Analysis of xx-top500-300-base.sdk
Contents
Original Sudoku
level: medium
position: .5.4.........3.8..........13...8.7...6.....5....2........5.6.4.1.8...3........... initial
Autosolve
position: .514.8.366..1358.4483.6.5.13.568471.86.3.145..1425.683.3.5.6.481.8...3655.68.3..7 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E1: 7,9 => CTR => E1: 2 * PRF # E1: 2 => SOL * PRF # F3: 7,9 => SOL * DIS # F3: 2 => CTR => F3: 7,9 * DIS # H3: 7,9 => CTR => H3: 2 * PRF # H3: 2 => SOL * DIS # H2: 2,9 => CTR => H2: 7 * PRF # H2: 7 => SOL * PRF # H3: 2,9 => SOL * DIS # H3: 7 => CTR => H3: 2,9 * DIS # A1: 2,9 => CTR => A1: 7 * PRF # A1: 7 => SOL * PRF # E1: 2,9 => SOL * DIS # E1: 7 => CTR => E1: 2,9 * DIS # G7: 2,9 => CTR => G7: 1 * DIS # C5: 2,9 => CTR => C5: 7 * PRF # C5: 7 => SOL * PRF # B2: 2,9 => SOL * DIS # B2: 7 => CTR => B2: 2,9 * DIS # B8: 2,9 => CTR => B8: 4,7 * DIS # B9: 2,9 => CTR => B9: 4 * DIS # C5: 2 => CTR => C5: 7,9 * DIS # A7: 7,9 => CTR => A7: 2 * DIS # C5: 2 => CTR => C5: 7,9 * DIS # E1: 7,9 => CTR => E1: 2 * PRF # E1: 2 => SOL * PRF # E7: 7,9 => SOL * DIS # E7: 1,2 => CTR => E7: 7,9 * DIS # E8: 7,9 => CTR => E8: 2,4 * PRF # F3: 7,9 => SOL * DIS # F3: 2 => CTR => F3: 7,9 * DIS # F8: 7,9 => CTR => F8: 2 * PRF # F8: 2 => SOL * DIS # C5: 2,9 => CTR => C5: 7 * PRF # C5: 7 => SOL * PRF # E7: 7,9 => SOL * DIS # E7: 1,2 => CTR => E7: 7,9 * DIS # E8: 7,9 => CTR => E8: 2,4 * DIS # F8: 7,9 => CTR => F8: 2 * PRF # F8: 2 => SOL * PRF # B8: 7,9 => SOL * DIS # B8: 2,4 => CTR => B8: 7,9 * DIS # G7: 2,9 => CTR => G7: 1 * DIS # B9: 2,9 => CTR => B9: 4 * DIS # E9: 2,9 => CTR => E9: 1,4 * DIS # H2: 2,9 => CTR => H2: 7 * PRF # H2: 7 => SOL * PRF # H3: 2,9 => SOL * DIS # H3: 7 => CTR => H3: 2,9 * CNT 49 HDP CHAINS / 63 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E1: 7,9 => CTR => E1: 2 * PRF E1: 2 => SOL * STA E1: 2 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .5.4.........3.8..........13...8.7...6.....5....2........5.6.4.1.8...3........... | initial |
| .514.8.366..1358.4483.6.5.13.568471.86.3.145..1425.683.3.5.6.481.8...3655.68.3..7 | autosolve |
| 751428936692135874483769521325684719867391452914257683239576148178942365546813297 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) D3: 7,9 G1: 2,9 B4: 2,9 A6: 7,9 E5: 7,9 F6: 7,9 I4: 2,9 I5: 2,9 D8: 7,9 H9: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E7,E9: 1.. / E7 = 1 => 0 pairs (X) / E9 = 1 => 11 pairs (_) G7,G9: 1.. / G7 = 1 => 11 pairs (_) / G9 = 1 => 0 pairs (X) E7,G7: 1.. / E7 = 1 => 0 pairs (X) / G7 = 1 => 11 pairs (_) E9,G9: 1.. / E9 = 1 => 11 pairs (_) / G9 = 1 => 0 pairs (X) E1,F3: 2.. / E1 = 2 => 0 pairs (*) / F3 = 2 => 0 pairs (X) B4,C5: 2.. / B4 = 2 => 11 pairs (_) / C5 = 2 => 0 pairs (X) I4,I5: 2.. / I4 = 2 => 0 pairs (X) / I5 = 2 => 11 pairs (_) F3,H3: 2.. / F3 = 2 => 0 pairs (X) / H3 = 2 => 0 pairs (_) B4,I4: 2.. / B4 = 2 => 11 pairs (_) / I4 = 2 => 0 pairs (X) C5,I5: 2.. / C5 = 2 => 0 pairs (X) / I5 = 2 => 11 pairs (_) A1,A7: 2.. / A1 = 2 => 0 pairs (X) / A7 = 2 => 15 pairs (_) F3,F8: 2.. / F3 = 2 => 0 pairs (X) / F8 = 2 => 0 pairs (_) B8,B9: 4.. / B8 = 4 => 0 pairs (X) / B9 = 4 => 10 pairs (_) E8,E9: 4.. / E8 = 4 => 10 pairs (_) / E9 = 4 => 0 pairs (X) B8,E8: 4.. / B8 = 4 => 0 pairs (X) / E8 = 4 => 10 pairs (_) B9,E9: 4.. / B9 = 4 => 10 pairs (_) / E9 = 4 => 0 pairs (X) H2,H3: 7.. / H2 = 7 => 0 pairs (*) / H3 = 7 => 0 pairs (X) C5,A6: 7.. / C5 = 7 => 0 pairs (*) / A6 = 7 => 0 pairs (X) E5,F6: 7.. / E5 = 7 => 0 pairs (X) / F6 = 7 => 0 pairs (_) A1,E1: 7.. / A1 = 7 => 0 pairs (*) / E1 = 7 => 0 pairs (X) C5,E5: 7.. / C5 = 7 => 0 pairs (*) / E5 = 7 => 0 pairs (X) A6,F6: 7.. / A6 = 7 => 0 pairs (X) / F6 = 7 => 0 pairs (_) B2,B8: 7.. / B2 = 7 => 0 pairs (X) / B8 = 7 => 0 pairs (_) D3,D8: 7.. / D3 = 7 => 0 pairs (*) / D8 = 7 => 0 pairs (X) E5,F6: 9.. / E5 = 9 => 0 pairs (*) / F6 = 9 => 0 pairs (X) I4,I5: 9.. / I4 = 9 => 11 pairs (_) / I5 = 9 => 0 pairs (X) B4,I4: 9.. / B4 = 9 => 0 pairs (X) / I4 = 9 => 11 pairs (_) A6,F6: 9.. / A6 = 9 => 0 pairs (*) / F6 = 9 => 0 pairs (X) D3,D8: 9.. / D3 = 9 => 0 pairs (X) / D8 = 9 => 0 pairs (_) * DURATION: 0:00:47.636271 START: 13:12:25.194313 END: 13:13:12.830584 2017-05-04 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B4,D3,D8,E5,F6,G1,H9,I4,I5) * .514.8.366..1358.4483.6.5.13.568471.86.3.145..1425.683.3.5.6.481.8...3655.68.3..7 * PAIR D3: 7,9 BLK 2 E1: 7,9,2 # reduction candidate for 7,9 E1: 7,9 => CTR * .51478.3667.1358.44839625713.568471.86739145291425768373.5.6.481.87.9365596843127 E1: 2 => SOLVED * 751428936692135874483769521325684719867391452914257683239576148178942365546813297 F3: 7,9,2 # reduction candidate for 7,9 F3: 7,9 => SOLVED * 751428936692135874483769521325684719867391452914257683239576148178942365546813297 F3: 2 => CTR * .51478.3667.1358.44839625713.568471.86739145291425768373.5.6.481.87.9365596843127 * PAIR D3: 7,9 ROW 3 H3: 7,9,2 # reduction candidate for 7,9 H3: 7,9 => CTR * .51478.3667.1358.44839625713.568471.86739145291425768373.5.6.481.87.9365596843127 H3: 2 => SOLVED * 751428936692135874483769521325684719867391452914257683239576148178942365546813297 * PAIR G1: 2,9 BLK 3 H2: 2,9,7 # reduction candidate for 2,9 H2: 2,9 => CTR * .51478.3667.1358.44839625713.568471.86739145291425768373.5.6.481.87.9365596843127 H2: 7 => SOLVED * 751428936692135874483769521325684719867391452914257683239576148178942365546813297 H3: 2,9,7 # reduction candidate for 2,9 H3: 2,9 => SOLVED * 751428936692135874483769521325684719867391452914257683239576148178942365546813297 H3: 7 => CTR * .51478.3667.1358.44839625713.568471.86739145291425768373.5.6.481.87.9365596843127 * PAIR G1: 2,9 ROW 1 A1: 2,9,7 # reduction candidate for 2,9 A1: 2,9 => CTR * 2514789366791358.44839625713.568471.86739145291425768373.5.6.481.87.93655.68.3..7 A1: 7 => SOLVED * 751428936692135874483769521325684719867391452914257683239576148178942365546813297 E1: 2,9,7 # reduction candidate for 2,9 E1: 2,9 => SOLVED * 751428936692135874483769521325684719867391452914257683239576148178942365546813297 E1: 7 => CTR * 2514789366791358.44839625713.568471.86739145291425768373.5.6.481.87.93655.68.3..7 * PAIR G1: 2,9 COL G G7: 2,9,1 # reduction candidate for 2,9 G7: 2,9 => CTR * .51478.3667.1358.44839625713.568471.86739145291425768373.516.481.87.9365596843127 G7: 1 # 11 pairs G9: 2,9,1 # reduction candidate for 2,9 G9: 2,9 # 11 pairs * PAIR B4: 2,9 BLK 4 C5: 2,9,7 # reduction candidate for 2,9 C5: 2,9 => CTR * .514.8.366..1358.4483.6.5.13.568471.86.37145.714259683.375.6.481.8...3655.68.3..7 C5: 7 => SOLVED * 751428936692135874483769521325684719867391452914257683239576148178942365546813297 * PAIR B4: 2,9 COL B B2: 2,9,7 # reduction candidate for 2,9 B2: 2,9 => SOLVED * 751428936692135874483769521325684719867391452914257683239576148178942365546813297 B2: 7 => CTR * .51478.3667.1358.44839625713.568471.86739145291425768373.5.6.481.87.9365596843127 B8: 2,9,4,7 # reduction candidate for 2,9 B8: 2,9 => CTR * .51478.3667.1358.44839625713.568471.86739145291425768373.5.6.481.874.3655468.3..7 B8: 4,7 # 13 pairs B9: 2,9,4 # reduction candidate for 2,9 B9: 2,9 => CTR * .51478.3667.1358.44839625713.568471.86739145291425768373.516.48148729365596843127 B9: 4 # 10 pairs * PAIR A6: 7,9 BLK 4 C5: 7,9,2 # reduction candidate for 7,9 C5: 2 => CTR * .514.8.366..1358.4483.6.5.13.568471.862371459714259683.375.6.481.8...3655.68.3..7 C5: 7,9 # 11 pairs * PAIR A6: 7,9 COL A A1: 7,9,2 # reduction candidate for 7,9 A1: 7,9 # 15 pairs A7: 7,9,2 # reduction candidate for 7,9 A7: 7,9 => CTR * 2514789366..1358244839625713.568471.86739145291425768373.5.6.481.8...3655.68.3..7 A7: 2 # 15 pairs * PAIR E5: 7,9 ROW 5 C5: 7,9,2 # reduction candidate for 7,9 C5: 2 => CTR * .514.8.366..1358.4483.6.5.13.568471.862371459714259683.375.6.481.8...3655.68.3..7 C5: 7,9 # 11 pairs * PAIR E5: 7,9 COL E E1: 