Analysis of zz-www.sudokuoftheday.co.uk-20060828-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006
level: medium
position: .6.45..3.....7...8...1.....75.........1.....484.9........6..2.....5.98.392...35.7 initial
Autosolve
position: .6.45..3....37...8...19....75.2.4.....17.5..484.9.1......6.72.....5298.392.8.35.7 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A2: 1,2 => SOL * DIS # G2: 1,9 => CTR => G2: 4,6 * PRF # C1: 2,8 => SOL * PRF # F3: 8 => SOL * DIS # C4: 6 => CTR => C4: 3,9 * DIS # G5: 6 => CTR => G5: 3,9 * DIS # E5: 3,6 => CTR => E5: 8 * DIS # C6: 3,6 => CTR => C6: 2 * DIS # C7: 8 => CTR => C7: 3,5 * DIS # B3: 3,8 => CTR => B3: 7 * PRF # B3: 7 => SOL * PRF # A8: 4,6 => SOL * DIS # A8: 1 => CTR => A8: 4,6 * DIS # C8: 4,6 => CTR => C8: 7 * PRF # C8: 7 => SOL * DIS # H9: 1 => CTR => H9: 4,6 * DIS # H7: 4 => CTR => H7: 1,9 * DIS # I4: 1,9 => CTR => I4: 6 * DIS # H9: 1 => CTR => H9: 4,6 * PRF # A8: 4,6 => SOL * DIS # A8: 1 => CTR => A8: 4,6 * DIS # C8: 4,6 => CTR => C8: 7 * PRF # C8: 7 => SOL * CNT 23 HDP CHAINS / 52 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A2: 1,2 => SOL * STA A2: 1,2 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .6.45..3.....7...8...1.....75.........1.....484.9........6..2.....5.98.392...35.7 | initial |
| .6.45..3....37...8...19....75.2.4.....17.5..484.9.1......6.72.....5298.392.8.35.7 | autosolve |
| 168452739295376418374198652759234186631785924842961375583647291417529863926813547 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) A1: 1,2 B2: 1,9 F1: 2,8 F2: 2,6 B5: 3,9 E6: 3,6 A7: 3,5 B7: 3,8 B8: 1,7 C9: 4,6 E7: 1,4 E9: 1,4 I7: 1,9 H8: 4,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A8,B8: 1.. / A8 = 1 => 0 pairs (X) / B8 = 1 => 0 pairs (_) E7,E9: 1.. / E7 = 1 => 0 pairs (X) / E9 = 1 => 14 pairs (_) E9,H9: 1.. / E9 = 1 => 14 pairs (_) / H9 = 1 => 0 pairs (X) B2,B8: 1.. / B2 = 1 => 0 pairs (X) / B8 = 1 => 0 pairs (_) A5,C6: 2.. / A5 = 2 => 0 pairs (X) / C6 = 2 => 22 pairs (_) A5,H5: 2.. / A5 = 2 => 0 pairs (X) / H5 = 2 => 22 pairs (_) G2,G3: 4.. / G2 = 4 => 20 pairs (_) / G3 = 4 => 14 pairs (_) E7,E9: 4.. / E7 = 4 => 14 pairs (_) / E9 = 4 => 0 pairs (X) E7,H7: 4.. / E7 = 4 => 14 pairs (_) / H7 = 4 => 0 pairs (X) H6,I6: 5.. / H6 = 5 => 0 pairs (X) / I6 = 5 => 17 pairs (_) A7,C7: 5.. / A7 = 5 => 14 pairs (_) / C7 = 5 => 15 pairs (_) I3,I6: 5.. / I3 = 5 => 0 pairs (X) / I6 = 5 => 17 pairs (_) F2,F3: 6.. / F2 = 6 => 14 pairs (_) / F3 = 6 => 18 pairs (_) H8,H9: 6.. / H8 = 6 => 24 pairs (_) / H9 = 6 => 13 pairs (_) F2,G2: 6.. / F2 = 6 => 14 pairs (_) / G2 = 6 => 18 pairs (_) C9,H9: 6.. / C9 = 6 => 24 pairs (_) / H9 = 6 => 13 pairs (_) A5,A8: 6.. / A5 = 6 => 24 pairs (_) / A8 = 6 => 0 pairs (X) G6,H6: 7.. / G6 = 7 => 0 pairs (X) / H6 = 7 => 21 pairs (_) B8,C8: 7.. / B8 = 7 => 0 pairs (X) / C8 = 7 => 0 pairs (_) C1,G1: 