Analysis of zz-www.sudokuoftheday.co.uk-20190201-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: ..........32...1.67.124...5..7136.....58..7....8.5.6.....4.58..2....3.9.....8.... initial
Autosolve
position: ...361....325..1.676124...5..7136.586.58..7..3.8.5.6.....4.58..28...359.....8.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 4,9 => CTR => A1: 5,8 * DIS # B1: 4,9 => CTR => B1: 5 * DIS # C9: 4,9 => CTR => C9: 3,6 * DIS # F2: 8 => CTR => F2: 7,9 * DIS # H1: 4,8 => CTR => H1: 2,7 * DIS # A2: 9 => CTR => A2: 4,8 * DIS # A1: 4,9 => CTR => A1: 5,8 * DIS # A9: 4,9 => CTR => A9: 1,5 * DIS # F6: 2,9 => CTR => F6: 4,7 * DIS # I5: 2,9 => CTR => I5: 1,3,4 * DIS # D9: 6 => CTR => D9: 7,9 * DIS # A9: 1,9 => CTR => A9: 4,5 * PRF # B9: 7,9 => SOL * DIS # I8: 4 => CTR => I8: 1,7 * CNT 14 HDP CHAINS / 57 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 4,9 => CTR => A1: 5,8 * DIS A1: 5,8 # B1: 4,9 => CTR => B1: 5 * DIS A1: 5,8 + B1: 5 # C9: 4,9 => CTR => C9: 3,6 * PRF A1: 5,8 + B1: 5 + C9: 3,6 # F2: 7,9 => SOL * STA A1: 5,8 + B1: 5 + C9: 3,6 + F2: 7,9 * CNT 4 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..........32...1.67.124...5..7136.....58..7....8.5.6.....4.58..2....3.9.....8.... | initial |
| ...361....325..1.676124...5..7136.586.58..7..3.8.5.6.....4.58..28...359.....8.... | autosolve |
| 859361274432597186761248935927136458645829713318754629193475862284613597576982341 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) C1: 4,9 E2: 7,9 F3: 8,9 H2: 4,8 G3: 3,9 H3: 3,8 A4: 4,9 E5: 2,9 D6: 7,9 A7: 1,9 B7: 7,9 C8: 4,6 D8: 6,7 E8: 1,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B5,B6: 1.. / B5 = 1 => 14 pairs (_) / B6 = 1 => 17 pairs (_) A7,A9: 1.. / A7 = 1 => 13 pairs (_) / A9 = 1 => 0 pairs (X) E7,E8: 1.. / E7 = 1 => 0 pairs (X) / E8 = 1 => 14 pairs (_) E8,I8: 1.. / E8 = 1 => 14 pairs (_) / I8 = 1 => 0 pairs (X) E7,F9: 2.. / E7 = 2 => 0 pairs (X) / F9 = 2 => 17 pairs (_) B4,G4: 2.. / B4 = 2 => 15 pairs (_) / G4 = 2 => 23 pairs (_) E5,E7: 2.. / E5 = 2 => 17 pairs (_) / E7 = 2 => 0 pairs (X) G3,H3: 3.. / G3 = 3 => 0 pairs (X) / H3 = 3 => 17 pairs (_) H5,I5: 3.. / H5 = 3 => 0 pairs (X) / I5 = 3 => 16 pairs (_) C7,C9: 3.. / C7 = 3 => 14 pairs (_) / C9 = 3 => 0 pairs (X) G3,G9: 3.. / G3 = 3 => 0 pairs (X) / G9 = 3 => 17 pairs (_) F5,F6: 4.. / F5 = 4 => 14 pairs (_) / F6 = 4 => 21 pairs (_) A2,H2: 4.. / A2 = 4 => 0 pairs (*) / H2 = 4 => 0 pairs (X) C8,I8: 