Analysis of zz-www.sudokuoftheday.co.uk-20190311-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019
level: medium
position: ..........6.7....4...81.7...2..81.4....4.......5.9...2.4.35..2995.....1.......43. initial
Autosolve
position: ...9......6.7....4...81.7...2.581.4....4.....4.569...2.4.35..299532...17...1.9435 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B5: 1,8 => SOL * PRF # E1: 2,3 => SOL * DIS # E1: 4,6 => CTR => E1: 2,3 * DIS # F1: 2,3 => CTR => F1: 4,5,6 * DIS # F2: 2,3 => CTR => F2: 5 * DIS # F3: 2,3 => CTR => F3: 4,5,6 * DIS # E5: 2,3 => CTR => E5: 7 * PRF # E5: 7 => SOL * DIS # B1: 1,8 => CTR => B1: 3,7 * DIS # F5: 3,7 => CTR => F5: 2 * PRF # G5: 3,9 => SOL * DIS # G2: 3,9 => CTR => G2: 1,2,5 * DIS # A4: 7 => CTR => A4: 3,6 * PRF # B5: 1,8 => SOL * PRF # G5: 1,3 => SOL * DIS # B6: 1,3 => CTR => B6: 8 * PRF # B6: 8 => SOL * DIS # H5: 7,8 => CTR => H5: 5,6,9 * PRF # H5: 5,6,9 => SOL * DIS # A9: 7,8 => CTR => A9: 2,6 * PRF # C9: 7,8 => SOL * DIS # B1: 7,8 => CTR => B1: 1,3 * PRF # B1: 1,3 => SOL * DIS # F8: 4,6 => CTR => F8: 8 * DIS # E1: 4,6 => CTR => E1: 2,3 * PRF # E1: 2,3 => SOL * DIS # F7: 8 => CTR => F7: 6,7 * DIS # A9: 6,7 => CTR => A9: 2,8 * DIS # C9: 6,7 => CTR => C9: 2,8 * DIS # F7: 6,8 => CTR => F7: 7 * PRF # F7: 7 => SOL * DIS # F8: 4 => CTR => F8: 6,8 * CNT 32 HDP CHAINS / 61 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # B5: 1,8 => SOL * STA B5: 1,8 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..........6.7....4...81.7...2..81.4....4.......5.9...2.4.35..2995.....1.......43. | initial |
| ...9......6.7....4...81.7...2.581.4....4.....4.569...2.4.35..299532...17...1.9435 | autosolve |
| 734926581861735294592814763327581946619472358485693172146357829953248617278169435 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) B3: 3,9 E2: 2,3 I1: 1,8 I3: 3,6 F6: 3,7 G4: 3,9 I4: 3,6 I5: 1,8 G6: 1,3 H6: 7,8 B9: 7,8 E8: 4,6 E9: 6,7 G7: 6,8 G8: 6,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A7,C7: 1.. / A7 = 1 => 16 pairs (_) / C7 = 1 => 16 pairs (_) B6,G6: 1.. / B6 = 1 => 0 pairs (X) / G6 = 1 => 0 pairs (_) I1,I5: 1.. / I1 = 1 => 0 pairs (*) / I5 = 1 => 0 pairs (X) G1,G2: 2.. / G1 = 2 => 15 pairs (_) / G2 = 2 => 17 pairs (_) E5,F5: 2.. / E5 = 2 => 0 pairs (X) / F5 = 2 => 17 pairs (_) A9,C9: 2.. / A9 = 2 => 19 pairs (_) / C9 = 2 => 16 pairs (_) I3,I4: 3.. / I3 = 3 => 17 pairs (_) / I4 = 3 => 0 pairs (X) C1,C3: 4.. / C1 = 4 => 17 pairs (_) / C3 = 4 => 15 pairs (_) E8,F8: 4.. / E8 = 4 => 15 pairs (_) / F8 = 4 => 0 pairs (X) C3,F3: 4.. / C3 = 4 => 15 pairs (_) / F3 = 4 => 17 pairs (_) E1,E8: 4.. / E1 = 4 => 0 pairs (X) / E8 = 4 => 15 pairs (_) G5,H5: 5.. / G5 = 5 => 15 pairs (_) / H5 = 5 => 0 pairs (*) I4,H5: 6.. / I4 = 6 => 17 pairs (_) / H5 = 6 => 0 pairs (X) G7,G8: 6.. / G7 = 6 => 0 pairs (X) / G8 = 6 => 13 pairs (_) I3,I4: 6.. / I3 = 6 => 0 pairs (X) / I4 = 6 => 17 pairs (_) A4,C4: 7.. / A4 = 7 => 0 pairs (X) / C4 = 7 => 16 pairs (_) H5,H6: 7.. / H5 = 7 => 0 pairs (X) / H6 = 7 => 0 pairs (_) F7,E9: 7.. / F7 = 7 => 0 pairs (*) / E9 = 7 => 0 pairs (X) F6,H6: 7.. / F6 = 7 => 0 pairs (X) / H6 = 7 => 0 pairs (_) B1,B9: 7.. / B1 = 7 => 0 pairs (X) / B9 = 7 => 0 pairs (_) E5,E9: 7.. / E5 = 7 => 0 pairs (*) / E9 = 7 => 0 pairs (X) F7,F8: 8.. / F7 = 8 => 0 pairs (X) / F8 = 8 => 13 pairs (_) G7,G8: 8.. / G7 = 8 => 13 pairs (_) / G8 = 8 => 0 pairs (X) B6,H6: 8.. / B6 = 8 => 0 pairs (*) / H6 = 8 => 0 pairs (X) F7,G7: 8.. / F7 = 8 => 0 pairs (X) / G7 = 8 => 13 pairs (_) F8,G8: 8.. / F8 = 8 => 13 pairs (_) / G8 = 8 => 0 pairs (X) I1,I5: 8.. / I1 = 8 => 0 pairs (X) / I5 = 8 => 0 pairs (_) C4,G4: 9.. / C4 = 9 => 0 pairs (X) / G4 = 9 => 15 pairs (_) B3,B5: 9.. / B3 = 9 => 16 pairs (_) / B5 = 9 => 0 pairs (X) * DURATION: 0:00:43.248509 START: 04:25:33.626905 END: 04:26:16.875414 2019-05-01 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B9,E2,E8,E9,F6,G4,G6,G7,G8,H6,I1,I3,I4,I5) * ...9......6.7....4...81.7...2.581.4....4.....4.569...2.4.35..299532...17...1.9435 * PAIR B3: 3,9 COL B B5: 3,9,1,8 # reduction candidate for 3,9 B5: 1,8 => SOLVED * 734926581861735294592814763327581946619472358485693172146357829953248617278169435 B5: 3,9 # 17 pairs * PAIR E2: 2,3 BLK 2 E1: 2,3,4,6 # reduction candidate for 2,3 E1: 2,3 => SOLVED * 734926581861735294592814763327581946619472358485693172146357829953248617278169435 E1: 4,6 => CTR * .7.9....8.6.7....4...81.7.3327581946.9.4...71415697382.4.35..299532...17.8.179435 F1: 2,3,4,5,6 # reduction candidate for 2,3 F1: 2,3 => CTR * .7.9....8.6.7.5.94...81.7.3327581946.9.4...71415697382.4.35..299532...17.8.179435 F1: 4,5,6 # 15 pairs F2: 2,3,5 # reduction candidate for 2,3 F2: 2,3 => CTR * 37.9..2...6.7....4.9.81.7.3729581346...4.....4.569.182.4.35..299532...17.8.179435 F2: 5 # 16 pairs F3: 2,3,4,5,6 # reduction candidate for 2,3 F3: 2,3 => CTR * .7.9...58.6.7.5.94594812763.2.581.46...42.571415697382.4.35..299532...17.8.179435 F3: 4,5,6 # 15 pairs * PAIR E2: 2,3 ROW 2 A2: 2,3,1,5,8 # reduction candidate for 2,3 A2: 2,3 # 22 pairs G2: 2,3,1,5,9 # reduction candidate for 2,3 G2: 2,3 # 18 pairs * PAIR E2: 2,3 COL E E5: 2,3,7 # reduction candidate for 2,3 E5: 2,3 => CTR * .7.9....8.6.7....4...81.7.3327581946.9.4...71415697382.4.35..299532...17.8.179435 E5: 7 => SOLVED * 734926581861735294592814763327581946619472358485693172146357829953248617278169435 * PAIR I1: 1,8 ROW 1 A1: 1,8,2,3,5,7 # reduction candidate for 1,8 A1: 1,8 # 18 pairs B1: 1,8,3,7 # reduction candidate for 1,8 B1: 1,8 => CTR * ...9....1.6.7.5..4...81.7...2.581.4..1.472..8485693172.4.357829953248617.7.169435 B1: 3,7 # 16 pairs C1: 1,8,2,4,7 # reduction candidate for 1,8 C1: 1,8 # 18 pairs * PAIR I3: 3,6 ROW 3 F3: 3,6,2,4,5 # reduction candidate for 3,6 F3: 3,6 # 18 pairs F3: 2,4,5 # 16 pairs * PAIR F6: 3,7 BLK 5 E5: 3,7,2 # reduction candidate for 3,7 E5: 3,7 # 17 pairs F5: 3,7,2 # reduction candidate for 3,7 F5: 3,7 => CTR * 37.9....8.6.73...4.9.81.7.3.2.581946.3.42..71415697382.4.35..299532...17.8.179435 F5: 2 # 17 pairs * PAIR G4: 3,9 BLK 6 G5: 3,9,1,5 # reduction candidate for 3,9 G5: 3,9 => SOLVED * 734926581861735294592814763327581946619472358485693172146357829953248617278169435 G5: 1,5 # 16 pairs * PAIR G4: 3,9 COL G G2: 3,9,1,2,5 # reduction candidate for 3,9 G2: 3,9 => CTR * .3.94.2.1.6.7....4...81.7...2.581.4....4..5.848569.172.4.35..299532...17.7.169435 G2: 1,2,5 # 15 pairs * PAIR I4: 3,6 ROW 4 A4: 3,6,7 # reduction candidate for 3,6 A4: 7 => CTR * .37924561.6.73...4.9481.7.372.581346316472..8485693172641357829953248617.7.169435 A4: 3,6 # 16 pairs * PAIR I5: 1,8 ROW 5 A5: 1,8,3,6 # reduction candidate for 1,8 A5: 1,8 # 19 pairs B5: 1,8,3,9 # reduction candidate for 1,8 B5: 1,8 => SOLVED * 734926581861735294592814763327581946619472358485693172146357829953248617278169435 B5: 3,9 # 17 pairs C5: 1,8,6,9 # reduction candidate for 1,8 C5: 1,8 # 19 pairs * PAIR G6: 1,3 BLK 6 G5: 1,3,5,9 # reduction candidate for 1,3 G5: 1,3 => SOLVED * 734926581861735294592814763327581946619472358485693172146357829953248617278169435 G5: 5,9 # 16 pairs * PAIR G6: 1,3 ROW 6 B6: 1,3,8 # reduction candidate for 1,3 B6: 1,3 => CTR * .7.9....8.6.7....4...81.7.3327581946...4..57141569738274135..299532...17.8.179435 B6: 8 => SOLVED * 734926581861735294592814763327581946619472358485693172146357829953248617278169435 * PAIR G6: 1,3 COL G G1: 1,3,2,5 # reduction candidate for 1,3 G1: 1,3 # 18 pairs G2: 1,3,2,5,9 # reduction candidate for 1,3 G2: 1,3 # 16 pairs * PAIR H6: 7,8 BLK 6 H5: 7,8,5,6,9 # reduction candidate for 7,8 H5: 7,8 => CTR * ...9......6.7....4.9.81.7.3327581946..94..5.141569738274135..299532...17.8.1.9435 H5: 5,6,9 => SOLVED * 734926581861735294592814763327581946619472358485693172146357829953248617278169435 * PAIR B9: 7,8 BLK 7 A9: 7,8,2,6 # reduction candidate for 7,8 A9: 7,8 => CTR * 53792...1.6.7.5..42..81.75..2.581.4..1.4725.8485693172.4.357829953248617872169435 A9: 2,6 # 16 pairs C9: 7,8,2,6 # reduction candidate for 7,8 C9: 7,8 => SOLVED * 734926581861735294592814763327581946619472358485693172146357829953248617278169435 