7.. / C1 = 7 => 0 pairs (X) / G1 = 7 => 0 pairs (_) B3,B8: 7.. / B3 = 7 => 0 pairs (*) / B8 = 7 => 0 pairs (X) H3,H6: 7.. / H3 = 7 => 0 pairs (X) / H6 = 7 => 21 pairs (_) F1,F3: 8.. / F1 = 8 => 14 pairs (_) / F3 = 8 => 0 pairs (*) E4,E5: 8.. / E4 = 8 => 0 pairs (X) / E5 = 8 => 16 pairs (_) H4,H5: 8.. / H4 = 8 => 16 pairs (_) / H5 = 8 => 0 pairs (X) B7,C7: 8.. / B7 = 8 => 15 pairs (_) / C7 = 8 => 0 pairs (X) C1,F1: 8.. / C1 = 8 => 0 pairs (*) / F1 = 8 => 0 pairs (X) E4,H4: 8.. / E4 = 8 => 0 pairs (X) / H4 = 8 => 16 pairs (_) E5,H5: 8.. / E5 = 8 => 16 pairs (_) / H5 = 8 => 0 pairs (X) B3,B7: 8.. / B3 = 8 => 0 pairs (X) / B7 = 8 => 15 pairs (_) C4,B5: 9.. / C4 = 9 => 0 pairs (*) / B5 = 9 => 0 pairs (X) H7,I7: 9.. / H7 = 9 => 16 pairs (_) / I7 = 9 => 19 pairs (_) B2,B5: 9.. / B2 = 9 => 0 pairs (*) / B5 = 9 => 0 pairs (X) * DURATION: 0:00:38.622392 START: 02:08:53.741450 END: 02:09:32.363842 2019-05-01 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A7,B2,B5,B7,B8,C9,E6,E7,E9,F1,F2,H8,I7) * .6.45..3....37...8...19....75.2.4.....17.5..484.9.1......6.72.....5298.392.8.35.7 * PAIR A1: 1,2 BLK 1 A2: 1,2,4,5 # reduction candidate for 1,2 A2: 1,2 => SOLVED * 168452739295376418374198652759234186631785924842961375583647291417529863926813547 A2: 4,5 # 15 pairs * PAIR A1: 1,2 ROW 1 I1: 1,2,9 # reduction candidate for 1,2 I1: 9 # 26 pairs I1: 1,2 # 17 pairs * PAIR B2: 1,9 ROW 2 G2: 1,9,4,6 # reduction candidate for 1,9 G2: 1,9 => CTR * 16.458.32.9.376158...1924767592.4..1.317.5..484.9.1..5...6.72.....5298.392.8.35.7 G2: 4,6 # 15 pairs H2: 1,9,2,5 # reduction candidate for 1,9 H2: 1,9 # 22 pairs * PAIR F1: 2,8 BLK 2 F3: 2,8,6 # reduction candidate for 2,8 F3: 6 # 18 pairs F3: 2,8 # 14 pairs * PAIR F1: 2,8 ROW 1 C1: 2,8,7,9 # reduction candidate for 2,8 C1: 2,8 => SOLVED * 168452739295376418374198652759234186631785924842961375583647291417529863926813547 C1: 7,9 # 15 pairs * PAIR F2: 2,6 BLK 2 F3: 2,6,8 # reduction candidate for 2,6 F3: 8 => SOLVED * 168452739295376418374198652759234186631785924842961375583647291417529863926813547 F3: 2,6 # 14 pairs * PAIR B5: 3,9 BLK 4 C4: 3,9,6 # reduction candidate for 3,9 C4: 6 => CTR * .6.45..3....37...8...19....7562.4....917.5..484.9.1......6.72..61.5298.392.8.35.7 C4: 3,9 # 17 pairs * PAIR B5: 3,9 ROW 5 G5: 3,9,6 # reduction candidate for 3,9 G5: 6 => CTR * .6.45.73..9.376..8.7.19.4.67592643....17.56.484.9.1......6.72..617529843924813567 G5: 3,9 # 18 pairs * PAIR E6: 3,6 BLK 5 E4: 3,6,8 # reduction candidate for 3,6 E4: 3,6 # 16 pairs E5: 3,6,8 # reduction candidate for 3,6 E5: 3,6 => CTR * 16.45.73..9.37...8.7.19....7592843162.17.5.8484.9.1......6.72..617529843924813567 E5: 8 # 16 pairs * PAIR E6: 3,6 ROW 6 C6: 3,6,2 # reduction candidate for 3,6 C6: 3,6 => CTR * 16.45.73..9.37...8.7.19....7592.4...2317.5984846931......6.72..617529843924813567 C6: 