Analysis of zz-www.sudokuoftheday.co.uk-20060608-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006
level: medium
position: .7..9....9...2576...1...3.....6.....1.52...8..4..8......84..9166...3..7..2....... initial
Autosolve
position: .7..9....9...2576...1...3.....6.....1.52...8..4..8......84.291661..3..7..2....... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 3,8 => CTR => A1: 2,4,5 * DIS # D2: 3,8 => CTR => D2: 1 * DIS # B4: 3,8 => CTR => B4: 9 * DIS # C1: 3,4 => CTR => C1: 2,6 * PRF # E4: 4,7 => SOL * DIS # F5: 4,7 => CTR => F5: 3,9 * DIS # I5: 4,7 => CTR => I5: 3,9 * DIS # E3: 4,7 => CTR => E3: 6 * PRF # E3: 6 => SOL * DIS # A7: 3,5 => CTR => A7: 7 * PRF # A7: 7 => SOL * DIS # C9: 7 => CTR => C9: 4,9 * DIS # E9: 5,7 => CTR => E9: 1,6 * PRF # A7: 5,7 => SOL * DIS # A7: 3 => CTR => A7: 5,7 * DIS # E4: 5,7 => CTR => E4: 1,4 * PRF # E4: 1,4 => SOL * DIS # D9: 8,9 => CTR => D9: 1,5,7 * DIS # F9: 8,9 => CTR => F9: 1,6,7 * CNT 19 HDP CHAINS / 38 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 3,8 => CTR => A1: 2,4,5 * DIS A1: 2,4,5 # D2: 3,8 => CTR => D2: 1 * DIS A1: 2,4,5 + D2: 1 # B4: 3,8 => CTR => B4: 9 * DIS A1: 2,4,5 + D2: 1 + B4: 9 # F3: 4,6 => CTR => F3: 7,8 * DIS A1: 2,4,5 + D2: 1 + B4: 9 + F3: 7,8 # D9: 5,9 => CTR => D9: 7,8 * PRF A1: 2,4,5 + D2: 1 + B4: 9 + F3: 7,8 + D9: 7,8 # E4: 4,7 => SOL * STA A1: 2,4,5 + D2: 1 + B4: 9 + F3: 7,8 + D9: 7,8 + E4: 4,7 * CNT 6 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .7..9....9...2576...1...3.....6.....1.52...8..4..8......84..9166...3..7..2....... | initial |
| .7..9....9...2576...1...3.....6.....1.52...8..4..8......84.291661..3..7..2....... | autosolve |
| 276394158983125764451867392892641537165273489347589621738452916614938275529716843 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) B2: 3,8 C2: 3,4 D3: 7,8 E5: 4,7 G5: 4,6 B7: 3,5 C8: 4,9 E7: 5,7 F8: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D2,I2: 1.. / D2 = 1 => 13 pairs (_) / I2 = 1 => 0 pairs (X) E4,E9: 1.. / E4 = 1 => 0 pairs (X) / E9 = 1 => 0 pairs (_) G8,I8: 2.. / G8 = 2 => 9 pairs (_) / I8 = 2 => 9 pairs (_) A7,B7: 3.. / A7 = 3 => 0 pairs (X) / B7 = 3 => 0 pairs (_) H9,I9: 3.. / H9 = 3 => 9 pairs (_) / I9 = 3 => 10 pairs (_) C2,I2: 4.. / C2 = 4 => 0 pairs (X) / I2 = 4 => 14 pairs (_) E4,D6: 5.. / E4 = 5 => 0 pairs (X) / D6 = 5 => 0 pairs (_) B3,B7: 5.. / B3 = 5 => 0 pairs (*) / B7 = 5 => 0 pairs (X) C1,B3: 6.. / C1 = 6 => 0 pairs (*) / B3 = 6 => 0 pairs (X) B5,C6: 6.. / B5 = 6 => 0 pairs (*) / C6 = 6 => 0 pairs (X) G5,G6: 6.. / G5 = 6 => 0 pairs (X) / G6 = 6 => 0 pairs (_) E9,F9: 6.. / E9 = 6 => 0 pairs (X) / F9 = 6 => 0 pairs (_) C1,F1: 6.. / C1 = 6 => 0 pairs (*) / F1 = 6 => 0 pairs (X) B5,G5: 6.. / B5 = 6 => 0 pairs (*) / G5 = 6 => 0 pairs (X) C6,G6: 6.. / C6 = 6 => 0 pairs (X) / G6 = 6 => 0 pairs (_) B3,B5: 6.. / B3 = 6 => 0 pairs (X) / B5 = 6 => 0 pairs (_) C1,C6: 6.. / C1 = 6 => 0 pairs (*) / C6 = 6 => 0 pairs (X) E3,E9: 6.. / E3 = 6 => 0 pairs (*) / E9 = 6 => 0 pairs (X) A7,E7: 7.. / A7 = 7 => 0 pairs (*) / E7 = 7 => 0 pairs (X) A4,B4: 8.. / A4 = 8 => 10 pairs (_) / B4 = 8 => 0 pairs (X) H3,I3: 9.. / H3 = 9 => 9 pairs (_) / I3 = 9 => 9 pairs (_) B4,B5: 9.. / B4 = 9 => 10 pairs (_) / B5 = 9 => 0 pairs (X) C8,C9: 9.. / C8 = 9 => 0 pairs (X) / C9 = 9 => 16 pairs (_) * DURATION: 0:00:23.260523 START: 23:42:40.349334 END: 23:43:03.609857 2019-04-30 * CP COUNT: (23) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B7,C2,C8,D3,E5,E7,F8,G5) * .7..9....9...2576...1...3.....6.....1.52...8..4..8......84.291661..3..7..2....... * PAIR B2: 3,8 BLK 1 A1: 3,8,2,4,5 # reduction candidate for 3,8 A1: 3,8 => CTR * .7..9....9.4.2576...1...3.....65....1.524.68..46.8......8472916619538.7.427.16... A1: 2,4,5 # 9 pairs * PAIR B2: 3,8 ROW 2 D2: 3,8,1 # reduction candidate for 3,8 D2: 3,8 => CTR * .7..9....9.4.25761..1...3.....65....1.524.68..46.8......8472916619538.7.427.16... D2: 1 # 13 pairs * PAIR B2: 3,8 COL B B4: 3,8,9 # reduction candidate for 3,8 B4: 3,8 => CTR * .7..96...9...2576..61...3.....6.....1952..68..46.8.....5847291661..3..7..2..6.... B4: 9 # 10 pairs * PAIR C2: 3,4 BLK 1 A1: 3,4,2,5,8 # reduction candidate for 3,4 A1: 3,4 # 15 pairs C1: 3,4,2,6 # reduction candidate for 3,4 C1: 3,4 => CTR * .7..96...9...2576..61...3.....6.....1.52..68..46.8.....5847291661..3..7..2..6.... C1: 2,6 # 10 pairs * PAIR D3: 7,8 BLK 2 F3: 7,8,4,6 # reduction candidate for 7,8 F3: 7,8 # 17 pairs F3: 4,6 # 10 pairs * PAIR D3: 7,8 COL D D9: 7,8,1,5,9 # reduction candidate for 7,8 D9: 7,8 # 18 pairs D9: 1,5,9 # 9 pairs * PAIR E5: 4,7 BLK 5 E4: 4,7,1,5 # reduction candidate for 4,7 E4: 4,7 => SOLVED * 276394158983125764451867392892641537165273489347589621738452916614938275529716843 E4: 1,5 # 10 pairs F4: 4,7,1,3,9 # reduction candidate for 4,7 F4: 4,7 # 12 pairs F5: 4,7,3,9 # reduction candidate for 4,7 F5: 4,7 => CTR * .7..9....9...2576..61...3.....6.....1.52..68..46.8.....5847291661..3..7..2..6.... F5: 3,9 # 10 pairs * PAIR E5: 4,7 ROW 5 I5: 4,7,3,9 # reduction candidate for 4,7 I5: 4,7 => CTR * .7..9....9...2576..61...3.....6.....1.52..68..46.8.....5847291661..3..7..2..6.... I5: 3,9 # 10 pairs * PAIR E5: 4,7 COL E E3: 4,7,6 # reduction candidate for 4,7 E3: 4,7 => CTR * .76.9.1..98.125764.51.463..89.614...16527.48..4758.6.1738452916614.3..7.529.6.8.. E3: 6 => SOLVED * 276394158983125764451867392892641537165273489347589621738452916614938275529716843 * PAIR B7: 3,5 BLK 7 A7: 3,5,7 # reduction candidate for 3,5 A7: 3,5 => CTR * .7..96...9...2576...1...3.....6.....1.524.68..46.8......847291661..3..7..2....... A7: 7 => SOLVED * 276394158983125764451867392892641537165273489347589621738452916614938275529716843 * PAIR C8: 4,9 BLK 7 C9: 4,9,7 # reduction candidate for 4,9 C9: 7 => CTR * .7..9....9...2576...1...3.....65....1.524.68..46.8......8472916619538.7.427.16... C9: 4,9 # 18 pairs * PAIR E7: 5,7 BLK 8 D9: 5,7,1,8,9 # reduction candidate for 5,7 D9: 5,7 # 23 pairs E9: 5,7,1,6 # reduction candidate for 5,7 E9: 5,7 => CTR * .7..9....9...2576...1.6.3.....61....16524..8..4..8......84.291661..3..7..2....... E9: 1,6 # 10 pairs * PAIR E7: 5,7 ROW 7 A7: 5,7,3 # reduction candidate for 5,7 A7: 5,7 => SOLVED * 276394158983125764451867392892641537165273489347589621738452916614938275529716843 A7: 3 => CTR * .7..96...9...2576...1...3.....6.....1.524.68..46.8....35847291661..3..7..2....... * PAIR E7: 5,7 COL E E4: 5,7,1,4 # reduction candidate for 5,7 E4: 5,7 => CTR * .76.9....9...2576...1.6.3.....6.....16524..8..4..8......84.291661..3..7..2..16... E4: 1,4 => SOLVED * 276394158983125764451867392892641537165273489347589621738452916614938275529716843 * PAIR F8: 8,9 BLK 8 D8: 8,9,5 # reduction candidate for 8,9 D8: 8,9 # 23 pairs D9: 8,9,1,5,7 # reduction candidate for 8,9 D9: 8,9 => CTR * .76.9....9...2576...1.6.3.....65....16524..8..4..8......847291661.53..7..2..16... D9: 1,5,7 # 9 pairs F9: 8,9,1,6,7 # reduction candidate for 8,9 F9: 8,9 => CTR * .7..9....9...2576...1...3.....61....1.52...8..4.58......845291661..3..7.52..6.... F9: 1,6,7 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060608-absurd-base-pr-000.dot * REASONING * DIS # A1: 3,8 => CTR => A1: 2,4,5 * DIS # D2: 3,8 => CTR => D2: 1 * DIS # B4: 3,8 => CTR => B4: 9 * DIS # C1: 3,4 => CTR => C1: 2,6 * PRF # E4: 4,7 => SOL * DIS # F5: 4,7 => CTR => F5: 3,9 * DIS # I5: 4,7 => CTR => I5: 3,9 * DIS # E3: 4,7 => CTR => E3: 6 * PRF # E3: 6 => SOL * DIS # A7: 3,5 => CTR => A7: 7 * PRF # A7: 7 => SOL * DIS # C9: 7 => CTR => C9: 4,9 * DIS # E9: 5,7 => CTR => E9: 1,6 * PRF # A7: 5,7 => SOL * DIS # A7: 3 => CTR => A7: 5,7 * DIS # E4: 5,7 => CTR => E4: 1,4 * PRF # E4: 1,4 => SOL * DIS # D9: 8,9 => CTR => D9: 1,5,7 * DIS # F9: 8,9 => CTR => F9: 1,6,7 * CNT 19 HDP CHAINS / 38 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B7,C2,C8,D3,E5,E7,F8,G5) * .7..9....9...2576...1...3.....6.....1.52...8..4..8......84.291661..3..7..2....... * PAIR B2: 3,8 BLK 1 A1: 3,8,2,4,5 # reduction candidate for 3,8 A1: 3,8 => CTR * .7..9....9.4.2576...1...3.....65....1.524.68..46.8......8472916619538.7.427.16... * PAIR B2: 3,8 ROW 2 D2: 3,8,1 # reduction candidate for 3,8 D2: 3,8 => CTR * .7..9....9.4.25761..1...3.....65....1.524.68..46.8......8472916619538.7.427.16... * PAIR B2: 3,8 COL B B4: 3,8,9 # reduction candidate for 3,8 B4: 3,8 => CTR * .7..96...9..12576..61...3.....6.....1952..68..46.8.....5847291661..3..7..2..61... * PAIR RESTART * PAIR D3: 7,8 BLK 2 F3: 7,8,4,6 # reduction candidate for 7,8 F3: 4,6 => CTR * .7..96...9..12576..61.743..89.6.....13524.68..46.8......84.291661..3..7..2....... * PAIR D3: 7,8 COL D D9: 7,8,5,9 # reduction candidate for 7,8 D9: 5,9 => CTR * .7.39....983125764..1...3..89.65....1.524.68..46.8......847291661..3..7..2..16... * PAIR RESTART * PAIR E5: 4,7 BLK 5 E4: 4,7,1,5 # reduction candidate for 4,7 E4: 4,7 => SOLVED * 276394158983125764451867392892641537165273489347589621738452916614938275529716843 * DURATION: 0:00:07.626379 START: 23:43:22.705853 END: 23:43:30.332232 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060608-absurd-base-pr-001.dot * REASONING * DIS # A1: 3,8 => CTR => A1: 2,4,5 * DIS A1: 2,4,5 # D2: 3,8 => CTR => D2: 1 * DIS A1: 2,4,5 + D2: 1 # B4: 3,8 => CTR => B4: 9 * DIS A1: 2,4,5 + D2: 1 + B4: 9 # F3: 4,6 => CTR => F3: 7,8 * DIS A1: 2,4,5 + D2: 1 + B4: 9 + F3: 7,8 # D9: 5,9 => CTR => D9: 7,8 * PRF A1: 2,4,5 + D2: 1 + B4: 9 + F3: 7,8 + D9: 7,8 # E4: 4,7 => SOL * STA A1: 2,4,5 + D2: 1 + B4: 9 + F3: 7,8 + D9: 7,8 + E4: 4,7 * CNT 6 HDP CHAINS / 8 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060608, absurd
Solution
position: 276394158983125764451867392892641537165273489347589621738452916614938275529716843 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:
* DIS # A1: 3,8 => CTR => A1: 2,4,5 * INC # A1: 2,4,5 => UNS * DIS # D2: 3,8 => CTR => D2: 1 * INC # D2: 1 => UNS * DIS # B4: 3,8 => CTR => B4: 9 * INC # B4: 9 => UNS * INC # A1: 3,4 => UNS * DIS # C1: 3,4 => CTR => C1: 2,6 * INC # C1: 2,6 => UNS * INC # F3: 7,8 => UNS * INC # F3: 4,6 => UNS * INC # D9: 7,8 => UNS * INC # D9: 1,5,9 => UNS * PRF # E4: 4,7 => SOL * INC # E4: 1,5 => UNS * INC # F4: 4,7 => UNS * DIS # F5: 4,7 => CTR => F5: 3,9 * INC # F5: 3,9 => UNS * DIS # I5: 4,7 => CTR => I5: 3,9 * INC # I5: 3,9 => UNS * DIS # E3: 4,7 => CTR => E3: 6 * PRF # E3: 6 => SOL * DIS # A7: 3,5 => CTR => A7: 7 * PRF # A7: 7 => SOL * INC # C9: 4,9 => UNS * DIS # C9: 7 => CTR => C9: 4,9 * INC # D9: 5,7 => UNS * DIS # E9: 5,7 => CTR => E9: 1,6 * INC # E9: 1,6 => UNS * PRF # A7: 5,7 => SOL * DIS # A7: 3 => CTR => A7: 5,7 * DIS # E4: 5,7 => CTR => E4: 1,4 * PRF # E4: 1,4 => SOL * INC # D8: 8,9 => UNS * DIS # D9: 8,9 => CTR => D9: 1,5,7 * INC # D9: 1,5,7 => UNS * DIS # F9: 8,9 => CTR => F9: 1,6,7 * INC # F9: 1,6,7 => UNS * CNT 38 HDP CHAINS / 38 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 3,8 => CTR => A1: 2,4,5 * DIS A1: 2,4,5 # D2: 3,8 => CTR => D2: 1 * DIS A1: 2,4,5 + D2: 1 # B4: 3,8 => CTR => B4: 9 * INC A1: 2,4,5 + D2: 1 + B4: 9 # F3: 7,8 => UNS * DIS A1: 2,4,5 + D2: 1 + B4: 9 # F3: 4,6 => CTR => F3: 7,8 * INC A1: 2,4,5 + D2: 1 + B4: 9 + F3: 7,8 # D9: 7,8 => UNS * DIS A1: 2,4,5 + D2: 1 + B4: 9 + F3: 7,8 # D9: 5,9 => CTR => D9: 7,8 * PRF A1: 2,4,5 + D2: 1 + B4: 9 + F3: 7,8 + D9: 7,8 # E4: 4,7 => SOL * STA A1: 2,4,5 + D2: 1 + B4: 9 + F3: 7,8 + D9: 7,8 + E4: 4,7 * CNT 8 HDP CHAINS / 8 HYP OPENED