Analysis of zz-www.sudokuoftheday.co.uk-20190113-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019
level: medium
position: ...7...54....5..2.354..18.69......6.7.53..4..2.619.7....1.3.......5..2.....4.8..7 initial
Autosolve
position: ...7.3.54..7.54.2.3549218769...47.6.7.53..4..2461957...71.3.......57.2.....418..7 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B1: 6,8 => SOL * DIS # G2: 1,9 => CTR => G2: 3 * PRF # B4: 3,8 => SOL * DIS # B4: 1 => CTR => B4: 3,8 * DIS # C8: 9 => CTR => C8: 3,8 * PRF # B4: 3 => SOL * DIS # F7: 9 => CTR => F7: 2,6 * PRF # I4: 1,5 => SOL * DIS # I4: 2 => CTR => I4: 1,5 * DIS # I5: 1,9 => CTR => I5: 2 * PRF # I5: 2 => SOL * DIS # H8: 3,4,8 => CTR => H8: 1,9 * DIS # H8: 3,8 => CTR => H8: 1,4,9 * DIS # A7: 5,6 => CTR => A7: 4,8 * DIS # G9: 3,9 => CTR => G9: 5,6 * DIS # F7: 9 => CTR => F7: 2,6 * DIS # F7: 6,9 => CTR => F7: 2 * PRF # F7: 2 => SOL * DIS # H8: 3,9 => CTR => H8: 1,4,8 * DIS # I8: 3,9 => CTR => I8: 1,8 * DIS # G9: 3,9 => CTR => G9: 5,6 * CNT 21 HDP CHAINS / 44 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # B1: 6,8 => SOL * STA B1: 6,8 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...7...54....5..2.354..18.69......6.7.53..4..2.619.7....1.3.......5..2.....4.8..7 | initial |
| ...7.3.54..7.54.2.3549218769...47.6.7.53..4..2461957...71.3.......57.2.....418..7 | autosolve |
| 182763954697854321354921876938247165715386492246195783871632549463579218529418637 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) E1: 6,8 D2: 6,8 G1: 1,9 C4: 3,8 B5: 1,8 D4: 2,8 E5: 6,8 F5: 2,6 G4: 1,5 H5: 1,9 H6: 3,8 I6: 3,8 A9: 5,6 D7: 2,6 F8: 6,9 H9: 3,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,A2: 1.. / A1 = 1 => 20 pairs (_) / A2 = 1 => 26 pairs (_) B4,B5: 1.. / B4 = 1 => 0 pairs (X) / B5 = 1 => 0 pairs (_) H8,I8: 1.. / H8 = 1 => 16 pairs (_) / I8 = 1 => 0 pairs (X) A1,G1: 1.. / A1 = 1 => 20 pairs (_) / G1 = 1 => 26 pairs (_) H5,H8: 1.. / H5 = 1 => 0 pairs (X) / H8 = 1 => 16 pairs (_) B1,C1: 2.. / B1 = 2 => 17 pairs (_) / C1 = 2 => 19 pairs (_) D4,F5: 2.. / D4 = 2 => 0 pairs (*) / F5 = 2 => 0 pairs (X) I4,I5: 2.. / I4 = 2 => 0 pairs (X) / I5 = 2 => 0 pairs (_) B9,C9: 2.. / B9 = 2 => 19 pairs (_) / C9 = 2 => 17 pairs (_) D7,F7: 2.. / D7 = 2 => 0 pairs (X) / F7 = 2 => 0 pairs (_) D4,I4: 2.. / D4 = 2 => 0 pairs (*) / I4 = 2 => 0 pairs (X) F5,I5: 2.. / F5 = 2 => 0 pairs (X) / I5 = 2 => 0 pairs (_) B1,B9: 2.. / B1 = 2 => 17 pairs (_) / B9 = 2 => 19 pairs (_) C1,C9: 2.. / C1 = 2 => 19 pairs (_) / C9 = 2 => 17 pairs (_) D4,D7: 2.. / D4 = 2 => 0 pairs (*) / D7 = 2 => 0 pairs (X) F5,F7: 2.. / F5 = 2 => 0 pairs (X) / F7 = 2 => 0 pairs (_) G2,I2: 3.. / G2 = 3 => 17 pairs (_) / I2 = 3 => 0 pairs (X) B4,C4: 3.. / B4 = 3 => 0 pairs (*) / C4 = 3 => 0 pairs (X) H6,I6: 3.. / H6 = 3 => 0 pairs (X) / I6 = 3 => 16 pairs (_) G2,G9: 3.. / G2 = 3 => 17 pairs (_) / G9 = 3 => 0 pairs (X) A7,A8: 4.. / A7 = 4 => 0 pairs (X) / A8 = 4 => 16 pairs (_) H7,H8: 4.. / H7 = 4 => 16 pairs (_) / H8 = 4 => 0 pairs (X) A7,H7: 4.. / A7 = 4 => 0 pairs (X) / H7 = 4 => 16 pairs (_) A8,H8: 4.. / A8 = 4 => 16 pairs (_) / H8 = 4 => 0 pairs (X) G4,I4: 5.. / G4 = 5 => 21 pairs (_) / I4 = 5 => 0 pairs (*) A7,A9: 5.. / A7 = 5 => 0 pairs (X) / A9 = 5 => 15 pairs (_) A9,G9: 5.. / A9 = 5 => 15 pairs (_) / G9 = 5 => 0 pairs (X) I4,I7: 5.. / I4 = 5 => 0 pairs (*) / I7 = 5 => 0 pairs (X) E1,D2: 6.. / E1 = 6 => 0 pairs (*) / D2 = 6 => 0 pairs (X) E5,F5: 6.. / E5 = 6 => 0 pairs (X) / F5 = 6 => 0 pairs (_) G7,G9: 6.. / G7 = 6 => 0 pairs (X) / G9 = 6 => 17 pairs (_) D2,D7: 6.. / D2 = 6 => 0 pairs (X) / D7 = 6 => 0 pairs (_) E1,E5: 6.. / E1 = 6 => 0 pairs (*) / E5 = 6 => 0 pairs (X) E1,D2: 8.. / E1 = 8 => 0 pairs (X) / D2 = 8 => 0 pairs (_) D4,E5: 8.. / D4 = 8 => 0 pairs (X) / E5 = 8 => 0 pairs (_) H6,I6: 8.. / H6 = 8 => 16 pairs (_) / I6 = 8 => 0 pairs (X) B5,E5: 8.. / B5 = 8 => 0 pairs (X) / E5 = 8 => 0 pairs (_) D2,D4: 8.. / D2 = 8 => 0 pairs (*) / D4 = 8 => 0 pairs (X) E1,E5: 8.. / E1 = 8 => 0 pairs (X) / E5 = 8 => 0 pairs (_) H5,I5: 9.. / H5 = 9 => 16 pairs (_) / I5 = 9 => 0 pairs (X) F7,F8: 9.. / F7 = 9 => 0 pairs (X) / F8 = 9 => 22 pairs (_) * DURATION: 0:00:51.378264 START: 02:55:01.393402 END: 02:55:52.771666 2019-05-01 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B5,C4,D2,D4,D7,E1,E5,F5,F8,G1,G4,H5,H6,H9,I6) * ...7.3.54..7.54.2.3549218769...47.6.7.53..4..2461957...71.3.......57.2.....418..7 * PAIR E1: 6,8 ROW 1 A1: 6,8,1 # reduction candidate for 6,8 A1: 6,8 # 26 pairs B1: 6,8,2,9 # reduction candidate for 6,8 B1: 6,8 => SOLVED * 182763954697854321354921876938247165715386492246195783871632549463579218529418637 B1: 2,9 # 17 pairs * PAIR D2: 6,8 ROW 2 A2: 6,8,1 # reduction candidate for 6,8 A2: 6,8 # 20 pairs B2: 6,8,9 # reduction candidate for 6,8 B2: 6,8 # 26 pairs * PAIR G1: 1,9 BLK 3 G2: 1,9,3 # reduction candidate for 1,9 G2: 1,9 => CTR * .2.7.3.54..7654.23354921876913847562785362419246195738.712396.5.395762.1562418397 G2: 3 # 17 pairs I2: 1,9,3 # reduction candidate for 1,9 I2: 1,9 # 17 pairs * PAIR C4: 3,8 BLK 4 B4: 3,8,1 # reduction candidate for 3,8 B4: 3,8 => SOLVED * 182763954697854321354921876938247165715386492246195783871632549463579218529418637 B4: 1 => CTR * 162783954897654123354921876913847562785362419246195738471239685..857.2415..418..7 * PAIR C4: 3,8 COL C C8: 3,8,9 # reduction candidate for 3,8 C8: 9 => CTR * ...7.3.54..7654.2.3549218769..847.627853624..2461957...71239..5.395762..5.2418..7 C8: 3,8 # 19 pairs * PAIR B5: 1,8 BLK 4 B4: 1,8,3 # reduction candidate for 1,8 B4: 3 => SOLVED * 182763954697854321354921876938247165715386492246195783871632549463579218529418637 B4: 1,8 # 19 