2 # 22 pairs G6: 3,6,7 # reduction candidate for 3,6 G6: 3,6 # 21 pairs * PAIR A7: 3,5 BLK 7 C7: 3,5,8 # reduction candidate for 3,5 C7: 8 => CTR * 26.458.3.41.3726.838.1964.2753264.8.6917.5324842931...5386.72..17.5298.392.8.35.7 C7: 3,5 # 15 pairs * PAIR A7: 3,5 COL A A3: 3,5,2,4 # reduction candidate for 3,5 A3: 2,4 # 19 pairs A3: 3,5 # 16 pairs * PAIR B7: 3,8 BLK 7 C7: 3,8,5 # reduction candidate for 3,8 C7: 5 # 15 pairs C7: 3,8 # 14 pairs * PAIR B7: 3,8 COL B B3: 3,8,7 # reduction candidate for 3,8 B3: 3,8 => CTR * 26.458.3..1.3726.8...1964.2753264.8.6917.5324842931......6.72..17.5298.392.8.35.7 B3: 7 => SOLVED * 168452739295376418374198652759234186631785924842961375583647291417529863926813547 * PAIR C9: 4,6 BLK 7 A8: 4,6,1 # reduction candidate for 4,6 A8: 4,6 => SOLVED * 168452739295376418374198652759234186631785924842961375583647291417529863926813547 A8: 1 => CTR * 26.458.3..1.3726.8...1964.275.2.4.8.6917853248429317.....6.72..17.5298.392.8.35.7 C8: 4,6,7 # reduction candidate for 4,6 C8: 4,6 => CTR * 26.458.3..1.3726.8...1964.2753264.8.6917.5324842931......6.72..17.5298.392.8.35.7 C8: 7 => SOLVED * 168452739295376418374198652759234186631785924842961375583647291417529863926813547 * PAIR C9: 4,6 ROW 9 H9: 4,6,1 # reduction candidate for 4,6 H9: 1 => CTR * .6945873..1.37..98...19..5.7532.4.8.691785324842931......617249...529863926843517 H9: 4,6 # 14 pairs * PAIR E7: 1,4 ROW 7 H7: 1,4,9 # reduction candidate for 1,4 H7: 1,4 # 19 pairs H7: 9 # 16 pairs * PAIR E9: 1,4 ROW 9 H9: 1,4,6 # reduction candidate for 1,4 H9: 1,4 # 24 pairs H9: 6 # 13 pairs * PAIR I7: 1,9 BLK 9 H7: 1,9,4 # reduction candidate for 1,9 H7: 4 => CTR * .6945873..1.37..98...19..5.7532.4.8.691785324842931......617249...529863926843517 H7: 1,9 # 14 pairs * PAIR I7: 1,9 COL I I1: 1,9,2 # reduction candidate for 1,9 I1: 1,9 # 27 pairs I4: 1,9,6 # reduction candidate for 1,9 I4: 1,9 => CTR * 16.458.32.9.37...8...19....7592.4..1.317.5..484.9.1....8.6.72.9.175298.392.8.35.7 I4: 6 # 27 pairs * PAIR H8: 4,6 BLK 9 H9: 4,6,1 # reduction candidate for 4,6 H9: 1 => CTR * .6945873..1.37..98...19..5.7532.4.8.691785324842931......617249...529863926843517 H9: 4,6 # 14 pairs * PAIR H8: 4,6 ROW 8 A8: 4,6,1 # reduction candidate for 4,6 A8: 4,6 => SOLVED * 168452739295376418374198652759234186631785924842961375583647291417529863926813547 A8: 1 => CTR * 26.458.3..1.3726.8...1964.275.2.4.8.6917853248429317.....6.72..17.5298.392.8.35.7 C8: 4,6,7 # reduction candidate for 4,6 C8: 4,6 => CTR * 26.458.3..1.3726.8...1964.2753264.8.6917.5324842931......6.72..17.5298.392.8.35.7 C8: 7 => SOLVED * 168452739295376418374198652759234186631785924842961375583647291417529863926813547 * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060828-absurd-base-pr-000.dot * REASONING * PRF # A2: 1,2 => SOL * DIS # G2: 1,9 => CTR => G2: 4,6 * PRF # C1: 