4.. / C8 = 4 => 17 pairs (_) / I8 = 4 => 0 pairs (X) A1,B1: 5.. / A1 = 5 => 0 pairs (X) / B1 = 5 => 13 pairs (_) A9,B9: 5.. / A9 = 5 => 13 pairs (_) / B9 = 5 => 0 pairs (X) A1,A9: 5.. / A1 = 5 => 0 pairs (X) / A9 = 5 => 13 pairs (_) B1,B9: 5.. / B1 = 5 => 13 pairs (_) / B9 = 5 => 0 pairs (X) D8,D9: 6.. / D8 = 6 => 17 pairs (_) / D9 = 6 => 0 pairs (X) H7,H9: 6.. / H7 = 6 => 15 pairs (_) / H9 = 6 => 0 pairs (X) C7,H7: 6.. / C7 = 6 => 0 pairs (X) / H7 = 6 => 15 pairs (_) C8,D8: 6.. / C8 = 6 => 0 pairs (X) / D8 = 6 => 17 pairs (_) E2,F2: 7.. / E2 = 7 => 17 pairs (_) / F2 = 7 => 19 pairs (_) H1,I1: 7.. / H1 = 7 => 14 pairs (_) / I1 = 7 => 20 pairs (_) D6,F6: 7.. / D6 = 7 => 17 pairs (_) / F6 = 7 => 16 pairs (_) B7,B9: 7.. / B7 = 7 => 13 pairs (_) / B9 = 7 => 0 pairs (*) A1,A2: 8.. / A1 = 8 => 14 pairs (_) / A2 = 8 => 0 pairs (X) F2,F3: 8.. / F2 = 8 => 0 pairs (X) / F3 = 8 => 17 pairs (_) A1,H1: 8.. / A1 = 8 => 14 pairs (_) / H1 = 8 => 0 pairs (X) F3,H3: 8.. / F3 = 8 => 17 pairs (_) / H3 = 8 => 0 pairs (X) F3,G3: 9.. / F3 = 9 => 0 pairs (X) / G3 = 9 => 17 pairs (_) D6,D9: 9.. / D6 = 9 => 16 pairs (_) / D9 = 9 => 17 pairs (_) * DURATION: 0:00:32.616326 START: 03:23:07.091381 END: 03:23:39.707707 2019-05-01 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A7,B7,C1,C8,D6,D8,E2,E5,E8,F3,G3,H2,H3) * ...361....325..1.676124...5..7136.586.58..7..3.8.5.6.....4.58..28...359.....8.... * PAIR C1: 4,9 BLK 1 A1: 4,9,5,8 # reduction candidate for 4,9 A1: 4,9 => CTR * .593612878325..146761248935.271364586.58..7.33.875.6.91.34.586.28...359.5..98.371 A1: 5,8 # 15 pairs B1: 4,9,5 # reduction candidate for 4,9 B1: 4,9 => CTR * 5.93612878325..146761248935.271364586.58..7.33.875.6.9.734.586.28.673591.5.98.37. B1: 5 # 13 pairs A2: 4,9,8 # reduction candidate for 4,9 A2: 4,9 # 14 pairs * PAIR C1: 4,9 ROW 1 G1: 4,9,2 # reduction candidate for 4,9 G1: 4,9 # 18 pairs I1: 4,9,2,7 # reduction candidate for 4,9 I1: 4,9 # 17 pairs * PAIR C1: 4,9 COL C C9: 4,9,3,6 # reduction candidate for 4,9 C9: 4,9 => CTR * ...361....3257.1.676124.935..7136.586.582.7..3.89576....3495862286713594...6823.. C9: 3,6 # 15 pairs * PAIR E2: 7,9 BLK 2 F2: 7,9,8 # reduction candidate for 7,9 F2: 8 => CTR * 854361...9325781467612493854.7136.586.58..7..3.8.5.6..1..4.58..28671359454.682... F2: 7,9 # 17 pairs * PAIR E2: 7,9 COL E E7: 7,9,1,2 # reduction candidate for 7,9 E7: 7,9 # 17 pairs E7: 1,2 # 15 pairs * PAIR F3: 8,9 BLK 2 F2: 8,9,7 # reduction candidate for 8,9 F2: 7 # 19 pairs F2: 8,9 # 17 pairs * PAIR H2: 4,8 BLK 3 H1: 4,8,2,7 # reduction candidate for 4,8 H1: 4,8 => CTR * ..93612.7.325..1.67612489359271364586.58..7.33.875.6.91.34.586.28...359....98.37. H1: 2,7 # 15 pairs * PAIR H2: 4,8 ROW 2 A2: 4,8,9 # reduction candidate for 4,8 A2: 9 => CTR * 854361...9325781467612493854.7136.586.58..7..3.8.5.6..1..4.58..28671359454.682... A2: 4,8 # 17 pairs * PAIR A4: 4,9 BLK 4 B4: 4,9,2 # reduction candidate for 4,9 B4: 4,9 # 23 pairs B5: 4,9,1,2 # reduction candidate for 4,9 B5: 4,9 # 19 pairs B6: 4,9,1,2 # reduction candidate for 4,9 B6: 4,9 # 16 pairs * PAIR A4: 4,9 ROW 4 G4: 4,9,2 # reduction candidate for 4,9 G4: 2 # 23 pairs G4: 4,9 # 15 pairs * PAIR A4: 4,9 COL A A1: 4,9,5,8 # reduction candidate for 4,9 A1: 4,9 => CTR * .593612878325..146761248935.271364586.58..7.33.875.6.91.34.586.28...359.5..98.371 A1: 5,8 # 15 pairs A2: 4,9,8 # reduction candidate for 4,9 A2: 4,9 # 14 pairs A9: 4,9,1,5 # reduction candidate for 4,9 A9: 4,9 => CTR * 5..361.878325..146761248935..7136.586.58..7.33.8.5.6.91.34.586228..13594.5.982... A9: 1,5 # 15 pairs * PAIR E5: 2,9 BLK 5 F5: 2,9,4 # reduction candidate for 2,9 F5: 2,9 # 21 pairs F6: 2,9,4,7 # reduction candidate for 2,9 F6: 2,9 => CTR * ..9361.7..32579186761248935..7136.586.58947.33.87526.9.734258612846135971569873.. F6: 4,7 # 15 pairs * PAIR E5: 2,9 ROW 5 B5: 2,9,1,4 # reduction candidate for 2,9 B5: 2,9 # 19 pairs I5: 2,9,1,3,4 # reduction candidate for 2,9 I5: 2,9 => CTR * 854361...9325781467612493854.7136.586158.473.3.8.5.6.41..4.58..28671359.5...8.... I5: 1,3,4 # 14 pairs * PAIR E5: 2,9 COL E E7: 2,9,1,7 # reduction candidate for 2,9 E7: 1,7 # 19 pairs E7: 2,9 # 17 pairs * PAIR D6: 7,9 BLK 5 F6: 7,9,2,4 # reduction candidate for 7,9 F6: 7,9 # 19 pairs F6: 2,4 # 17 pairs * PAIR D6: 7,9 COL D D9: 7,9,6 # reduction candidate for 7,9 D9: 6 => CTR * ...361....3257.1.676124.935..7136.586.582471.3.89576.....495862286713594...6823.. D9: 7,9 # 17 pairs * PAIR A7: 1,9 BLK 7 A9: 1,9,4,5 # reduction candidate for 1,9 A9: 1,9 => CTR * 5..361.878325..1467612489354971362586.58..7..3.8.5.6.....4.58..28...359.....8.... A9: 4,5 # 14 pairs * PAIR A7: 1,9 ROW 7 E7: 1,9,2,7 # reduction candidate for 1,9 E7: 1,9 # 17 pairs E7: 2,7 # 15 pairs * PAIR B7: 7,9 BLK 7 B9: 7,9,4,5 # reduction candidate for 7,9 B9: 7,9 => SOLVED * 859361274432597186761248935927136458645829713318754629193475862284613597576982341 