Analysis of zz-www.sudokuoftheday.co.uk-20060526-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006
level: medium
position: .6...9.3.....7....4.3...792....8..2.98.4.65..3.51......1............41.7..9.1..6. initial
Autosolve
position: .6..4983..9..7....453861792....8..2.98.4.65..3.51......1............41.7..9.1..6. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I2: 1,5 => CTR => I2: 4,6 * DIS # I2: 1,5 => CTR => I2: 4,6 * DIS # G6: 9 => CTR => G6: 4,6 * DIS # C4: 4,7 => CTR => C4: 1,6 * PRF # B6: 4,7 => SOL * DIS # B6: 2 => CTR => B6: 4,7 * DIS # B9: 4,7 => CTR => B9: 2,3 * PRF # B9: 2,3 => SOL * DIS # E7: 2,3 => CTR => E7: 5 * PRF # E8: 2,9 => SOL * DIS # B6: 4 => CTR => B6: 2,7 * DIS # F9: 2,7 => CTR => F9: 3,8 * DIS # C5: 1,7 => CTR => C5: 2 * PRF # C5: 2 => SOL * DIS # I4: 4,9 => CTR => I4: 1,3 * PRF # B9: 2,3 => SOL * DIS # B9: 4,7 => CTR => B9: 2,3 * DIS # D8: 2,3 => CTR => D8: 6,9 * DIS # I7: 5,8 => CTR => I7: 3,4,9 * DIS # I9: 5,8 => CTR => I9: 3,4 * CNT 20 HDP CHAINS / 41 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I2: 1,5 => CTR => I2: 4,6 * DIS I2: 4,6 # G6: 9 => CTR => G6: 4,6 * DIS I2: 4,6 + G6: 4,6 # C4: 4,7 => CTR => C4: 1,6 * DIS I2: 4,6 + G6: 4,6 + C4: 1,6 # E7: 2,3 => CTR => E7: 5 * PRF I2: 4,6 + G6: 4,6 + C4: 1,6 + E7: 5 # F7: 3 => SOL * STA I2: 4,6 + G6: 4,6 + C4: 1,6 + E7: 5 + F7: 3 * CNT 5 HDP CHAINS / 10 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .6...9.3.....7....4.3...792....8..2.98.4.65..3.51......1............41.7..9.1..6. | initial |
| .6..4983..9..7....453861792....8..2.98.4.65..3.51......1............41.7..9.1..6. | autosolve |
| 167249835298375416453861792641587923982436571375192648714653289836924157529718364 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) D1: 2,5 I1: 1,5 G2: 4,6 B4: 4,7 E5: 2,3 E6: 2,9 F6: 2,7 H5: 1,7 I5: 1,3 B8: 2,3 H8: 5,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H2,H5: 1.. / H2 = 1 => 18 pairs (_) / H5 = 1 => 0 pairs (X) C5,B6: 2.. / C5 = 2 => 0 pairs (*) / B6 = 2 => 0 pairs (X) G7,G9: 2.. / G7 = 2 => 13 pairs (_) / G9 = 2 => 12 pairs (_) C5,E5: 2.. / C5 = 2 => 0 pairs (*) / E5 = 2 => 0 pairs (X) D2,F2: 3.. / D2 = 3 => 13 pairs (_) / F2 = 3 => 13 pairs (_) B8,B9: 3.. / B8 = 3 => 10 pairs (_) / B9 = 3 => 0 pairs (X) E5,I5: 3.. / E5 = 3 => 0 pairs (*) / I5 = 3 => 0 pairs (X) C7,B9: 4.. / C7 = 4 => 18 pairs (_) / B9 = 4 => 0 pairs (X) C4,C7: 4.. / C4 = 4 => 0 pairs (X) / C7 = 4 => 18 pairs (_) D4,F4: 5.. / D4 = 5 => 20 pairs (_) / F4 = 5 => 12 pairs (_) E7,E8: 5.. / E7 = 5 => 12 pairs (_) / E8 = 5 => 0 pairs (X) D1,I1: 5.. / D1 = 5 => 0 pairs (X) / I1 = 5 => 17 pairs (_) A9,I9: 5.. / A9 = 5 => 11 pairs (_) / I9 = 5 => 0 pairs (X) F2,F4: 5.. / F2 = 5 => 20 pairs (_) / F4 = 5 => 12 pairs (_) G2,I2: 6.. / G2 = 6 => 0 pairs (X) / I2 = 6 => 13 pairs (_) A4,C4: 6.. / A4 = 6 => 13 pairs (_) / C4 = 6 => 0 pairs (X) G6,I6: 6.. / G6 = 6 => 13 pairs (_) / I6 = 6 => 0 pairs (X) D7,D8: 6.. / D7 = 6 => 11 pairs (_) / D8 = 6 => 0 pairs (X) G2,G6: 6.. / G2 = 6 => 0 pairs (X) / G6 = 6 => 13 pairs (_) I2,I6: 6.. / I2 = 6 => 13 pairs (_) / I6 = 6 => 0 pairs (X) A1,C1: 7.. / A1 = 7 => 0 pairs (X) / C1 = 7 => 17 pairs (_) H5,H6: 7.. / H5 = 7 => 18 pairs (_) / H6 = 7 => 0 pairs (X) C5,H5: 7.. / C5 = 7 => 0 pairs (X) / H5 = 7 => 18 pairs (_) A2,C2: 8.. / A2 = 8 => 14 pairs (_) / C2 = 8 => 13 pairs (_) H6,I6: 8.. / H6 = 8 => 0 pairs (X) / I6 = 8 => 13 pairs (_) F7,F9: 8.. / F7 = 8 => 0 pairs (X) / F9 = 8 => 11 pairs (_) D4,E6: 9.. / D4 = 9 => 0 pairs (X) / E6 = 9 => 13 pairs (_) D8,E8: 9.. / D8 = 9 => 13 pairs (_) / E8 = 9 => 0 pairs (X) G7,I7: 9.. / G7 = 9 => 0 pairs (X) / I7 = 9 => 11 pairs (_) D4,D8: 9.. / D4 = 9 => 0 pairs (X) / D8 = 9 => 13 pairs (_) E6,E8: 9.. / E6 = 9 => 13 pairs (_) / E8 = 9 => 0 pairs (X) * DURATION: 0:00:31.256117 START: 23:25:31.415522 END: 23:26:02.671639 2019-04-30 * CP COUNT: (31) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B8,D1,E5,E6,F6,G2,H5,H8,I1,I5) * .6..4983..9..7....453861792....8..2.98.4.65..3.51......1............41.7..9.1..6. * PAIR D1: 2,5 BLK 2 D2: 2,5,3 # reduction candidate for 2,5 D2: 2,5 # 13 pairs F2: 2,5,3 # reduction candidate for 2,5 F2: 2,5 # 13 pairs * PAIR I1: 1,5 BLK 3 H2: 1,5,4 # reduction candidate for 1,5 H2: 1,5 # 13 pairs I2: 1,5,4,6 # reduction candidate for 1,5 I2: 1,5 => CTR * .6..4983..9..7.64.453861792....8..2.98.4.65133.51...7..1............41.7..9.1..6. I2: 4,6 # 13 pairs * PAIR G2: 4,6 BLK 3 I2: 4,6,1,5 # reduction candidate for 4,6 I2: 1,5 => CTR * .6..4983..9..7.64.453861792....8..2.98.4.65133.51...7..1............41.7..9.1..6. I2: 4,6 # 13 pairs * PAIR G2: 4,6 COL G G6: 4,6,9 # reduction candidate for 4,6 G6: 9 => CTR * .6..4983..9..7.6..453861792...985.2.98.4365.13.5127986.1..58.49....94157549.1..68 G6: 4,6 # 14 pairs * PAIR B4: 4,7 BLK 4 C4: 4,7,1,6 # reduction candidate for 4,7 C4: 4,7 => CTR * 167249835.9..7..1.453861792674.8.921981426573325197.48.1.63.4.9.3.954187..9.1..6. C4: 1,6 # 18 pairs B6: 4,7,2 # reduction candidate for 4,7 B6: 4,7 => SOLVED * 167249835298375416453861792641587923982436571375192648714653289836924157529718364 B6: 2 => CTR * .6..4983..9..7..1.453861792.74.8.921981426573325197.48.1.63.25..3.954187..971.36. * PAIR B4: 4,7 COL B B9: 4,7,2,3 # reduction candidate for 4,7 B9: 4,7 => CTR * .6..4983..9..7..1.453861792.74.8.921981426573325197.48.1.63.25..3.954187..971.36. B9: 2,3 => SOLVED * 167249835298375416453861792641587923982436571375192648714653289836924157529718364 * PAIR E5: 2,3 COL E E7: 2,3,5 # reduction candidate for 2,3 E7: 2,3 => CTR * .6..4983..9..7.4.6453861792....8..2.98.4265.3325197648.1.63..5..3.9541875.9718.6. E7: 5 # 12 pairs E8: 2,3,5,9 # reduction candidate for 2,3 E8: 2,3 # 16 pairs * PAIR E6: 2,9 COL E E8: 2,9,3,5 # reduction candidate for 2,9 E8: 2,9 => SOLVED * 167249835298375416453861792641587923982436571375192648714653289836924157529718364 E8: 3,5 # 14 pairs * PAIR F6: 2,7 ROW 6 B6: 2,7,4 # reduction candidate for 2,7 B6: 4 => CTR * .6..4983..9..7....453861792....8..2.9824365713451.7.8..14....5......41.7..9.1..6. B6: 