Analysis of xx-top500-019-base.sdk
Contents
Original Sudoku
level: medium
position: 8..72........6..3.......6...3....5.....6..4..2..........41..........8.2..6.....7. initial
Autosolve
position: 8.672394.4...6.23.3.2..46..63..475.2.876.24.324.3..76.7241368....34781261682..374 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 1,5 => CTR => B2: 7,9 * DIS # B3: 1,5 => CTR => B3: 7,9 * PRF # B2: 5,9 => SOL * DIS # D2: 5,9 => CTR => D2: 8 * PRF # D2: 8 => SOL * DIS # C6: 1 => CTR => C6: 5,9 * DIS # E3: 8 => CTR => E3: 1,9 * PRF # B2: 1,9 => SOL * DIS # I2: 1,5 => CTR => I2: 7,8 * DIS # I3: 1,5 => CTR => I3: 7,8 * DIS # C6: 5 => CTR => C6: 1,9 * DIS # H4: 1,9 => CTR => H4: 8 * DIS # C6: 1 => CTR => C6: 5,9 * DIS # E6: 1,5 => CTR => E6: 8,9 * DIS # H4: 1 => CTR => H4: 8,9 * DIS # D3: 8,9 => CTR => D3: 5 * DIS # H4: 1,9 => CTR => H4: 8 * DIS # E5: 5 => CTR => E5: 1,9 * PRF # B2: 5,9 => SOL * DIS # E6: 5,9 => CTR => E6: 1,8 * DIS # F6: 1 => CTR => F6: 5,9 * CNT 21 HDP CHAINS / 50 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B2: 1,5 => CTR => B2: 7,9 * DIS B2: 7,9 # B3: 1,5 => CTR => B3: 7,9 * PRF B2: 7,9 + B3: 7,9 # E3: 1,9 => SOL * STA B2: 7,9 + B3: 7,9 + E3: 1,9 * CNT 3 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 8..72........6..3.......6...3....5.....6..4..2..........41..........8.2..6.....7. | initial |
| 8.672394.4...6.23.3.2..46..63..475.2.876.24.324.3..76.7241368....34781261682..374 | autosolve |
| 816723945495861237372594618631947582587612493249385761724136859953478126168259374 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) B1: 1,5 C2: 5,9 F2: 1,9 I1: 1,5 C4: 1,9 A5: 5,9 D4: 8,9 H5: 1,9 A8: 5,9 B8: 5,9 E9: 5,9 F9: 5,9 H7: 5,9 I7: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F2,E3: 1.. / F2 = 1 => 15 pairs (_) / E3 = 1 => 0 pairs (X) C4,C6: 1.. / C4 = 1 => 15 pairs (_) / C6 = 1 => 0 pairs (X) B1,I1: 1.. / B1 = 1 => 12 pairs (_) / I1 = 1 => 0 pairs (X) C4,H4: 1.. / C4 = 1 => 15 pairs (_) / H4 = 1 => 0 pairs (X) E5,H5: 1.. / E5 = 1 => 14 pairs (_) / H5 = 1 => 19 pairs (_) F2,F6: 1.. / F2 = 1 => 15 pairs (_) / F6 = 1 => 0 pairs (X) D2,D3: 5.. / D2 = 5 => 0 pairs (X) / D3 = 5 => 15 pairs (_) A5,C6: 5.. / A5 = 5 => 13 pairs (_) / C6 = 5 => 0 pairs (X) A8,B8: 5.. / A8 = 5 => 0 pairs (X) / B8 = 5 => 13 pairs (_) E9,F9: 5.. / E9 = 5 => 12 pairs (_) / F9 = 5 => 15 pairs (_) H7,I7: 5.. / H7 = 5 => 14 pairs (_) / I7 = 5 => 0 pairs (X) B1,I1: 5.. / B1 = 5 => 0 pairs (X) / I1 = 5 => 12 pairs (_) A5,E5: 5.. / A5 = 5 => 13 pairs (_) / E5 = 5 => 0 pairs (X) A5,A8: 5.. / A5 = 5 => 13 pairs (_) / A8 = 5 => 0 pairs (X) C2,C6: 5.. / C2 = 5 => 13 pairs (_) / C6 = 5 => 0 pairs (X) F6,F9: 5.. / F6 = 5 => 12 pairs (_) / F9 = 5 => 15 pairs (_) H3,H7: 5.. / H3 = 5 => 0 pairs (X) / H7 = 5 => 14 pairs (_) B2,B3: 7.. / B2 = 7 => 14 pairs (_) / B3 = 7 => 0 pairs (*) I2,I3: 7.. / I2 = 7 => 0 pairs (*) / I3 = 7 => 0 pairs (X) B2,I2: 7.. / B2 = 7 => 14 pairs (_) / I2 = 7 => 0 pairs (*) B3,I3: 