7,9,2 # reduction candidate for 7,9 E1: 7,9 => CTR * .51478.3667.1358.44839625713.568471.86739145291425768373.5.6.481.87.9365596843127 E1: 2 => SOLVED * 751428936692135874483769521325684719867391452914257683239576148178942365546813297 E7: 7,9,1,2 # reduction candidate for 7,9 E7: 7,9 => SOLVED * 751428936692135874483769521325684719867391452914257683239576148178942365546813297 E7: 1,2 => CTR * .51478.3667.1358.44839625713.568471.86739145291425768373.5.6.481.87.9365596843127 E8: 7,9,2,4 # reduction candidate for 7,9 E8: 7,9 => CTR * .5142893667.1358.4483.6.5.13.568471.86.3.145..1425.683.3.5.6.48148..23655.68431.7 E8: 2,4 # 11 pairs * PAIR F6: 7,9 COL F F3: 7,9,2 # reduction candidate for 7,9 F3: 7,9 => SOLVED * 751428936692135874483769521325684719867391452914257683239576148178942365546813297 F3: 2 => CTR * .51478.3667.1358.44839625713.568471.86739145291425768373.5.6.481.87.9365596843127 F8: 7,9,2 # reduction candidate for 7,9 F8: 7,9 => CTR * .51478.3667.1358.44839625713.568471.86739145291425768373.5.6.481.87.9365596843127 F8: 2 => SOLVED * 751428936692135874483769521325684719867391452914257683239576148178942365546813297 * PAIR I5: 2,9 ROW 5 C5: 2,9,7 # reduction candidate for 2,9 C5: 2,9 => CTR * .514.8.366..1358.4483.6.5.13.568471.86.37145.714259683.375.6.481.8...3655.68.3..7 C5: 7 => SOLVED * 751428936692135874483769521325684719867391452914257683239576148178942365546813297 * PAIR D8: 7,9 BLK 8 E7: 7,9,1,2 # reduction candidate for 7,9 E7: 7,9 => SOLVED * 751428936692135874483769521325684719867391452914257683239576148178942365546813297 E7: 1,2 => CTR * .51478.3667.1358.44839625713.568471.86739145291425768373.5.6.481.87.9365596843127 E8: 7,9,2,4 # reduction candidate for 7,9 E8: 7,9 => CTR * .5142893667.1358.4483.6.5.13.568471.86.3.145..1425.683.3.5.6.48148..23655.68431.7 E8: 2,4 # 11 pairs F8: 7,9,2 # reduction candidate for 7,9 F8: 7,9 => CTR * .51478.3667.1358.44839625713.568471.86739145291425768373.5.6.481.87.9365596843127 F8: 2 => SOLVED * 751428936692135874483769521325684719867391452914257683239576148178942365546813297 * PAIR D8: 7,9 ROW 8 B8: 7,9,2,4 # reduction candidate for 7,9 B8: 7,9 => SOLVED * 751428936692135874483769521325684719867391452914257683239576148178942365546813297 B8: 2,4 => CTR * .51478.3667.1358.44839625713.568471.86739145291425768373.5.6.481.87.9365596843127 * PAIR H9: 2,9 BLK 9 G7: 2,9,1 # reduction candidate for 2,9 G7: 2,9 => CTR * .51478.3667.1358.44839625713.568471.86739145291425768373.516.481.87.9365596843127 G7: 1 # 11 pairs G9: 2,9,1 # reduction candidate for 2,9 G9: 2,9 # 11 pairs * PAIR H9: 2,9 ROW 9 B9: 2,9,4 # reduction candidate for 2,9 B9: 2,9 => CTR * .51478.3667.1358.44839625713.568471.86739145291425768373.516.48148729365596843127 B9: 4 # 10 pairs E9: 2,9,1,4 # reduction candidate for 2,9 E9: 2,9 => CTR * .51478.3667.1358.44839625713.568471.86739145291425768373.516.481.8.4.3655468.31.7 E9: 1,4 # 11 pairs * PAIR H9: 2,9 COL H H2: 2,9,7 # reduction candidate for 2,9 H2: 2,9 => CTR * .51478.3667.1358.44839625713.568471.86739145291425768373.5.6.481.87.9365596843127 H2: 7 => SOLVED * 751428936692135874483769521325684719867391452914257683239576148178942365546813297 H3: 2,9,7 # reduction candidate for 2,9 H3: 2,9 => SOLVED * 751428936692135874483769521325684719867391452914257683239576148178942365546813297 H3: 7 => CTR * .51478.3667.1358.44839625713.568471.86739145291425768373.5.6.481.87.9365596843127 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-300-base-pr-000.dot * REASONING * DIS # E1: 7,9 => CTR => E1: 2 * PRF # E1: 2 => SOL * PRF # F3: 7,9 => SOL * DIS # F3: 2 => CTR => F3: 7,9 * DIS # H3: 7,9 => CTR => H3: 2 * PRF # H3: 2 => SOL * DIS # H2: 2,9 => CTR => H2: 7 * PRF # H2: 7 => SOL * PRF # H3: 2,9 => SOL * DIS # H3: 7 => CTR => H3: 2,9 * DIS # A1: 2,9 => CTR => A1: 7 * PRF # A1: 7 => SOL * PRF # E1: 2,9 => SOL * DIS # E1: 7 => CTR => E1: 2,9 * DIS # G7: 2,9 => CTR => G7: 1 * DIS # C5: 2,9 => CTR => C5: 7 * PRF # C5: 7 => SOL * PRF # B2: 2,9 => SOL * DIS # B2: 7 => CTR => B2: 2,9 * DIS # B8: 2,9 => CTR => B8: 4,7 * DIS # B9: 2,9 => CTR => B9: 4 * DIS # C5: 2 => CTR => C5: 7,9 * DIS # A7: 7,9 => CTR => A7: 2 * DIS # C5: 2 => CTR => C5: 7,9 * DIS # E1: 7,9 => CTR => E1: 2 * PRF # E1: 2 => SOL * PRF # E7: 7,9 => SOL * DIS # E7: 1,2 => CTR => E7: 7,9 * DIS # E8: 7,9 => CTR => E8: 2,4 * PRF # F3: 7,9 => SOL * DIS # F3: 2 => CTR => F3: 7,9 * DIS # F8: 7,9 => CTR => F8: 2 * PRF # F8: 2 => SOL * DIS # C5: 2,9 => CTR => C5: 7 * PRF # C5: 7 => SOL * PRF # E7: 7,9 => SOL * DIS # E7: 1,2 => CTR => E7: 7,9 * DIS # E8: 7,9 => CTR => E8: 2,4 * DIS # F8: 7,9 => CTR => F8: 2 * PRF # F8: 2 => SOL * PRF # B8: 7,9 => SOL * DIS # B8: 2,4 => CTR => B8: 7,9 * DIS # G7: 2,9 => CTR => G7: 1 * DIS # B9: 2,9 => CTR => B9: 4 * DIS # E9: 2,9 => CTR => E9: 1,4 * DIS # H2: 2,9 => CTR => H2: 7 * PRF # H2: 7 => SOL * PRF # H3: 2,9 => SOL * DIS # H3: 7 => CTR => H3: 2,9 * CNT 49 HDP CHAINS / 63 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B4,D3,D8,E5,F6,G1,H9,I4,I5) * .514.8.366..1358.4483.6.5.13.568471.86.3.145..1425.683.3.5.6.481.8...3655.68.3..7 * PAIR D3: 7,9 BLK 2 E1: 7,9,2 # reduction candidate for 7,9 E1: 7,9 => CTR * .51478.3667.1358.44839625713.568471.86739145291425768373.5.6.481.87.9365596843127 