2,8 => SOL * PRF # F3: 8 => SOL * DIS # C4: 6 => CTR => C4: 3,9 * DIS # G5: 6 => CTR => G5: 3,9 * DIS # E5: 3,6 => CTR => E5: 8 * DIS # C6: 3,6 => CTR => C6: 2 * DIS # C7: 8 => CTR => C7: 3,5 * DIS # B3: 3,8 => CTR => B3: 7 * PRF # B3: 7 => SOL * PRF # A8: 4,6 => SOL * DIS # A8: 1 => CTR => A8: 4,6 * DIS # C8: 4,6 => CTR => C8: 7 * PRF # C8: 7 => SOL * DIS # H9: 1 => CTR => H9: 4,6 * DIS # H7: 4 => CTR => H7: 1,9 * DIS # I4: 1,9 => CTR => I4: 6 * DIS # H9: 1 => CTR => H9: 4,6 * PRF # A8: 4,6 => SOL * DIS # A8: 1 => CTR => A8: 4,6 * DIS # C8: 4,6 => CTR => C8: 7 * PRF # C8: 7 => SOL * CNT 23 HDP CHAINS / 52 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A7,B2,B5,B7,B8,C9,E6,E7,E9,F1,F2,H8,I7) * .6.45..3....37...8...19....75.2.4.....17.5..484.9.1......6.72.....5298.392.8.35.7 * PAIR A1: 1,2 BLK 1 A2: 1,2,4,5 # reduction candidate for 1,2 A2: 1,2 => SOLVED * 168452739295376418374198652759234186631785924842961375583647291417529863926813547 * DURATION: 0:00:01.828846 START: 02:10:06.476357 END: 02:10:08.305203 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060828-absurd-base-pr-001.dot * REASONING * PRF # A2: 1,2 => SOL * STA A2: 1,2 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060828, absurd
Solution
position: 168452739295376418374198652759234186631785924842961375583647291417529863926813547 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 # A2: 1,2 => SOL * INC # A2: 4,5 => UNS * INC # I1: 1,2 => UNS * INC # I1: 9 => UNS * DIS # G2: 1,9 => CTR => G2: 4,6 * INC # G2: 4,6 => UNS * INC # H2: 1,9 => UNS * INC # F3: 2,8 => UNS * INC # F3: 6 => UNS * PRF # C1: 2,8 => SOL * INC # C1: 7,9 => UNS * INC # F3: 2,6 => UNS * PRF # F3: 8 => SOL * INC # C4: 3,9 => UNS * DIS # C4: 6 => CTR => C4: 3,9 * INC # G5: 3,9 => UNS * DIS # G5: 6 => CTR => G5: 3,9 * INC # E4: 3,6 => UNS * DIS # E5: 3,6 => CTR => E5: 8 * INC # E5: 8 => UNS * DIS # C6: 3,6 => CTR => C6: 2 * INC # C6: 2 => UNS * INC # G6: 3,6 => UNS * INC # C7: 3,5 => UNS * DIS # C7: 8 => CTR => C7: 3,5 * INC # A3: 3,5 => UNS * INC # A3: 2,4 => UNS * INC # C7: 3,8 => UNS * INC # C7: 5 => UNS * DIS # B3: 3,8 => CTR => B3: 7 * PRF # B3: 7 => SOL * PRF # A8: 4,6 => SOL * DIS # A8: 1 => CTR => A8: 4,6 * DIS # C8: 4,6 => CTR => C8: 7 * PRF # C8: 7 => SOL * INC # H9: 4,6 => UNS * DIS # H9: 1 => CTR => H9: 4,6 * INC # H7: 1,4 => UNS * INC # H7: 9 => UNS * INC # H9: 1,4 => UNS * INC # H9: 6 => UNS * INC # H7: 1,9 => UNS * DIS # H7: 4 => CTR => H7: 1,9 * INC # I1: 1,9 => UNS * DIS # I4: 1,9 => CTR => I4: 6 * INC # I4: 6 => UNS * INC # H9: 4,6 => UNS * DIS # H9: 1 => CTR => H9: 4,6 * PRF # A8: 4,6 => SOL * DIS # A8: 1 => CTR => A8: 4,6 * DIS # C8: 4,6 => CTR => C8: 7 * PRF # C8: 7 => SOL * CNT 52 HDP CHAINS / 52 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A2: 1,2 => SOL * STA A2: 1,2 * CNT 1 HDP CHAINS / 1 HYP OPENED