Analysis of zz-www.sudokuoftheday.co.uk-20060901-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Sep&YEAR=2006
level: medium
position: .3..7...5..89..41...4..2.36..583.....6.2.7.8.....5...............9....625.1...7.8 initial
Autosolve
position: .36.7...5258963417..45.2.36..583.6...632.758.8..65....6......5.3.9..51625.13.67.8 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 1,9 => CTR => A3: 7 * DIS # F1: 1,4 => CTR => F1: 8 * DIS # D7: 7 => CTR => D7: 1,4 * DIS # F1: 4 => CTR => F1: 1,8 * DIS # E7: 1,8 => CTR => E7: 2,4,9 * DIS # G1: 8 => CTR => G1: 2,9 * PRF # H4: 2,9 => SOL * DIS # H6: 2,9 => CTR => H6: 4,7 * PRF # G1: 2 => SOL * DIS # B6: 2,7 => CTR => B6: 1,9 * PRF # H6: 2,7 => SOL * DIS # B7: 2,4 => CTR => B7: 7,8 * PRF # E9: 9 => SOL * DIS # D7: 4,7 => CTR => D7: 1 * PRF # B8: 4,7 => SOL * DIS # E7: 4,8 => CTR => E7: 1,2,9 * DIS # B8: 7 => CTR => B8: 4,8 * PRF # I7: 3,9 => SOL * PRF # G6: 3,9 => SOL * PRF # I7: 3 => SOL * PRF # E9: 4,9 => SOL * DIS # H4: 4,9 => CTR => H4: 2,7 * CNT 22 HDP CHAINS / 52 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A3: 1,9 => CTR => A3: 7 * DIS A3: 7 # F1: 1,4 => CTR => F1: 8 * DIS A3: 7 + F1: 8 # H6: 2,9 => CTR => H6: 4,7 * DIS A3: 7 + F1: 8 + H6: 4,7 # B7: 2,7 => CTR => B7: 8 * PRF A3: 7 + F1: 8 + H6: 4,7 + B7: 8 => SOL * STA A3: 7 + F1: 8 + H6: 4,7 + B7: 8 * CNT 5 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .3..7...5..89..41...4..2.36..583.....6.2.7.8.....5...............9....625.1...7.8 | initial |
| .36.7...5258963417..45.2.36..583.6...632.758.8..65....6......5.3.9..51625.13.67.8 | autosolve |
| 136478295258963417794512836475831629963247581812659374687124953349785162521396748 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) A1: 1,9 D1: 1,4 E3: 1,8 H1: 2,9 G3: 8,9 C6: 2,7 C7: 2,7 B9: 2,4 D8: 4,7 E8: 4,8 G7: 3,9 H9: 4,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,D7: 1.. / D1 = 1 => 0 pairs (X) / D7 = 1 => 12 pairs (_) G1,H1: 2.. / G1 = 2 => 0 pairs (*) / H1 = 2 => 0 pairs (X) E7,E9: 2.. / E7 = 2 => 0 pairs (*) / E9 = 2 => 0 pairs (X) B4,H4: 2.. / B4 = 2 => 15 pairs (_) / H4 = 2 => 0 pairs (*) B9,E9: 2.. / B9 = 2 => 0 pairs (*) / E9 = 2 => 0 pairs (X) C6,C7: 2.. / C6 = 2 => 0 pairs (*) / C7 = 2 => 0 pairs (X) G1,G6: 2.. / G1 = 2 => 0 pairs (*) / G6 = 2 => 0 pairs (X) G6,I6: 3.. / G6 = 3 => 0 pairs (*) / I6 = 3 => 0 pairs (X) G7,I7: 3.. / G7 = 3 => 13 pairs (_) / I7 = 3 => 0 pairs (*) G6,G7: 3.. / G6 = 3 => 0 pairs (*) / G7 = 3 => 0 pairs (X) I6,I7: 3.. / I6 = 3 => 13 