Analysis of zz-www.sudokuoftheday.co.uk-20190215-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019
level: medium
position: 5.4.9.....3...192..1...5.....1..3.587.....1.........3.37..5...21...6.....6.3.954. initial
Autosolve
position: 5.4.9.....3...192591..35.....1..3.587.3...1.........3.379.5...2145.6.....6.3.954. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C3: 6,7 => CTR => C3: 2,8 * PRF # B6: 2,8 => SOL * DIS # C2: 6,8 => CTR => C2: 7 * PRF # C3: 6,8 => SOL * DIS # D2: 6,8 => CTR => D2: 4,7 * DIS # B6: 2,9 => CTR => B6: 5,8 * DIS # I5: 6,9 => CTR => I5: 4 * PRF # D5: 6,9 => SOL * DIS # C6: 2,8 => CTR => C6: 6 * DIS # D7: 4,8 => CTR => D7: 1 * DIS # F6: 4,8 => CTR => F6: 6,7 * DIS # E6: 2,4,8 => CTR => E6: 1,7 * DIS # H7: 1 => CTR => H7: 6,8 * DIS # G3: 6,8 => CTR => G3: 4,7 * DIS # I1: 1,7 => CTR => I1: 3,6 * CNT 15 HDP CHAINS / 42 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C3: 6,7 => CTR => C3: 2,8 * PRF C3: 2,8 # B6: 2,8 => SOL * STA C3: 2,8 + B6: 2,8 * CNT 2 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 5.4.9.....3...192..1...5.....1..3.587.....1.........3.37..5...21...6.....6.3.954. | initial |
| 5.4.9.....3...192591..35.....1..3.587.3...1.........3.379.5...2145.6.....6.3.954. | autosolve |
| 524796813637481925918235476291643758753928164486517239379154682145862397862379541 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) B1: 2,8 A2: 6,8 B4: 2,9 H5: 6,9 A9: 2,8 C9: 2,8 F7: 4,8 E9: 1,7 G7: 6,8 I9: 1,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H1,I1: 1.. / H1 = 1 => 15 pairs (_) / I1 = 1 => 0 pairs (X) D6,E6: 1.. / D6 = 1 => 0 pairs (X) / E6 = 1 => 15 pairs (_) D7,E9: 1.. / D7 = 1 => 15 pairs (_) / E9 = 1 => 0 pairs (X) H7,I9: 1.. / H7 = 1 => 0 pairs (X) / I9 = 1 => 15 pairs (_) D7,H7: 1.. / D7 = 1 => 15 pairs (_) / H7 = 1 => 0 pairs (X) E9,I9: 1.. / E9 = 1 => 0 pairs (X) / I9 = 1 => 15 pairs (_) D6,D7: 1.. / D6 = 1 => 0 pairs (X) / D7 = 1 => 15 pairs (_) E6,E9: 1.. / E6 = 1 => 15 pairs (_) / E9 = 1 => 0 pairs (X) H1,H7: 1.. / H1 = 1 => 15 pairs (_) / H7 = 1 => 0 pairs (X) I1,I9: 1.. / I1 = 1 => 0 pairs (X) / I9 = 1 => 15 pairs (_) B1,C3: 2.. / B1 = 2 => 0 pairs (*) / C3 = 2 => 0 pairs (X) G4,G6: 2.. / G4 = 2 => 0 pairs (X) / G6 = 2 => 11 pairs (_) A9,C9: 2.. / A9 = 2 => 11 pairs (_) / C9 = 2 => 0 pairs (*) D8,F8: 2.. / D8 = 2 => 0 pairs (X) / F8 = 2 => 11 pairs (_) C3,D3: 2.. / C3 = 2 => 11 pairs (_) / D3 = 2 => 0 pairs (*) B5,E5: 2.. / B5 = 2 => 0 pairs (X) / E5 = 2 => 11 pairs (_) F1,F8: 2.. / F1 = 2 => 0 pairs (X) / F8 = 2 => 11 pairs (_) G1,I1: 3.. / G1 = 3 => 18 pairs (_) / I1 = 3 => 15 pairs (_) G8,I8: 3.. / G8 = 3 => 15 pairs (_) / I8 = 3 => 18 pairs (_) G1,G8: 3.. / G1 = 3 => 18 pairs (_) / G8 = 3 => 15 pairs (_) I1,I8: 3.. / I1 = 3 => 15 pairs (_) / I8 = 3 => 18 pairs (_) D2,E2: 4.. / D2 = 4 => 12 pairs (_) / E2 = 4 => 0 pairs (X) G3,I3: 4.. / G3 = 4 => 11 pairs (_) / I3 = 4 => 0 pairs (X) A4,A6: 4.. / A4 = 4 => 11 pairs (_) / A6 = 4 => 11 pairs (_) D7,F7: 4.. / D7 = 4 => 0 pairs (X) / F7 = 4 => 11 pairs (_) B5,B6: 5.. / B5 = 5 => 0 pairs (*) / B6 = 5 => 0 pairs (X) D5,D6: 5.. / D5 = 5 => 10 pairs (_) / D6 = 5 => 0 pairs (*) B5,D5: 5.. / B5 = 5 => 0 pairs (*) / D5 = 5 => 0 pairs (X) B6,D6: 5.. / B6 = 5 => 10 pairs (_) / D6 = 5 => 0 pairs (*) G7,H7: 6.. / G7 = 6 => 10 pairs (_) / H7 = 6 => 14 pairs (_) C2,C3: 7.. / C2 = 7 => 11 pairs (_) / C3 = 7 => 0 pairs (X) E9,I9: 7.. / E9 = 7 => 15 pairs (_) / I9 = 7 => 0 pairs (X) A9,C9: 8.. / A9 = 8 => 0 pairs (*) / C9 = 8 => 0 pairs (X) H8,I8: 9.. / H8 = 9 => 18 pairs (_) / I8 = 9 => 16 pairs (_) B4,D4: 9.. / B4 = 9 => 16 pairs (_) / D4 = 9 => 0 pairs (X) H5,H8: 9.. / H5 = 9 => 16 pairs (_) / H8 = 9 => 18 pairs (_) * DURATION: 0:00:41.638523 START: 03:45:00.562275 END: 03:45:42.200798 2019-05-01 * CP COUNT: (36) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A9,B1,B4,C9,E9,F7,G7,H5,I9) * 5.4.9.....3...192591..35.....1..3.587.3...1.........3.379.5...2145.6.....6.3.954. * PAIR B1: 2,8 BLK 1 C3: 2,8,6,7 # reduction candidate for 2,8 C3: 6,7 => CTR * 524.9.....3...192591.235....91..3.5878352.1...5.9...3.379.5...2145.62....6.3.954. C3: 2,8 # 13 pairs * PAIR B1: 2,8 ROW 1 D1: 2,8,6,7 # reduction candidate for 2,8 D1: 2,8 # 13 pairs F1: 2,8,6,7 # reduction candidate for 2,8 F1: 2,8 # 12 pairs * PAIR B1: 2,8 COL B B5: 2,8,5,9 # reduction candidate for 2,8 B5: 2,8 # 15 pairs B6: 2,8,5,9 # reduction candidate for 2,8 B6: 2,8 => SOLVED * 524796813637481925918235476291643758753928164486517239379154682145862397862379541 B6: 5,9 # 11 pairs * PAIR A2: 6,8 BLK 1 C2: 6,8,7 # reduction candidate for 6,8 C2: 6,8 => CTR * 524.9.....3...1925917235....91.437587835261.........3.379.5...2145.62....6.3.954. C2: 7 # 11 pairs C3: 6,8,2,7 # reduction candidate for 6,8 C3: 6,8 => SOLVED * 524796813637481925918235476291643758753928164486517239379154682145862397862379541 C3: 2,7 # 11 pairs * PAIR A2: 6,8 ROW 2 D2: 6,8,4,7 # reduction candidate for 6,8 D2: 6,8 => CTR * 5.4.9..13.37.41925916235487691423758723586194458917236379154862145862379.6.379541 D2: 4,7 # 11 pairs * PAIR A2: 6,8 COL A A6: 6,8,2,4 # reduction candidate for 6,8 A6: 6,8 # 12 pairs A6: 2,4 # 11 pairs * PAIR B4: 2,9 