B9: 4,5 # 14 pairs * PAIR B7: 7,9 ROW 7 E7: 7,9,1,2 # reduction candidate for 7,9 E7: 7,9 # 17 pairs E7: 1,2 # 15 pairs * PAIR C8: 4,6 BLK 7 C9: 4,6,3,9 # reduction candidate for 4,6 C9: 4,6 # 17 pairs C9: 3,9 # 15 pairs * PAIR D8: 6,7 BLK 8 D9: 6,7,9 # reduction candidate for 6,7 D9: 9 # 17 pairs D9: 6,7 # 16 pairs * PAIR E8: 1,7 BLK 8 E7: 1,7,2,9 # reduction candidate for 1,7 E7: 1,7 # 19 pairs E7: 2,9 # 17 pairs * PAIR E8: 1,7 ROW 8 I8: 1,7,4 # reduction candidate for 1,7 I8: 4 => CTR * ...361....3257.1.676124.935..7136.586.582.7..3.89576.....495862286713594...6823.. I8: 1,7 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190201-absurd-base-pr-000.dot * REASONING * DIS # A1: 4,9 => CTR => A1: 5,8 * DIS # B1: 4,9 => CTR => B1: 5 * DIS # C9: 4,9 => CTR => C9: 3,6 * DIS # F2: 8 => CTR => F2: 7,9 * DIS # H1: 4,8 => CTR => H1: 2,7 * DIS # A2: 9 => CTR => A2: 4,8 * DIS # A1: 4,9 => CTR => A1: 5,8 * DIS # A9: 4,9 => CTR => A9: 1,5 * DIS # F6: 2,9 => CTR => F6: 4,7 * DIS # I5: 2,9 => CTR => I5: 1,3,4 * DIS # D9: 6 => CTR => D9: 7,9 * DIS # A9: 1,9 => CTR => A9: 4,5 * PRF # B9: 7,9 => SOL * DIS # I8: 4 => CTR => I8: 1,7 * CNT 14 HDP CHAINS / 57 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A7,B7,C1,C8,D6,D8,E2,E5,E8,F3,G3,H2,H3) * ...361....325..1.676124...5..7136.586.58..7..3.8.5.6.....4.58..28...359.....8.... * PAIR C1: 4,9 BLK 1 A1: 4,9,5,8 # reduction candidate for 4,9 A1: 4,9 => CTR * .593612878325..146761248935.271364586.58..7.33.875.6.91.34.586.28...359.5..98.371 B1: 4,9,5 # reduction candidate for 4,9 B1: 4,9 => CTR * 5.93612878325..146761248935.271364586.58..7.33.875.6.9.734.586.28.673591.5.98.37. * RESTART * PAIR C1: 4,9 ROW 1 G1: 4,9,2 # reduction candidate for 4,9 G1: 4,9 # 18 pairs I1: 4,9,2,7 # reduction candidate for 4,9 I1: 4,9 # 17 pairs * PAIR C1: 4,9 COL C C9: 4,9,3,6 # reduction candidate for 4,9 C9: 4,9 => CTR * 85.361....3257.1.676124.935..7136.586.582.7..3.89576..1.34958622867135945..6823.. * PAIR RESTART * PAIR C1: 4,9 ROW 1 G1: 4,9,2 # reduction candidate for 4,9 G1: 4,9 # 19 pairs I1: 4,9,2,7 # reduction candidate for 4,9 I1: 4,9 # 18 pairs * PAIR E2: 7,9 BLK 2 F2: 7,9,8 # reduction candidate for 7,9 F2: 7,9 => SOLVED * 859361274432597186761248935927136458645829713318754629193475862284613597576982341 * DURATION: 0:00:06.572568 START: 03:24:11.834450 END: 03:24:18.407018 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190201-absurd-base-pr-001.dot * REASONING * DIS # A1: 4,9 => CTR => A1: 5,8 * DIS A1: 5,8 # B1: 4,9 => CTR => B1: 5 * DIS A1: 5,8 + B1: 5 # C9: 4,9 => CTR => C9: 3,6 * PRF A1: 5,8 + B1: 5 + C9: 3,6 # F2: 7,9 => SOL * STA A1: 5,8 + B1: 5 + C9: 3,6 + F2: 7,9 * CNT 4 HDP CHAINS / 8 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190201, absurd