pairs (_) / I7 = 3 => 0 pairs (*) D1,F1: 4.. / D1 = 4 => 12 pairs (_) / F1 = 4 => 0 pairs (X) A4,A5: 4.. / A4 = 4 => 19 pairs (_) / A5 = 4 => 15 pairs (_) I7,H9: 4.. / I7 = 4 => 15 pairs (_) / H9 = 4 => 0 pairs (*) A3,B3: 7.. / A3 = 7 => 16 pairs (_) / B3 = 7 => 0 pairs (X) H4,H6: 7.. / H4 = 7 => 15 pairs (_) / H6 = 7 => 0 pairs (*) D7,D8: 7.. / D7 = 7 => 0 pairs (X) / D8 = 7 => 13 pairs (_) B8,D8: 7.. / B8 = 7 => 0 pairs (X) / D8 = 7 => 13 pairs (_) A3,A4: 7.. / A3 = 7 => 16 pairs (_) / A4 = 7 => 0 pairs (X) C6,C7: 7.. / C6 = 7 => 15 pairs (_) / C7 = 7 => 0 pairs (*) F1,E3: 8.. / F1 = 8 => 16 pairs (_) / E3 = 8 => 0 pairs (X) G1,G3: 8.. / G1 = 8 => 0 pairs (X) / G3 = 8 => 16 pairs (_) B7,B8: 8.. / B7 = 8 => 0 pairs (*) / B8 = 8 => 0 pairs (X) F1,G1: 8.. / F1 = 8 => 16 pairs (_) / G1 = 8 => 0 pairs (X) E3,G3: 8.. / E3 = 8 => 0 pairs (X) / G3 = 8 => 16 pairs (_) B8,E8: 8.. / B8 = 8 => 13 pairs (_) / E8 = 8 => 0 pairs (*) F1,F7: 8.. / F1 = 8 => 16 pairs (_) / F7 = 8 => 0 pairs (X) E9,H9: 9.. / E9 = 9 => 0 pairs (*) / H9 = 9 => 0 pairs (X) * DURATION: 0:00:32.534615 START: 02:16:34.918153 END: 02:17:07.452768 2019-05-01 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B9,C6,C7,D1,D8,E3,E8,G3,G7,H1,H9) * .36.7...5258963417..45.2.36..583.6...632.758.8..65....6......5.3.9..51625.13.67.8 * PAIR A1: 1,9 BLK 1 A3: 1,9,7 # reduction candidate for 1,9 A3: 1,9 => CTR * .36.7.2952589634179745128367.583.62.4632975818.265..7.6.71.93543.97.51625.13.67.8 A3: 7 # 16 pairs B3: 1,9,7 # reduction candidate for 1,9 B3: 1,9 # 16 pairs * PAIR A1: 1,9 COL A A4: 1,9,4,7 # reduction candidate for 1,9 A4: 1,9 # 20 pairs A5: 1,9,4 # reduction candidate for 1,9 A5: 1,9 # 19 pairs * PAIR D1: 1,4 BLK 2 F1: 1,4,8 # reduction candidate for 1,4 F1: 1,4 => CTR * .36.7.825258963417..4582936.2583.6...632.758.89765.2436.2..8354389745162541326798 F1: 8 # 16 pairs * PAIR D1: 1,4 COL D D7: 1,4,7 # reduction candidate for 1,4 D7: 7 => CTR * .36174825258963417..4582936.2583.6...6324758.8..65....6......5.3.9..51625.13.67.8 D7: 1,4 # 13 pairs * PAIR E3: 1,8 BLK 2 F1: 1,8,4 # reduction candidate for 1,8 F1: 4 => CTR * .36.74825258963417..4582936.2583.6...6324758.8..65....6......5.3.9..51625.13.67.8 F1: 1,8 # 12 pairs * PAIR E3: 1,8 COL E E7: 1,8,2,4,9 # reduction candidate for 1,8 E7: 1,8 => CTR * .36478925258963417794512836925834671.6329758.8.765.2436.2..93543.9.45162541326798 E7: 2,4,9 # 12 pairs * PAIR H1: 2,9 BLK 3 G1: 2,9,8 # reduction candidate for 2,9 G1: 8 => CTR * .36.7.825258963417..4582936.2583.6...632.758.89765.2436.2..8354389745162541326798 G1: 2,9 # 16 pairs * PAIR H1: 2,9 COL H H4: 2,9,4,7 # reduction candidate for 2,9 H4: 2,9 => SOLVED * 136478295258963417794512836475831629963247581812659374687124953349785162521396748 H4: 4,7 # 15 pairs H6: 2,9,4,7 # reduction candidate for 2,9 H6: 2,9 => CTR * .36.7...52589634177.45.2.36.2583.67..632.758.8..65....6......5.3.9..51625.13.6748 H6: 4,7 # 13 pairs * PAIR G3: 8,9 BLK 3 G1: 8,9,2 # reduction candidate for 8,9 G1: 2 => SOLVED * 136478295258963417794512836475831629963247581812659374687124953349785162521396748 G1: 8,9 # 15 pairs * PAIR C6: 2,7 BLK 4 B4: 2,7,1,9 # reduction candidate for 2,7 B4: 2,7 # 16 pairs B6: 2,7,1,9 # reduction candidate for 2,7 B6: 2,7 => CTR * .36.7...5258963417..45.2.36..583.6...632.758.8..65....6......5.3.9..51625.13.67.8 B6: 1,9 # 13 pairs * PAIR C6: 2,7 ROW 6 H6: 2,7,4,9 # reduction candidate for 2,7 H6: 2,7 => SOLVED * 136478295258963417794512836475831629963247581812659374687124953349785162521396748 H6: 4,9 # 15 pairs * PAIR C7: 2,7 BLK 7 B7: 2,7,4,8 # reduction candidate for 2,7 B7: 2,7 # 14 pairs B7: 4,8 # 13 pairs * PAIR B9: 2,4 BLK 7 B7: 2,4,7,8 # reduction candidate for 2,4 B7: 2,4 => CTR * .3647.295258963417..45.2836..583.62..632.758.8.265..7.6.7189.5.3897451625.13.67.8 B7: 7,8 # 13 pairs * PAIR B9: 2,4 ROW 9 E9: 2,4,9 # reduction candidate for 2,4 E9: 9 => SOLVED * 136478295258963417794512836475831629963247581812659374687124953349785162521396748 E9: 2,4 # 15 pairs * PAIR D8: 4,7 BLK 8 D7: 4,7,1 # reduction candidate for 4,7 D7: 4,7 => CTR * .36174825258963417..4582936.2583.6...6324758.8..65....6......5.3.9..51625.13.67.8 D7: 1 # 12 pairs * PAIR D8: 4,7 ROW 8 B8: 4,7,8 # reduction candidate for 4,7 B8: 4,7 => SOLVED * 136478295258963417794512836475831629963247581812659374687124953349785162521396748 B8: 8 # 13 pairs * PAIR E8: 4,8 BLK 8 E7: 4,8,1,2,9 # reduction candidate for 4,8 E7: 4,8 => CTR * .36478925258963417794512836925834671.6329758.8.765.2436.2..93543.9.45162541326798 E7: 1,2,9 # 12 pairs F7: 4,8,1,9 # reduction candidate for 4,8 F7: 4,8 # 16 pairs * PAIR E8: 4,8 ROW 8 B8: 4,8,7 # reduction candidate for 4,8 B8: 7 => CTR * .36.7...5258963417..45.2.36..583.6...632.758.8..65....68.....5.379485162541326798 B8: 4,8 # 13 pairs * PAIR G7: 3,9 BLK 9 I7: 3,9,4 # reduction candidate for 3,9 I7: 3,9 => SOLVED * 136478295258963417794512836475831629963247581812659374687124953349785162521396748 I7: 4 # 15 pairs * PAIR G7: 3,9 COL G G6: 3,9,2 # reduction candidate for 3,9 G6: 3,9 => SOLVED * 136478295258963417794512836475831629963247581812659374687124953349785162521396748 G6: 2 # 15 pairs * PAIR H9: 4,9 BLK 9 I7: 4,9,3 # reduction candidate for 4,9 I7: 3 => SOLVED * 136478295258963417794512836475831629963247581812659374687124953349785162521396748 I7: 4,9 # 13 pairs * PAIR H9: 4,9 ROW 9 E9: 4,9,2 # reduction candidate for 4,9 E9: 4,9 => SOLVED * 136478295258963417794512836475831629963247581812659374687124953349785162521396748 E9: 2 # 15 pairs * PAIR H9: 4,9 COL H H4: 4,9,2,7 # reduction candidate for 4,9 H4: 4,9 => CTR * .36.7...5258963417..45.2.36.2583.6...632.758.8.765....6.2....5.3.9..5162541326798 H4: 2,7 # 13 pairs H6: 4,9,2,7 # reduction candidate for 4,9 H6: 4,9 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060901-absurd-base-pr-000.dot * REASONING * DIS # A3: 1,9 => CTR => A3: 7 * DIS # F1: 1,4 => CTR => F1: 8 * DIS # D7: 7 => CTR => D7: 1,4 * DIS # F1: 4 => CTR => F1: 1,8 * DIS # E7: 1,8 => CTR => E7: 2,4,9 * DIS # G1: 8 => CTR => G1: 2,9 * PRF # H4: 2,9 => SOL * DIS # H6: 2,9 => CTR => H6: 4,7 * PRF # G1: 2 => SOL * DIS # B6: 2,7 => CTR => B6: 1,9 * PRF # H6: 2,7 => SOL * DIS # B7: 2,4 => CTR => B7: 7,8 * PRF # E9: 9 => SOL * DIS # D7: 4,7 => CTR => D7: 1 * PRF # B8: 4,7 => SOL * DIS # E7: 4,8 => CTR => E7: 1,2,9 * DIS # B8: 7 => CTR => B8: 4,8 * PRF # I7: 3,9 => SOL * PRF # G6: 3,9 => SOL * PRF # I7: 3 => SOL * PRF # E9: 4,9 => SOL * DIS # H4: 4,9 => CTR => H4: 2,7 * CNT 22 HDP CHAINS / 52 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B9,C6,C7,D1,D8,E3,E8,G3,G7,H1,H9) * .36.7...5258963417..45.2.36..583.6...632.758.8..65....6......5.3.9..51625.13.67.8 * PAIR A1: 1,9 BLK 1 A3: 1,9,7 # reduction candidate for 1,9 A3: 1,9 => CTR * .36.7.2952589634179745128367.583.62.4632975818.265..7.6.71.93543.97.51625.13.67.8 * RESTART * PAIR A1: 1,9 COL A A4: 1,9,4 # reduction candidate for 1,9 A4: 1,9 # 20 pairs A5: 1,9,4 # reduction candidate for 1,9 A5: 1,9 # 19 pairs * PAIR D1: 1,4 BLK 2 F1: 1,4,8 # reduction candidate for 1,4 F1: 1,4 => CTR * .36.7.8252589634177.4582936.2583.67..632.758.89765.2436.2..8354389745162541326798 * PAIR H1: 2,9 COL H H6: 2,9,4,7 # reduction candidate for 2,9 H6: 2,9 => CTR * 136478..5258963417794512836..583167..632.758181765....67218..5.389745162541326798 * PAIR RESTART * PAIR C7: 2,7 BLK 7 B7: 2,7,8 # reduction candidate for 2,7 B7: 2,7 => CTR * 136478925258963417794512836.2583167.463297581817654...6..18..5.389745162541326798 B7: 8 => SOLVED * 