E1: 2 => SOLVED * 751428936692135874483769521325684719867391452914257683239576148178942365546813297 * DURATION: 0:00:01.746411 START: 13:14:17.402131 END: 13:14:19.148542 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-300-base-pr-001.dot * REASONING * DIS # E1: 7,9 => CTR => E1: 2 * PRF E1: 2 => SOL * STA E1: 2 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 300 solution: 751428936692135874483769521325684719867391452914257683239576148178942365546813297 info: 2573 FNW S8.f 20250 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 751428936692135874483769521325684719867391452914257683239576148178942365546813297 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 # E1: 7,9 => CTR => E1: 2 * PRF # E1: 2 => SOL * PRF # F3: 7,9 => SOL * DIS # F3: 2 => CTR => F3: 7,9 * DIS # H3: 7,9 => CTR => H3: 2 * PRF # H3: 2 => SOL * DIS # H2: 2,9 => CTR => H2: 7 * PRF # H2: 7 => SOL * PRF # H3: 2,9 => SOL * DIS # H3: 7 => CTR => H3: 2,9 * DIS # A1: 2,9 => CTR => A1: 7 * PRF # A1: 7 => SOL * PRF # E1: 2,9 => SOL * DIS # E1: 7 => CTR => E1: 2,9 * DIS # G7: 2,9 => CTR => G7: 1 * INC # G7: 1 => UNS * INC # G9: 2,9 => UNS * DIS # C5: 2,9 => CTR => C5: 7 * PRF # C5: 7 => SOL * PRF # B2: 2,9 => SOL * DIS # B2: 7 => CTR => B2: 2,9 * DIS # B8: 2,9 => CTR => B8: 4,7 * INC # B8: 4,7 => UNS * DIS # B9: 2,9 => CTR => B9: 4 * INC # B9: 4 => UNS * INC # C5: 7,9 => UNS * DIS # C5: 2 => CTR => C5: 7,9 * INC # A1: 7,9 => UNS * DIS # A7: 7,9 => CTR => A7: 2 * INC # A7: 2 => UNS * INC # C5: 7,9 => UNS * DIS # C5: 2 => CTR => C5: 7,9 * DIS # E1: 7,9 => CTR => E1: 2 * PRF # E1: 2 => SOL * PRF # E7: 7,9 => SOL * DIS # E7: 1,2 => CTR => E7: 7,9 * DIS # E8: 7,9 => CTR => E8: 2,4 * INC # E8: 2,4 => UNS * PRF # F3: 7,9 => SOL * DIS # F3: 2 => CTR => F3: 7,9 * DIS # F8: 7,9 => CTR => F8: 2 * PRF # F8: 2 => SOL * DIS # C5: 2,9 => CTR => C5: 7 * PRF # C5: 7 => SOL * PRF # E7: 7,9 => SOL * DIS # E7: 1,2 => CTR => E7: 7,9 * DIS # E8: 7,9 => CTR => E8: 2,4 * INC # E8: 2,4 => UNS * DIS # F8: 7,9 => CTR => F8: 2 * PRF # F8: 2 => SOL * PRF # B8: 7,9 => SOL * DIS # B8: 2,4 => CTR => B8: 7,9 * DIS # G7: 2,9 => CTR => G7: 1 * INC # G7: 1 => UNS * INC # G9: 2,9 => UNS * DIS # B9: 2,9 => CTR => B9: 4 * INC # B9: 4 => UNS * DIS # E9: 2,9 => CTR => E9: 1,4 * INC # E9: 1,4 => UNS * DIS # H2: 2,9 => CTR => H2: 7 * PRF # H2: 7 => SOL * PRF # H3: 2,9 => SOL * DIS # H3: 7 => CTR => H3: 2,9 * CNT 63 HDP CHAINS / 63 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # E1: 7,9 => CTR => E1: 2 * PRF E1: 2 => SOL * STA E1: 2 * CNT 2 HDP CHAINS / 1 HYP OPENED