C9: 2,6 # 16 pairs * PAIR B9: 7,8 COL B B1: 7,8,1,3 # reduction candidate for 7,8 B1: 7,8 => CTR * .7.9....8.6.7....4...81.7.3327581946.9.4...71415697382.4.35..299532...17.8.179435 B1: 1,3 => SOLVED * 734926581861735294592814763327581946619472358485693172146357829953248617278169435 * PAIR E8: 4,6 BLK 8 F8: 4,6,8 # reduction candidate for 4,6 F8: 4,6 => CTR * .7.9....8.6.7....4...81.7.3327581946.9.4...71415697382.4.3586299532..817.8.179435 F8: 8 # 13 pairs * PAIR E8: 4,6 COL E E1: 4,6,2,3 # reduction candidate for 4,6 E1: 4,6 => CTR * .7.9....8.6.7....4...81.7.3327581946.9.4...71415697382.4.35..299532...17.8.179435 E1: 2,3 => SOLVED * 734926581861735294592814763327581946619472358485693172146357829953248617278169435 * PAIR E9: 6,7 BLK 8 F7: 6,7,8 # reduction candidate for 6,7 F7: 8 => CTR * .7.9....8.6.7....4...81.7.3327581946.9.4...71415697382.4.3586299532..817.8.179435 F7: 6,7 # 13 pairs * PAIR E9: 6,7 ROW 9 A9: 6,7,2,8 # reduction candidate for 6,7 A9: 6,7 => CTR * .7.9....8.6.7....4...81.7.3327581946.9.4...71415697382.4.35..299532...17.82179435 A9: 2,8 # 16 pairs C9: 6,7,2,8 # reduction candidate for 6,7 C9: 6,7 => CTR * .7.9....8.6.7....4...81.7.3327581946.9.4...71415697382.4.35..299532...1728.179435 C9: 2,8 # 16 pairs * PAIR G7: 6,8 ROW 7 F7: 6,8,7 # reduction candidate for 6,8 F7: 6,8 => CTR * .7.9....8.6.7....4...81.7.3327581946.9.4...71415697382.4.35..299532...17.8.179435 F7: 7 => SOLVED * 734926581861735294592814763327581946619472358485693172146357829953248617278169435 * PAIR G8: 6,8 ROW 8 F8: 6,8,4 # reduction candidate for 6,8 F8: 4 => CTR * .7.94...8.6.7....4..481.7.3327581946.9.4...71415697382.4.358629953264817.8.179435 F8: 6,8 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190311-absurd-base-pr-000.dot * REASONING * PRF # B5: 1,8 => SOL * PRF # E1: 2,3 => SOL * DIS # E1: 4,6 => CTR => E1: 2,3 * DIS # F1: 2,3 => CTR => F1: 4,5,6 * DIS # F2: 2,3 => CTR => F2: 5 * DIS # F3: 2,3 => CTR => F3: 4,5,6 * DIS # E5: 2,3 => CTR => E5: 7 * PRF # E5: 7 => SOL * DIS # B1: 1,8 => CTR => B1: 3,7 * DIS # F5: 3,7 => CTR => F5: 2 * PRF # G5: 3,9 => SOL * DIS # G2: 3,9 => CTR => G2: 1,2,5 * DIS # A4: 7 => CTR => A4: 3,6 * PRF # B5: 1,8 => SOL * PRF # G5: 1,3 => SOL * DIS # B6: 1,3 => CTR => B6: 8 * PRF # B6: 8 => SOL * DIS # H5: 7,8 => CTR => H5: 5,6,9 * PRF # H5: 5,6,9 => SOL * DIS # A9: 7,8 => CTR => A9: 2,6 * PRF # C9: 7,8 => SOL * DIS # B1: 7,8 => CTR => B1: 1,3 * PRF # B1: 1,3 => SOL * DIS # F8: 4,6 => CTR => F8: 8 * DIS # E1: 4,6 => CTR => E1: 2,3 * PRF # E1: 2,3 => SOL * DIS # F7: 8 => CTR => F7: 6,7 * DIS # A9: 6,7 => CTR => A9: 2,8 * DIS # C9: 6,7 => CTR => C9: 