7.. / B3 = 7 => 0 pairs (*) / I3 = 7 => 0 pairs (X) D4,E6: 8.. / D4 = 8 => 0 pairs (X) / E6 = 8 => 22 pairs (_) H4,I6: 8.. / H4 = 8 => 22 pairs (_) / I6 = 8 => 0 pairs (X) D2,I2: 8.. / D2 = 8 => 0 pairs (*) / I2 = 8 => 0 pairs (X) D4,H4: 8.. / D4 = 8 => 0 pairs (X) / H4 = 8 => 22 pairs (_) E6,I6: 8.. / E6 = 8 => 22 pairs (_) / I6 = 8 => 0 pairs (X) E3,E6: 8.. / E3 = 8 => 0 pairs (X) / E6 = 8 => 22 pairs (_) H3,H4: 8.. / H3 = 8 => 0 pairs (X) / H4 = 8 => 22 pairs (_) A8,B8: 9.. / A8 = 9 => 13 pairs (_) / B8 = 9 => 0 pairs (X) E9,F9: 9.. / E9 = 9 => 15 pairs (_) / F9 = 9 => 12 pairs (_) H7,I7: 9.. / H7 = 9 => 0 pairs (X) / I7 = 9 => 14 pairs (_) A5,A8: 9.. / A5 = 9 => 0 pairs (X) / A8 = 9 => 13 pairs (_) I6,I7: 9.. / I6 = 9 => 0 pairs (X) / I7 = 9 => 14 pairs (_) * DURATION: 0:00:57.760797 START: 03:13:23.359634 END: 03:14:21.120431 2017-05-04 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A8,B1,B8,C2,C4,D4,E9,F2,F9,H5,H7,I1,I7) * 8.672394.4...6.23.3.2..46..63..475.2.876.24.324.3..76.7241368....34781261682..374 * PAIR B1: 1,5 BLK 1 B2: 1,5,7,9 # reduction candidate for 1,5 B2: 1,5 => CTR * 8.672394.4.98612373725946..6319475829876524.324.3..76.7241368...934781261682..374 B2: 7,9 # 15 pairs B3: 1,5,7,9 # reduction candidate for 1,5 B3: 1,5 => CTR * 8.672394147986123.3.2..46.7631.475.29876524132453197687241368.9593478126168295374 B3: 7,9 # 15 pairs * PAIR C2: 5,9 BLK 1 B2: 5,9,1,7 # reduction candidate for 5,9 B2: 5,9 => SOLVED * 816723945495861237372594618631947582587612493249385761724136859953478126168259374 B2: 1,7 # 15 pairs B3: 5,9,1,7 # reduction candidate for 5,9 B3: 5,9 # 14 pairs * PAIR C2: 5,9 ROW 2 D2: 5,9,8 # reduction candidate for 5,9 D2: 5,9 => CTR * 8.672394.47..612383.28946.7631947582.87612493249385761724136859953478126168259374 D2: 8 => SOLVED * 816723945495861237372594618631947582587612493249385761724136859953478126168259374 * PAIR C2: 5,9 COL C C6: 5,9,1 # reduction candidate for 5,9 C6: 1 => CTR * 8.672394.4.5.6.23.3.25.46..6398475125876124932413..7687241368599534781261682..374 C6: 5,9 # 15 pairs * PAIR F2: 1,9 BLK 2 E3: 1,9,8 # reduction candidate for 1,9 E3: 8 => CTR * 8.672394.4...6123.3.2.846..63.8475.2.876.24.324.3..7687241368.9..34781261682..374 E3: 1,9 # 22 pairs * PAIR F2: 1,9 ROW 2 B2: 1,9,5,7 # reduction candidate for 1,9 B2: 1,9 => SOLVED * 816723945495861237372594618631947582587612493249385761724136859953478126168259374 B2: 5,7 # 15 pairs * PAIR F2: 1,9 COL F F6: 1,9,5 # reduction candidate for 1,9 F6: 1,9 # 15 pairs F6: 5 # 12 pairs * PAIR I1: 1,5 BLK 3 I2: 1,5,7,8 # reduction candidate for 1,5 I2: 1,5 => CTR * 8.672394.47.86.23.3.25.46.763.947582.876.24.324.38.76.724136859..34781261682..374 I2: 7,8 # 15 pairs H3: 1,5,8 # reduction candidate for 1,5 H3: 1,5 # 22 pairs I3: 1,5,7,8 # reduction candidate for 1,5 I3: 1,5 => CTR * 8.672394.4...6.237372..468.63.8475.2.876.24.324.3..768724136859..34781261682..374 I3: 7,8 # 15 pairs * PAIR C4: 1,9 BLK 4 C6: 1,9,5 # reduction candidate for 1,9 C6: 5 => CTR * 8.672394.4.9.6123.3.298465.631.475.29876524132453..76.7241368..593478126168295374 C6: 1,9 # 13 pairs * PAIR C4: 1,9 ROW 4 H4: 1,9,8 # reduction candidate for 1,9 H4: 1,9 => CTR * 8.672394.4...6.23.3.2..468.63.8475.2.876.24.324.3..768724136859..34781261682..374 H4: 8 # 22 pairs * PAIR A5: 5,9 BLK 4 C6: 5,9,1 # reduction candidate for 5,9 C6: 1 => CTR * 8.672394.4.5.6.23.3.25.46..6398475125876124932413..7687241368599534781261682..374 C6: 5,9 # 15 pairs * PAIR A5: 5,9 ROW 5 E5: 5,9,1 # reduction candidate for 5,9 E5: 5,9 # 19 pairs E5: 1 # 14 pairs * PAIR D4: 8,9 BLK 5 E6: 8,9,1,5 # reduction candidate for 8,9 E6: 1,5 => CTR * 8.672394.4...6.23.3.2.846..63.8475.2.876.24.324.3..7687241368.9..34781261682..374 E6: 8,9 # 17 pairs * PAIR D4: 8,9 ROW 4 H4: 8,9,1 # reduction candidate for 8,9 H4: 1 => CTR * 8.672394.4...6.23.3.2..468.63.847512.876124932413..7687241368599534781261682..374 H4: 8,9 # 15 pairs * PAIR D4: 8,9 COL D D2: 8,9,5 # reduction candidate for 8,9 D2: 8,9 # 15 pairs D3: 8,9,5 # reduction candidate for 8,9 D3: 8,9 => CTR * 8.672394.4795612383.28946.763..47582.876.24.324538.76.7241368..5934781261682.5374 D3: 5 # 15 pairs * PAIR H5: 1,9 BLK 6 H4: 1,9,8 # reduction candidate for 1,9 H4: 1,9 => CTR * 8.672394.4...6.23.3.2..468.63.8475.2.876.24.324.3..768724136859..34781261682..374 H4: 8 # 22 pairs I6: 1,9,8 # reduction candidate for 1,9 I6: 1,9 # 22 pairs * PAIR H5: 1,9 ROW 5 E5: 1,9,5 # reduction candidate for 1,9 E5: 5 => CTR * 8.672394.4.9.6123.3.298465.63..475.2.876524132453..76.7241368..593478126168295374 E5: 1,9 # 13 pairs * PAIR B8: 5,9 COL B B2: 5,9,1,7 # reduction candidate for 5,9 B2: 5,9 => SOLVED * 816723945495861237372594618631947582587612493249385761724136859953478126168259374 B2: 1,7 # 15 pairs B3: 5,9,1,7 # reduction candidate for 5,9 B3: 5,9 # 14 pairs * PAIR E9: 5,9 COL E E5: 5,9,1 # reduction candidate for 5,9 E5: 5,9 # 19 pairs E6: 5,9,1,8 # reduction candidate for 5,9 E6: 5,9 => CTR * 8.672394.4...6.23.3.2.846..63.8475.2.8761249324.3..7687241368599534781261682..374 E6: 1,8 # 15 pairs * PAIR F9: 5,9 COL F F6: 5,9,1 # reduction candidate for 5,9 F6: 1 => CTR * 8.672394.4...6923.392.146.7631947582.8765241324.3.176.7241368....34781261682.5374 F6: 5,9 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-019-base-pr-000.dot * REASONING * DIS # B2: 1,5 => CTR => B2: 7,9 * DIS # B3: 1,5 => CTR => B3: 7,9 * PRF # B2: 5,9 => SOL * DIS # D2: 5,9 => CTR => D2: 8 * PRF # D2: 8 => SOL * DIS # C6: 1 => CTR => C6: 5,9 * DIS # E3: 8 => CTR => E3: 1,9 * PRF # B2: 1,9 => SOL * DIS # I2: 1,5 => CTR => I2: 7,8 * DIS # I3: 1,5 => CTR => I3: 7,8 * DIS # C6: 5 => CTR => C6: 1,9 * DIS # H4: 1,9 => CTR => H4: 8 * DIS # C6: 1 => CTR => C6: 5,9 * DIS # E6: 1,5 => CTR => E6: 8,9 * DIS # H4: 1 => CTR => H4: 8,9 * DIS # D3: 8,9 => CTR => D3: 5 * DIS # H4: 1,9 => CTR => H4: 8 * DIS # E5: 5 => CTR => E5: 1,9 * PRF # B2: 5,9 => SOL * DIS # E6: 5,9 => CTR => E6: 1,8 * DIS # F6: 1 => CTR => F6: 5,9 * CNT 21 HDP CHAINS / 50 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A8,B1,B8,C2,C4,D4,E9,F2,F9,H5,H7,I1,I7) * 8.672394.4...6.23.3.2..46..63..475.2.876.24.324.3..76.7241368....34781261682..374 * PAIR B1: 1,5 BLK 1 B2: 1,5,7,9 # reduction candidate for 1,5 B2: 1,5 => CTR * 8.672394.4.98612373725946..6319475829876524.324.3..76.7241368...934781261682..374 B3: 1,5,7,9 # reduction candidate for 1,5 B3: 1,5 => CTR * 8.672394147986123.3.2..46.7631.475.29876524132453197687241368.9593478126168295374 * PAIR F2: 1,9 BLK 2 E3: 1,9,8 # reduction candidate for 1,9 E3: 1,9 => SOLVED * 816723945495861237372594618631947582587612493249385761724136859953478126168259374 * DURATION: 0:00:04.413853 START: 03:15:08.994780 END: 03:15:13.408633 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-019-base-pr-001.dot * REASONING * DIS # B2: 1,5 => CTR => B2: 7,9 * DIS B2: 7,9 # B3: 1,5 => CTR => B3: 7,9 * PRF B2: 7,9 + B3: 7,9 # E3: 1,9 => SOL * STA B2: 7,9 + B3: 7,9 + E3: 1,9 * CNT 3 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 019 solution: 816723945495861237372594618631947582587612493249385761724136859953478126168259374 info: 1311 FNBTWXY S8.f 38428 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 816723945495861237372594618631947582587612493249385761724136859953478126168259374 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 # B2: 1,5 => CTR => B2: 7,9 * INC # B2: 7,9 => UNS * DIS # B3: 1,5 => CTR => B3: 7,9 * INC # B3: 7,9 => UNS * PRF # B2: 5,9 => SOL * INC # B2: 1,7 => UNS * INC # B3: 5,9 => UNS * DIS # D2: 5,9 => CTR => D2: 8 * PRF # D2: 8 => SOL * INC # C6: 5,9 => UNS * DIS # C6: 1 => CTR => C6: 5,9 * INC # E3: 1,9 => UNS * DIS # E3: 8 => CTR => E3: 1,9 * PRF # B2: 1,9 => SOL * INC # B2: 5,7 => UNS * INC # F6: 1,9 => UNS * INC # F6: 5 => UNS * DIS # I2: 1,5 => CTR => I2: 7,8 * INC # I2: 7,8 => UNS * INC # H3: 1,5 => UNS * DIS # I3: 1,5 => CTR => I3: 7,8 * INC # I3: 7,8 => UNS * INC # C6: 1,9 => UNS * DIS # C6: 5 => CTR => C6: 1,9 * DIS # H4: 1,9 => CTR => H4: 8 * INC # H4: 8 => UNS * INC # C6: 5,9 => UNS * DIS # C6: 1 => CTR => C6: 5,9 * INC # E5: 5,9 => UNS * INC # E5: 1 => UNS * INC # E6: 8,9 => UNS * DIS # E6: 1,5 => CTR => E6: 8,9 * INC # H4: 8,9 => UNS * DIS # H4: 1 => CTR => H4: 8,9 * INC # D2: 8,9 => UNS * DIS # D3: 8,9 => CTR => D3: 5 * INC # D3: 5 => UNS * DIS # H4: 1,9 => CTR => H4: 8 * INC # H4: 8 => UNS * INC # I6: 1,9 => UNS * INC # E5: 1,9 => UNS * DIS # E5: 5 => CTR => E5: 1,9 * PRF # B2: 5,9 => SOL * INC # B2: 1,7 => UNS * INC # B3: 5,9 => UNS * INC # E5: 5,9 => UNS * DIS # E6: 5,9 => CTR => E6: 1,8 * INC # E6: 1,8 => UNS * INC # F6: 5,9 => UNS * DIS # F6: 1 => CTR => F6: 5,9 * CNT 50 HDP CHAINS / 50 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B2: 1,5 => CTR => B2: 7,9 * DIS B2: 7,9 # B3: 1,5 => CTR => B3: 7,9 * PRF B2: 7,9 + B3: 7,9 # E3: 1,9 => SOL * STA B2: 7,9 + B3: 7,9 + E3: 1,9 * CNT 3 HDP CHAINS / 3 HYP OPENED