BLK 4 B5: 2,9,5,8 # reduction candidate for 2,9 B5: 2,9 # 12 pairs B6: 2,9,5,8 # reduction candidate for 2,9 B6: 2,9 => CTR * 584.9..1.637.81925912.35.....1.43.58753.2.1.44..51..3.379154..2145.6.....6.379541 B6: 5,8 # 11 pairs * PAIR H5: 6,9 BLK 6 I5: 6,9,4 # reduction candidate for 6,9 I5: 6,9 => CTR * 58429..1.637481925912.35...4916237587235481..856917234379154..21458623..268379541 I5: 4 # 13 pairs I6: 6,9,4,7 # reduction candidate for 6,9 I6: 6,9 # 17 pairs * PAIR H5: 6,9 ROW 5 D5: 6,9,4,5,8 # reduction candidate for 6,9 D5: 6,9 => SOLVED * 524796813637481925918235476291643758753928164486517239379154682145862397862379541 D5: 4,5,8 # 10 pairs * PAIR A9: 2,8 COL A A6: 2,8,4,6 # reduction candidate for 2,8 A6: 2,8 # 12 pairs A6: 4,6 # 11 pairs * PAIR C9: 2,8 COL C C3: 2,8,6,7 # reduction candidate for 2,8 C3: 2,8 # 13 pairs C6: 2,8,6 # reduction candidate for 2,8 C6: 2,8 => CTR * 524.9...183...192591.235....91..325878352.1...52.8..3.379.5...2145.62...268319547 C6: 6 # 11 pairs * PAIR F7: 4,8 BLK 8 D7: 4,8,1 # reduction candidate for 4,8 D7: 4,8 => CTR * 584692371637481925912735486.219.3758793528164.581.6.39379854612145.6.893.6.319547 D7: 1 # 15 pairs * PAIR F7: 4,8 COL F F5: 4,8,6 # reduction candidate for 4,8 F5: 4,8 # 13 pairs F6: 4,8,6,7 # reduction candidate for 4,8 F6: 4,8 => CTR * 5.4.97.13.37.8192591..354.7..1.43.5878352619445.918736379154..2145862379862379541 F6: 6,7 # 11 pairs * PAIR E9: 1,7 COL E E6: 1,7,2,4,8 # reduction candidate for 1,7 E6: 2,4,8 => CTR * 5.4.9.3.1.3...192591..35.....19.3.58793528164.5.146739379854612145.6.893.6.319547 E6: 1,7 # 13 pairs * PAIR G7: 6,8 BLK 9 H7: 6,8,1 # reduction candidate for 6,8 H7: 1 => CTR * 584692371637481925912735486.219.3758793528164.581.6.39379854612145.6.893.6.319547 H7: 6,8 # 15 pairs * PAIR G7: 6,8 COL G G1: 6,8,3,7 # reduction candidate for 6,8 G1: 6,8 # 17 pairs G3: 6,8,4,7 # reduction candidate for 6,8 G3: 6,8 => CTR * 5.4.9..1..3...192591..35..4..1.234587235..1..458916237379154..2145862....6.3.954. G3: 4,7 # 11 pairs * PAIR I9: 1,7 COL I I1: 1,7,3,6 # reduction candidate for 1,7 I1: 1,7 => CTR * 584692371637481925912735486.219.3758793528164.581.6.39379854612145.6.893.6.319547 I1: 3,6 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190215-absurd-base-pr-000.dot * REASONING * DIS # C3: 6,7 => CTR => C3: 2,8 * PRF # B6: 2,8 => SOL * DIS # C2: 6,8 => CTR => C2: 7 * PRF # C3: 6,8 => SOL * DIS # D2: 6,8 => CTR => D2: 4,7 * DIS # B6: 2,9 => CTR => B6: 5,8 * DIS # I5: 6,9 => CTR => I5: 4 * PRF # D5: 6,9 => SOL * DIS # C6: 2,8 => CTR => C6: 6 * DIS # D7: 4,8 => CTR => D7: 