Solution
position: 859361274432597186761248935927136458645829713318754629193475862284613597576982341 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: 4,9 => CTR => A1: 5,8 * INC # A1: 5,8 => UNS * DIS # B1: 4,9 => CTR => B1: 5 * INC # B1: 5 => UNS * INC # A2: 4,9 => UNS * INC # G1: 4,9 => UNS * INC # I1: 4,9 => UNS * DIS # C9: 4,9 => CTR => C9: 3,6 * INC # C9: 3,6 => UNS * INC # F2: 7,9 => UNS * DIS # F2: 8 => CTR => F2: 7,9 * INC # E7: 7,9 => UNS * INC # E7: 1,2 => UNS * INC # F2: 8,9 => UNS * INC # F2: 7 => UNS * DIS # H1: 4,8 => CTR => H1: 2,7 * INC # H1: 2,7 => UNS * INC # A2: 4,8 => UNS * DIS # A2: 9 => CTR => A2: 4,8 * INC # B4: 4,9 => UNS * INC # B5: 4,9 => UNS * INC # B6: 4,9 => UNS * INC # G4: 4,9 => UNS * INC # G4: 2 => UNS * DIS # A1: 4,9 => CTR => A1: 5,8 * INC # A1: 5,8 => UNS * INC # A2: 4,9 => UNS * DIS # A9: 4,9 => CTR => A9: 1,5 * INC # A9: 1,5 => UNS * INC # F5: 2,9 => UNS * DIS # F6: 2,9 => CTR => F6: 4,7 * INC # F6: 4,7 => UNS * INC # B5: 2,9 => UNS * DIS # I5: 2,9 => CTR => I5: 1,3,4 * INC # I5: 1,3,4 => UNS * INC # E7: 2,9 => UNS * INC # E7: 1,7 => UNS * INC # F6: 7,9 => UNS * INC # F6: 2,4 => UNS * INC # D9: 7,9 => UNS * DIS # D9: 6 => CTR => D9: 7,9 * DIS # A9: 1,9 => CTR => A9: 4,5 * INC # A9: 4,5 => UNS * INC # E7: 1,9 => UNS * INC # E7: 2,7 => UNS * PRF # B9: 7,9 => SOL * INC # B9: 4,5 => UNS * INC # E7: 7,9 => UNS * INC # E7: 1,2 => UNS * INC # C9: 4,6 => UNS * INC # C9: 3,9 => UNS * INC # D9: 6,7 => UNS * INC # D9: 9 => UNS * INC # E7: 1,7 => UNS * INC # E7: 2,9 => UNS * INC # I8: 1,7 => UNS * DIS # I8: 4 => CTR => I8: 1,7 * CNT 57 HDP CHAINS / 57 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 4,9 => CTR => A1: 5,8 * DIS A1: 5,8 # B1: 4,9 => CTR => B1: 5 * INC A1: 5,8 + B1: 5 # G1: 4,9 => UNS * INC A1: 5,8 + B1: 5 # I1: 4,9 => UNS * DIS A1: 5,8 + B1: 5 # C9: 4,9 => CTR => C9: 3,6 * INC A1: 5,8 + B1: 5 + C9: 3,6 # G1: 4,9 => UNS * INC A1: 5,8 + B1: 5 + C9: 3,6 # I1: 4,9 => UNS * PRF A1: 5,8 + B1: 5 + C9: 3,6 # F2: 7,9 => SOL * STA A1: 5,8 + B1: 5 + C9: 3,6 + F2: 7,9 * CNT 8 HDP CHAINS / 8 HYP OPENED