136478295258963417794512836475831629963247581812659374687124953349785162521396748 * DURATION: 0:00:07.942761 START: 02:17:41.632238 END: 02:17:49.574999 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060901-absurd-base-pr-001.dot * REASONING * DIS # A3: 1,9 => CTR => A3: 7 * DIS A3: 7 # F1: 1,4 => CTR => F1: 8 * DIS A3: 7 + F1: 8 # H6: 2,9 => CTR => H6: 4,7 * DIS A3: 7 + F1: 8 + H6: 4,7 # B7: 2,7 => CTR => B7: 8 * PRF A3: 7 + F1: 8 + H6: 4,7 + B7: 8 => SOL * STA A3: 7 + F1: 8 + H6: 4,7 + B7: 8 * CNT 5 HDP CHAINS / 6 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Sep&YEAR=2006, 20060901, absurd
Solution
position: 136478295258963417794512836475831629963247581812659374687124953349785162521396748 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 # A3: 1,9 => CTR => A3: 7 * INC # A3: 7 => UNS * INC # B3: 1,9 => UNS * INC # A4: 1,9 => UNS * INC # A5: 1,9 => UNS * DIS # F1: 1,4 => CTR => F1: 8 * INC # F1: 8 => UNS * INC # D7: 1,4 => UNS * DIS # D7: 7 => CTR => D7: 1,4 * INC # F1: 1,8 => UNS * DIS # F1: 4 => CTR => F1: 1,8 * DIS # E7: 1,8 => CTR => E7: 2,4,9 * INC # E7: 2,4,9 => UNS * INC # G1: 2,9 => UNS * DIS # G1: 8 => CTR => G1: 2,9 * PRF # H4: 2,9 => SOL * INC # H4: 4,7 => UNS * DIS # H6: 2,9 => CTR => H6: 4,7 * INC # H6: 4,7 => UNS * INC # G1: 8,9 => UNS * PRF # G1: 2 => SOL * INC # B4: 2,7 => UNS * DIS # B6: 2,7 => CTR => B6: 1,9 * INC # B6: 1,9 => UNS * PRF # H6: 2,7 => SOL * INC # H6: 4,9 => UNS * INC # B7: 2,7 => UNS * INC # B7: 4,8 => UNS * DIS # B7: 2,4 => CTR => B7: 7,8 * INC # B7: 7,8 => UNS * INC # E9: 2,4 => UNS * PRF # E9: 9 => SOL * DIS # D7: 4,7 => CTR => D7: 1 * INC # D7: 1 => UNS * PRF # B8: 4,7 => SOL * INC # B8: 8 => UNS * DIS # E7: 4,8 => CTR => E7: 1,2,9 * INC # E7: 1,2,9 => UNS * INC # F7: 4,8 => UNS * INC # B8: 4,8 => UNS * DIS # B8: 7 => CTR => B8: 4,8 * PRF # I7: 3,9 => SOL * INC # I7: 4 => UNS * PRF # G6: 3,9 => SOL * INC # G6: 2 => UNS * INC # I7: 4,9 => UNS * PRF # I7: 3 => SOL * PRF # E9: 4,9 => SOL * INC # E9: 2 => UNS * DIS # H4: 4,9 => CTR => H4: 2,7 * INC # H4: 2,7 => UNS * INC # H6: 4,9 => UNS * CNT 52 HDP CHAINS / 52 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A3: 1,9 => CTR => A3: 7 * INC A3: 7 # A4: 1,9 => UNS * INC A3: 7 # A5: 1,9 => UNS * DIS A3: 7 # F1: 1,4 => CTR => F1: 8 * DIS A3: 7 + F1: 8 # H6: 2,9 => CTR => H6: 4,7 * DIS A3: 7 + F1: 8 + H6: 4,7 # B7: 2,7 => CTR => B7: 8 * PRF A3: 7 + F1: 8 + H6: 4,7 + B7: 8 => SOL * STA A3: 7 + F1: 8 + H6: 4,7 + B7: 8 * CNT 7 HDP CHAINS / 6 HYP OPENED