1,5 B5: 4 # 24 pairs B5: 1,5 # 23 pairs * PAIR F4: 4,9 BLK 5 D4: 4,9,5 # reduction candidate for 4,9 D4: 4,9 # 24 pairs D4: 5 # 23 pairs * PAIR F4: 4,9 COL F F2: 4,9,7 # reduction candidate for 4,9 F2: 4,9 => CTR * 425387196386149572..92653482.3974681.485.67299678124358.26.3917..4.21863631798254 F2: 7 => SOLVED * 425183796316497582879265341243579168158346279967812435582634917694751823731928654 * PAIR A7: 5,8 BLK 7 B7: 5,8,3 # reduction candidate for 5,8 B7: 3 => CTR * 425.837963.6..7582.892653412.3.791681.8..6279967812435832654917..4..18.3..1..8.54 B7: 5,8 # 28 pairs * PAIR A9: 6,7 BLK 7 A8: 6,7,5 # reduction candidate for 6,7 A8: 5 => CTR * 425.8..963.6...5.27.926534.2.3.7.6811.8..67299678124358326549175.4..18636.1..8254 A8: 6,7 # 24 pairs * PAIR F7: 3,4 BLK 8 E7: 3,4,5 # reduction candidate for 3,4 E7: 5 => CTR * 425.837963.6..7582..92653412.3.791681.8..62799678124358.2654917..4..18.3..1..8.54 E7: 3,4 # 28 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190401-absurd-base-pr-000.dot * REASONING * DIS # B3: 1,8 => CTR => B3: 7 * PRF # D2: 4,9 => SOL * DIS # D2: 1 => CTR => D2: 4,9 * DIS # F2: 4,9 => CTR => F2: 7 * PRF # F2: 7 => SOL * DIS # B3: 1,8 => CTR => B3: 7 * DIS # B5: 1 => CTR => B5: 4,5 * DIS # D4: 9 => CTR => D4: 4,5 * DIS # F2: 4,9 => CTR => F2: 7 * PRF # F2: 7 => SOL * DIS # B7: 3 => CTR => B7: 5,8 * DIS # A8: 5 => CTR => A8: 6,7 * DIS # E7: 5 => CTR => E7: 3,4 * CNT 13 HDP CHAINS / 26 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A7,A9,B2,B4,D1,E2,F1,F4,F7,G1,G4,G5,G9,H2,H4,H5,H8,I3,I4) * 425.8..963.6...5.2..926534.2.3.7......8..6..9967812435..26..917..4..18.3..1..8.54 * PAIR B2: 1,8 BLK 1 A3: 1,8,7 # reduction candidate for 1,8 A3: 1,8 # 24 pairs B3: 1,8,7 # reduction candidate for 1,8 B3: 1,8 => CTR * 425.8..963.6...5.27.926534.2.3.7.6811.8..67299678124358326549175.4..18636.1..8254 * RESTART * PAIR E2: 4,9 BLK 2 D2: 4,9,1 # reduction candidate for 4,9 D2: 4,9 => SOLVED * 425183796316497582879265341243579168158346279967812435582634917694751823731928654 * DURATION: 0:00:03.093298 START: 04:59:58.065802 END: 05:00:01.159100 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190401-absurd-base-pr-001.dot * REASONING * DIS # B3: 1,8 => CTR => B3: 7 * PRF B3: 7 # D2: 4,9 => SOL * STA B3: 7 + D2: 4,9 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190401, absurd
Solution
position: 425183796316497582879265341243579168158346279967812435582634917694751823731928654 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 # A3: 1,8 => UNS * DIS # B3: 1,8 => CTR => B3: 7 * INC # B3: 7 => UNS * PRF # D2: 4,9 => SOL * DIS # D2: 1 => CTR => D2: 4,9 * DIS # F2: 4,9 => CTR => F2: 7 * PRF # F2: 7 => SOL * INC # A3: 1,8 => UNS * DIS # B3: 1,8 => CTR => B3: 7 * INC # B3: 7 => UNS * INC # B5: 4,5 => UNS * DIS # B5: 1 => CTR => B5: 4,5 * INC # D4: 4,5 => UNS * DIS # D4: 9 => CTR => D4: 4,5 * INC # B5: 1,5 => UNS * INC # B5: 4 => UNS * INC # D4: 4,9 => UNS * INC # D4: 5 => UNS * DIS # F2: 4,9 => CTR => F2: 7 * PRF # F2: 7 => SOL * INC # B7: 5,8 => UNS * DIS # B7: 3 => CTR => B7: 5,8 * INC # A8: 6,7 => UNS * DIS # A8: 5 => CTR => A8: 6,7 * INC # E7: 3,4 => UNS * DIS # E7: 5 => CTR => E7: 3,4 * CNT 26 HDP CHAINS / 26 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A3: 1,8 => UNS * DIS # B3: 1,8 => CTR => B3: 7 * PRF B3: 7 # D2: 4,9 => SOL * STA B3: 7 + D2: 4,9 * CNT 3 HDP CHAINS / 3 HYP OPENED