1 * DIS # F6: 4,8 => CTR => F6: 6,7 * DIS # E6: 2,4,8 => CTR => E6: 1,7 * DIS # H7: 1 => CTR => H7: 6,8 * DIS # G3: 6,8 => CTR => G3: 4,7 * DIS # I1: 1,7 => CTR => I1: 3,6 * CNT 15 HDP CHAINS / 42 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A9,B1,B4,C9,E9,F7,G7,H5,I9) * 5.4.9.....3...192591..35.....1..3.587.3...1.........3.379.5...2145.6.....6.3.954. * PAIR B1: 2,8 BLK 1 C3: 2,8,6,7 # reduction candidate for 2,8 C3: 6,7 => CTR * 524.9.....3...192591.235....91..3.5878352.1...5.9...3.379.5...2145.62....6.3.954. * PAIR B1: 2,8 COL B B5: 2,8,5,9 # reduction candidate for 2,8 B5: 2,8 # 21 pairs B6: 2,8,5,9 # reduction candidate for 2,8 B6: 2,8 => SOLVED * 524796813637481925918235476291643758753928164486517239379154682145862397862379541 * DURATION: 0:00:03.514620 START: 03:46:07.888823 END: 03:46:11.403443 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190215-absurd-base-pr-001.dot * REASONING * DIS # C3: 6,7 => CTR => C3: 2,8 * PRF C3: 2,8 # B6: 2,8 => SOL * STA C3: 2,8 + B6: 2,8 * CNT 2 HDP CHAINS / 4 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190215, absurd
Solution
position: 524796813637481925918235476291643758753928164486517239379154682145862397862379541 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 # C3: 2,8 => UNS * DIS # C3: 6,7 => CTR => C3: 2,8 * INC # D1: 2,8 => UNS * INC # F1: 2,8 => UNS * INC # B5: 2,8 => UNS * PRF # B6: 2,8 => SOL * INC # B6: 5,9 => UNS * DIS # C2: 6,8 => CTR => C2: 7 * INC # C2: 7 => UNS * PRF # C3: 6,8 => SOL * INC # C3: 2,7 => UNS * DIS # D2: 6,8 => CTR => D2: 4,7 * INC # D2: 4,7 => UNS * INC # A6: 6,8 => UNS * INC # A6: 2,4 => UNS * INC # B5: 2,9 => UNS * DIS # B6: 2,9 => CTR => B6: 5,8 * INC # B6: 5,8 => UNS * DIS # I5: 6,9 => CTR => I5: 4 * INC # I5: 4 => UNS * INC # I6: 6,9 => UNS * PRF # D5: 6,9 => SOL * INC # D5: 4,5,8 => UNS * INC # A6: 2,8 => UNS * INC # A6: 4,6 => UNS * INC # C3: 2,8 => UNS * DIS # C6: 2,8 => CTR => C6: 6 * INC # C6: 6 => UNS * DIS # D7: 4,8 => CTR => D7: 1 * INC # D7: 1 => UNS * INC # F5: 4,8 => UNS * DIS # F6: 4,8 => CTR => F6: 6,7 * INC # F6: 6,7 => UNS * INC # E6: 1,7 => UNS * DIS # E6: 2,4,8 => CTR => E6: 1,7 * INC # H7: 6,8 => UNS * DIS # H7: 1 => CTR => H7: 6,8 * INC # G1: 6,8 => UNS * DIS # G3: 6,8 => CTR => G3: 4,7 * INC # G3: 4,7 => UNS * DIS # I1: 1,7 => CTR => I1: 3,6 * INC # I1: 3,6 => UNS * CNT 42 HDP CHAINS / 42 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C3: 2,8 => UNS * DIS # C3: 6,7 => CTR => C3: 2,8 * INC C3: 2,8 # B5: 2,8 => UNS * PRF C3: 2,8 # B6: 2,8 => SOL * STA C3: 2,8 + B6: 2,8 * CNT 4 HDP CHAINS / 4 HYP OPENED