pairs * PAIR F5: 2,6 COL F F7: 2,6,9 # reduction candidate for 2,6 F7: 9 => CTR * ...783.54897654.2.3549218769138475627853624..2461957...712396854..5762..5..418..7 F7: 2,6 # 22 pairs * PAIR G4: 1,5 BLK 6 I4: 1,5,2 # reduction candidate for 1,5 I4: 1,5 => SOLVED * 182763954697854321354921876938247165715386492246195783871632549463579218529418637 I4: 2 => CTR * ...783.54897654.2.3549218769138475627853624..2461957...7123..85..857.2415.9418.37 * PAIR H5: 1,9 BLK 6 I5: 1,9,2 # reduction candidate for 1,9 I5: 1,9 => CTR * ...783.54897654.2.3549218769138475627853624..2461957...7123..85..857.2415.9418.37 I5: 2 => SOLVED * 182763954697854321354921876938247165715386492246195783871632549463579218529418637 * PAIR H5: 1,9 COL H H8: 1,9,3,4,8 # reduction candidate for 1,9 H8: 3,4,8 => CTR * ...783.548.7654123354921876913847562785362419246195738.71239685.3.57.2.15..418397 H8: 1,9 # 16 pairs * PAIR H6: 3,8 COL H H8: 3,8,1,4,9 # reduction candidate for 3,8 H8: 3,8 => CTR * ...7.3.54..7.54.23354921876913847562785362419246195738871239645439576281562418397 H8: 1,4,9 # 16 pairs * PAIR I6: 3,8 COL I I8: 3,8,1,9 # reduction candidate for 3,8 I8: 3,8 # 20 pairs I8: 1,9 # 17 pairs * PAIR A9: 5,6 BLK 7 A7: 5,6,4,8 # reduction candidate for 5,6 A7: 5,6 => CTR * ...7.3.54..7.54.2.3549218769...47.657.53..4.2246195783.71.329484..5792.1...418..7 A7: 4,8 # 16 pairs * PAIR A9: 5,6 ROW 9 G9: 5,6,3,9 # reduction candidate for 5,6 G9: 3,9 => CTR * 62.783154..7654.2.3549218769..8475627853624..2461957...712396.5...5762..562418..7 G9: 5,6 # 18 pairs * PAIR D7: 2,6 BLK 8 F7: 2,6,9 # reduction candidate for 2,6 F7: 9 => CTR * ...783.54897654.2.3549218769138475627853624..2461957...712396854..5762..5..418..7 F7: 2,6 # 22 pairs * PAIR F8: 6,9 BLK 8 F7: 6,9,2 # reduction candidate for 6,9 F7: 6,9 => CTR * ...783.54897654.2.3549218769138475627853624..2461957...7123..85..857.2415.9418.37 F7: 2 => SOLVED * 182763954697854321354921876938247165715386492246195783871632549463579218529418637 * PAIR F8: 6,9 ROW 8 B8: 6,9,3,8 # reduction candidate for 6,9 B8: 6,9 # 21 pairs B8: 3,8 # 18 pairs * PAIR H9: 3,9 BLK 9 H8: 3,9,1,4,8 # reduction candidate for 3,9 H8: 3,9 => CTR * ...7.3.54..7.54.2335492187691384756.7.53..4192461957...71.3..4.4..57.2.1...418..7 H8: 1,4,8 # 16 pairs I8: 3,9,1,8 # reduction candidate for 3,9 I8: 3,9 => CTR * ...7.3.54..7.5432.3549218769...47.657.53..492246195783.71.329484..57.21....418.37 I8: 1,8 # 17 pairs G9: 3,9,5,6 # reduction candidate for 3,9 G9: 3,9 => CTR * 62.783154..7654.2.3549218769..8475627853624..2461957...712396.5...5762..562418..7 G9: 5,6 # 18 pairs * PAIR H9: 3,9 ROW 9 B9: 3,9,2,6 # reduction candidate for 3,9 B9: 3,9 # 20 pairs C9: 3,9,2 # reduction candidate for 3,9 C9: 3,9 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190113-absurd-base-pr-000.dot * REASONING * PRF # B1: 6,8 => SOL * DIS # G2: 1,9 => CTR => G2: 3 * PRF # B4: 3,8 => SOL * DIS # B4: 1 => CTR => B4: 3,8 * DIS # C8: 9 => CTR => C8: 3,8 * PRF # B4: 3 => SOL * DIS # F7: 9 => CTR => F7: 2,6 * PRF # I4: 1,5 => SOL * DIS # I4: 2 => CTR => I4: 1,5 * DIS # I5: 1,9 => CTR => I5: 2 * PRF # I5: 2 => SOL * DIS # H8: 3,4,8 => CTR => H8: 1,9 * DIS # H8: 3,8 => CTR => H8: 1,4,9 * DIS # A7: 5,6 => CTR => A7: 4,8 * DIS # G9: 3,9 => CTR => G9: 5,6 * DIS # F7: 9 => CTR => F7: 2,6 * DIS # F7: 6,9 => CTR => F7: 2 * PRF # F7: 2 => SOL * DIS # H8: 3,9 => CTR => H8: 1,4,8 * DIS # I8: 3,9 => CTR => I8: 1,8 * DIS # G9: 3,9 => CTR => G9: 5,6 * CNT 21 HDP CHAINS / 44 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B5,C4,D2,D4,D7,E1,E5,F5,F8,G1,G4,H5,H6,H9,I6) * ...7.3.54..7.54.2.3549218769...47.6.7.53..4..2461957...71.3.......57.2.....418..7 * PAIR E1: 6,8 ROW 1 A1: 6,8,1 # reduction candidate for 6,8 A1: 6,8 # 26 pairs B1: 6,8,2,9 # reduction candidate for 6,8 B1: 6,8 => SOLVED * 182763954697854321354921876938247165715386492246195783871632549463579218529418637 * DURATION: 0:00:02.242916 START: 02:56:22.179812 END: 02:56:24.422728 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190113-absurd-base-pr-001.dot * REASONING * PRF # B1: 6,8 => SOL * STA B1: 6,8 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190113, absurd
Solution
position: 182763954697854321354921876938247165715386492246195783871632549463579218529418637 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 # A1: 6,8 => UNS * PRF # B1: 6,8 => SOL * INC # B1: 2,9 => UNS * INC # A2: 6,8 => UNS * INC # B2: 6,8 => UNS * DIS # G2: 1,9 => CTR => G2: 3 * INC # G2: 3 => UNS * INC # I2: 1,9 => UNS * PRF # B4: 3,8 => SOL * DIS # B4: 1 => CTR => B4: 3,8 * INC # C8: 3,8 => UNS * DIS # C8: 9 => CTR => C8: 3,8 * INC # B4: 1,8 => UNS * PRF # B4: 3 => SOL * INC # F7: 2,6 => UNS * DIS # F7: 9 => CTR => F7: 2,6 * PRF # I4: 1,5 => SOL * DIS # I4: 2 => CTR => I4: 1,5 * DIS # I5: 1,9 => CTR => I5: 2 * PRF # I5: 2 => SOL * INC # H8: 1,9 => UNS * DIS # H8: 3,4,8 => CTR => H8: 1,9 * DIS # H8: 3,8 => CTR => H8: 1,4,9 * INC # H8: 1,4,9 => UNS * INC # I8: 3,8 => UNS * INC # I8: 1,9 => UNS * DIS # A7: 5,6 => CTR => A7: 4,8 * INC # A7: 4,8 => UNS * INC # G9: 5,6 => UNS * DIS # G9: 3,9 => CTR => G9: 5,6 * INC # F7: 2,6 => UNS * DIS # F7: 9 => CTR => F7: 2,6 * DIS # F7: 6,9 => CTR => F7: 2 * PRF # F7: 2 => SOL * INC # B8: 6,9 => UNS * INC # B8: 3,8 => UNS * DIS # H8: 3,9 => CTR => H8: 1,4,8 * INC # H8: 1,4,8 => UNS * DIS # I8: 3,9 => CTR => I8: 1,8 * INC # I8: 1,8 => UNS * DIS # G9: 3,9 => CTR => G9: 5,6 * INC # G9: 5,6 => UNS * INC # B9: 3,9 => UNS * INC # C9: 3,9 => UNS * CNT 44 HDP CHAINS / 44 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 6,8 => UNS * PRF # B1: 6,8 => SOL * STA B1: 6,8 * CNT 2 HDP CHAINS / 2 HYP OPENED