2,7 # 21 pairs * PAIR F6: 2,7 COL F F7: 2,7,3,8 # reduction candidate for 2,7 F7: 2,7 # 15 pairs F9: 2,7,3,8 # reduction candidate for 2,7 F9: 2,7 => CTR * .6..4983..9..7....453861792.74.8..2.98.4.657.325197.8..1...8.4..3.9.4157549712.6. F9: 3,8 # 12 pairs * PAIR H5: 1,7 ROW 5 C5: 1,7,2 # reduction candidate for 1,7 C5: 1,7 => CTR * .6..4983..9..7....453861792....8..2.98.426573325197.48.1.63..5..3.9541875.9718.6. C5: 2 => SOLVED * 167249835298375416453861792641587923982436571375192648714653289836924157529718364 * PAIR I5: 1,3 BLK 6 I4: 1,3,4,9 # reduction candidate for 1,3 I4: 4,9 => CTR * .67249835.9..7.416453861792.41.8.3299824365713751926487146.3......9.41.75.9.18.64 I4: 1,3 # 23 pairs * PAIR B8: 2,3 BLK 7 B9: 2,3,4,7 # reduction candidate for 2,3 B9: 2,3 => SOLVED * 167249835298375416453861792641587923982436571375192648714653289836924157529718364 B9: 4,7 => CTR * .6..4983..9..7..1.453861792.74.8.921981426573325197.48.1.63.25..3.954187..971.36. * PAIR B8: 2,3 ROW 8 D8: 2,3,6,9 # reduction candidate for 2,3 D8: 2,3 => CTR * .6..49835.9.573.1.453861792.7.985.2.982436571345127.8..1465........941.7..971..6. D8: 6,9 # 12 pairs E8: 2,3,5,9 # reduction candidate for 2,3 E8: 2,3 # 16 pairs * PAIR H8: 5,8 BLK 9 H7: 5,8,4 # reduction candidate for 5,8 H7: 5,8 # 19 pairs I7: 5,8,3,4,9 # reduction candidate for 5,8 I7: 5,8 => CTR * .6..49835.9..7..1.453861792.74.8532.98.4365.13.51......1....94..3...41.7549718263 I7: 3,4,9 # 11 pairs I9: 5,8,3,4 # reduction candidate for 5,8 I9: 5,8 => CTR * .6..4983..9..7..1.453861792674.8..2198142657.325197.8..1.....4..3.9.415754971..68 I9: 3,4 # 12 pairs * PAIR H8: 5,8 ROW 8 A8: 5,8,2,6 # reduction candidate for 5,8 A8: 5,8 # 14 pairs A8: 2,6 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060526-absurd-base-pr-000.dot * REASONING * DIS # I2: 1,5 => CTR => I2: 4,6 * DIS # I2: 1,5 => CTR => I2: 4,6 * DIS # G6: 9 => CTR => G6: 4,6 * DIS # C4: 4,7 => CTR => C4: 1,6 * PRF # B6: 4,7 => SOL * DIS # B6: 2 => CTR => B6: 4,7 * DIS # B9: 4,7 => CTR => B9: 2,3 * PRF # B9: 2,3 => SOL * DIS # E7: 2,3 => CTR => E7: 5 * PRF # E8: 2,9 => SOL * DIS # B6: 4 => CTR => B6: 2,7 * DIS # F9: 2,7 => CTR => F9: 3,8 * DIS # C5: 1,7 => CTR => C5: 2 * PRF # C5: 2 => SOL * DIS # I4: 4,9 => CTR => I4: 1,3 * PRF # B9: 2,3 => SOL * DIS # B9: 4,7 => CTR => B9: 2,3 * DIS # D8: 2,3 => CTR => D8: 6,9 * DIS # I7: 5,8 => CTR => I7: 3,4,9 * DIS # I9: 5,8 => CTR => I9: 3,4 * CNT 20 HDP CHAINS / 41 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B8,D1,E5,E6,F6,G2,H5,H8,I1,I5) * .6..4983..9..7....453861792....8..2.98.4.65..3.51......1............41.7..9.1..6. * PAIR D1: 2,5 BLK 2 D2: 2,5,3 # reduction candidate for 2,5 D2: 2,5 # 13 pairs F2: 2,5,3 # reduction candidate for 2,5 F2: 2,5 # 13 pairs * PAIR I1: 1,5 BLK 3 H2: 1,5,4 # reduction candidate for 1,5 H2: 1,5 # 13 pairs I2: 1,5,4,6 # reduction candidate for 1,5 I2: 1,5 => CTR * .6..4983..9..7.64.453861792....8..2.98.4.65133.51...7..1............41.7..9.1..6. * RESTART * PAIR G2: 4,6 COL G G6: 4,6,9 # reduction candidate for 4,6 G6: 9 => CTR * .6..49835.9..7.614453861792...985.2.98.4365713.5127986.1..58.49....94157549.1..68 * PAIR RESTART * PAIR B4: 4,7 BLK 4 C4: 4,7,1,6 # reduction candidate for 4,7 C4: 4,7 => CTR * 167249835.9..7..1.453861792674.8.921981426573325197.4..1......9.3.954187..9.1..6. * PAIR E5: 2,3 COL E E7: 2,3,5 # reduction candidate for 2,3 E7: 2,3 => CTR * 167249835.98.7.416453861792.4..8..2.98.4.657.3.519.6488146.7.5..3.954187579318264 * RESTART * PAIR RESTART * PAIR F6: 2,7 COL F F7: 2,7,3 # reduction candidate for 2,7 F7: 3 => SOLVED * 167249835298375416453861792641587923982436571375192648714653289836924157529718364 * DURATION: 0:00:07.723203 START: 23:26:27.993395 END: 23:26:35.716598 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060526-absurd-base-pr-001.dot * REASONING * DIS # I2: 1,5 => CTR => I2: 4,6 * DIS I2: 4,6 # G6: 9 => CTR => G6: 4,6 * DIS I2: 4,6 + G6: 4,6 # C4: 4,7 => CTR => C4: 1,6 * DIS I2: 4,6 + G6: 4,6 + C4: 1,6 # E7: 2,3 => CTR => E7: 5 * PRF I2: 4,6 + G6: 4,6 + C4: 1,6 + E7: 5 # F7: 3 => SOL * STA I2: 4,6 + G6: 4,6 + C4: 1,6 + E7: 5 + F7: 3 * CNT 5 HDP CHAINS / 10 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060526, absurd
Solution
position: 167249835298375416453861792641587923982436571375192648714653289836924157529718364 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 # D2: 2,5 => UNS * INC # F2: 2,5 => UNS * INC # H2: 1,5 => UNS * DIS # I2: 1,5 => CTR => I2: 4,6 * INC # I2: 4,6 => UNS * INC # I2: 4,6 => UNS * DIS # I2: 1,5 => CTR => I2: 4,6 * INC # G6: 4,6 => UNS * DIS # G6: 9 => CTR => G6: 4,6 * DIS # C4: 4,7 => CTR => C4: 1,6 * INC # C4: 1,6 => UNS * PRF # B6: 4,7 => SOL * DIS # B6: 2 => CTR => B6: 4,7 * DIS # B9: 4,7 => CTR => B9: 2,3 * PRF # B9: 2,3 => SOL * DIS # E7: 2,3 => CTR => E7: 5 * INC # E7: 5 => UNS * INC # E8: 2,3 => UNS * PRF # E8: 2,9 => SOL * INC # E8: 3,5 => UNS * INC # B6: 2,7 => UNS * DIS # B6: 4 => CTR => B6: 2,7 * INC # F7: 2,7 => UNS * DIS # F9: 2,7 => CTR => F9: 3,8 * INC # F9: 3,8 => UNS * DIS # C5: 1,7 => CTR => C5: 2 * PRF # C5: 2 => SOL * INC # I4: 1,3 => UNS * DIS # I4: 4,9 => CTR => I4: 1,3 * PRF # B9: 2,3 => SOL * DIS # B9: 4,7 => CTR => B9: 2,3 * DIS # D8: 2,3 => CTR => D8: 6,9 * INC # D8: 6,9 => UNS * INC # E8: 2,3 => UNS * INC # H7: 5,8 => UNS * DIS # I7: 5,8 => CTR => I7: 3,4,9 * INC # I7: 3,4,9 => UNS * DIS # I9: 5,8 => CTR => I9: 3,4 * INC # I9: 3,4 => UNS * INC # A8: 5,8 => UNS * INC # A8: 2,6 => UNS * CNT 41 HDP CHAINS / 41 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D2: 2,5 => UNS * INC # F2: 2,5 => UNS * INC # H2: 1,5 => UNS * DIS # I2: 1,5 => CTR => I2: 4,6 * INC I2: 4,6 # G6: 4,6 => UNS * DIS I2: 4,6 # G6: 9 => CTR => G6: 4,6 * DIS I2: 4,6 + G6: 4,6 # C4: 4,7 => CTR => C4: 1,6 * DIS I2: 4,6 + G6: 4,6 + C4: 1,6 # E7: 2,3 => CTR => E7: 5 * INC I2: 4,6 + G6: 4,6 + C4: 1,6 + E7: 5 # F7: 2,7 => UNS * PRF I2: 4,6 + G6: 4,6 + C4: 1,6 + E7: 5 # F7: 3 => SOL * STA I2: 4,6 + G6: 4,6 + C4: 1,6 + E7: 5 + F7: 3 * CNT 10 HDP CHAINS / 10 HYP OPENED