2,8 * DIS # F7: 6,8 => CTR => F7: 7 * PRF # F7: 7 => SOL * DIS # F8: 4 => CTR => F8: 6,8 * CNT 32 HDP CHAINS / 61 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B9,E2,E8,E9,F6,G4,G6,G7,G8,H6,I1,I3,I4,I5) * ...9......6.7....4...81.7...2.581.4....4.....4.569...2.4.35..299532...17...1.9435 * PAIR B3: 3,9 COL B B5: 3,9,1,8 # reduction candidate for 3,9 B5: 1,8 => SOLVED * 734926581861735294592814763327581946619472358485693172146357829953248617278169435 * DURATION: 0:00:02.967441 START: 04:27:09.155998 END: 04:27:12.123439 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190311-absurd-base-pr-001.dot * REASONING * PRF # B5: 1,8 => SOL * STA B5: 1,8 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190311, absurd
Solution
position: 734926581861735294592814763327581946619472358485693172146357829953248617278169435 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 # B5: 3,9 => UNS * PRF # B5: 1,8 => SOL * PRF # E1: 2,3 => SOL * DIS # E1: 4,6 => CTR => E1: 2,3 * DIS # F1: 2,3 => CTR => F1: 4,5,6 * INC # F1: 4,5,6 => UNS * DIS # F2: 2,3 => CTR => F2: 5 * INC # F2: 5 => UNS * DIS # F3: 2,3 => CTR => F3: 4,5,6 * INC # F3: 4,5,6 => UNS * INC # A2: 2,3 => UNS * INC # G2: 2,3 => UNS * DIS # E5: 2,3 => CTR => E5: 7 * PRF # E5: 7 => SOL * INC # A1: 1,8 => UNS * DIS # B1: 1,8 => CTR => B1: 3,7 * INC # B1: 3,7 => UNS * INC # C1: 1,8 => UNS * INC # F3: 3,6 => UNS * INC # F3: 2,4,5 => UNS * INC # E5: 3,7 => UNS * DIS # F5: 3,7 => CTR => F5: 2 * INC # F5: 2 => UNS * PRF # G5: 3,9 => SOL * INC # G5: 1,5 => UNS * DIS # G2: 3,9 => CTR => G2: 1,2,5 * INC # G2: 1,2,5 => UNS * INC # A4: 3,6 => UNS * DIS # A4: 7 => CTR => A4: 3,6 * INC # A5: 1,8 => UNS * PRF # B5: 1,8 => SOL * INC # B5: 3,9 => UNS * INC # C5: 1,8 => UNS * PRF # G5: 1,3 => SOL * INC # G5: 5,9 => UNS * DIS # B6: 1,3 => CTR => B6: 8 * PRF # B6: 8 => SOL * INC # G1: 1,3 => UNS * INC # G2: 1,3 => UNS * DIS # H5: 7,8 => CTR => H5: 5,6,9 * PRF # H5: 5,6,9 => SOL * DIS # A9: 7,8 => CTR => A9: 2,6 * INC # A9: 2,6 => UNS * PRF # C9: 7,8 => SOL * INC # C9: 2,6 => UNS * DIS # B1: 7,8 => CTR => B1: 1,3 * PRF # B1: 1,3 => SOL * DIS # F8: 4,6 => CTR => F8: 8 * INC # F8: 8 => UNS * DIS # E1: 4,6 => CTR => E1: 2,3 * PRF # E1: 2,3 => SOL * INC # F7: 6,7 => UNS * DIS # F7: 8 => CTR => F7: 6,7 * DIS # A9: 6,7 => CTR => A9: 2,8 * INC # A9: 2,8 => UNS * DIS # C9: 6,7 => CTR => C9: 2,8 * INC # C9: 2,8 => UNS * DIS # F7: 6,8 => CTR => F7: 7 * PRF # F7: 7 => SOL * INC # F8: 6,8 => UNS * DIS # F8: 4 => CTR => F8: 6,8 * CNT 61 HDP CHAINS / 61 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B5: 3,9 => UNS * PRF # B5: 1,8 => SOL * STA B5: 1,8 * CNT 2 HDP CHAINS / 2 HYP OPENED