Analysis of xx-top500-364-base.sdk
Contents
Original Sudoku
level: medium
position: ...2..4....5...8...3..7.......1.8.3.1..4............5..24...1......5....6........ initial
Autosolve
position: 9..283475475.1.823832574.1.25.1.87341.74352..348.2..515243..1..7...5.34.6.3.4.59. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # D6: 6,9 => SOL * DIS # D6: 7 => CTR => D6: 6,9 * DIS # F6: 6,9 => CTR => F6: 7 * PRF # F6: 7 => SOL * PRF # F7: 6,9 => SOL * DIS # F7: 7 => CTR => F7: 6,9 * DIS # I5: 6,9 => CTR => I5: 8 * PRF # I5: 8 => SOL * DIS # I5: 6,9 => CTR => I5: 8 * PRF # I5: 8 => SOL * PRF # D6: 6,9 => SOL * DIS # D6: 7 => CTR => D6: 6,9 * DIS # F6: 6,9 => CTR => F6: 7 * PRF # F6: 7 => SOL * PRF # I5: 6,8 => SOL * DIS # I5: 9 => CTR => I5: 6,8 * DIS # I5: 6,9 => CTR => I5: 8 * PRF # I5: 8 => SOL * PRF # D6: 6,9 => SOL * DIS # D6: 7 => CTR => D6: 6,9 * DIS # F6: 6,9 => CTR => F6: 7 * PRF # F6: 7 => SOL * PRF # B8: 1,9 => SOL * DIS # B8: 8 => CTR => B8: 1,9 * PRF # B8: 1,8 => SOL * DIS # B8: 9 => CTR => B8: 1,8 * PRF # F7: 6,9 => SOL * DIS # F7: 7 => CTR => F7: 6,9 * DIS # I7: 6,8 => CTR => I7: 7 * PRF # I7: 7 => SOL * CNT 30 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # D6: 6,9 => SOL * STA D6: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...2..4....5...8...3..7.......1.8.3.1..4............5..24...1......5....6........ | initial |
| 9..283475475.1.823832574.1.25.1.87341.74352..348.2..515243..1..7...5.34.6.3.4.59. | autosolve |
| 961283475475916823832574619256198734197435268348627951524369187719852346683741592 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (21) B1: 1,6 C1: 1,6 D2: 6,9 F2: 6,9 G3: 6,9 I3: 6,9 C4: 6,9 B5: 6,9 E4: 6,9 H5: 6,8 G6: 6,9 C8: 1,9 B9: 1,8 E7: 6,9 D8: 6,8 F8: 1,2 D9: 7,8 F9: 1,2 H7: 6,8 I8: 2,6 I9: 2,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,C1: 1.. / B1 = 1 => 0 pairs (X) / C1 = 1 => 0 pairs (_) F8,F9: 1.. / F8 = 1 => 0 pairs (X) / F9 = 1 => 0 pairs (_) B9,F9: 1.. / B9 = 1 => 0 pairs (X) / F9 = 1 => 0 pairs (_) C1,C8: 1.. / C1 = 1 => 0 pairs (*) / C8 = 1 => 0 pairs (X) F8,F9: 2.. / F8 = 2 => 0 pairs (*) / F9 = 2 => 0 pairs (X) I8,I9: 2.. / I8 = 2 => 0 pairs (X) / I9 = 2 => 0 pairs (_) F8,I8: 2.. / F8 = 2 => 0 pairs (*) / I8 = 2 => 0 pairs (X) F9,I9: 2.. / F9 = 2 => 0 pairs (X) / I9 = 2 => 0 pairs (_) B1,C1: 6.. / B1 = 6 => 0 pairs (*) / C1 = 6 => 0 pairs (X) D2,F2: 6.. / D2 = 6 => 0 pairs (X) / F2 = 6 => 22 pairs (_) G3,I3: 6.. / G3 = 6 => 0 pairs (*) / I3 = 6 => 0 pairs (X) C4,B5: 6.. / C4 = 6 => 0 pairs (*) / B5 = 6 => 0 pairs (X) C4,E4: 6.. / C4 = 6 => 0 pairs (*) / E4 = 6 => 0 pairs (X) D8,I8: 6.. / D8 = 6 => 0 pairs (X) / I8 = 6 => 0 pairs (_) B1,B5: 6.. / B1 = 6 => 0 pairs (*) / B5 = 6 => 0 pairs (X) C1,C4: 6.. / C1 = 6 => 0 pairs (X) / C4 = 6 => 0 pairs (_) E4,E7: 6.. / E4 = 6 => 0 pairs (X) / E7 = 6 => 0 pairs (_) G3,G6: 6.. / G3 = 6 => 0 pairs (*) / G6 = 6 => 0 pairs (X) H5,H7: 6.. / H5 = 6 => 0 pairs (*) / H7 = 6 => 0 pairs (X) D6,F6: 7.. / D6 = 7 => 0 pairs (X) / F6 = 7 => 0 pairs (_) F7,D9: 7.. / F7 = 7 => 0 pairs (X) / D9 = 7 => 0 pairs (_) I7,I9: 7.. / I7 = 7 => 0 pairs (*) / I9 = 7 => 0 pairs (X) F7,I7: 7.. / F7 = 7 => 0 pairs (X) / I7 = 7 => 0 pairs (_) D9,I9: 7.. / D9 = 7 => 0 pairs (*) / I9 = 7 => 0 pairs (X) D6,D9: 7.. / D6 = 7 => 0 pairs (X) / D9 = 7 => 0 pairs (_) F6,F7: 7.. / F6 = 7 => 0 pairs (*) / F7 = 7 => 0 pairs (X) H5,I5: 8.. / H5 = 8 => 0 pairs (X) / I5 = 8 => 0 pairs (_) B8,B9: 8.. / B8 = 8 => 0 pairs (X) / B9 = 8 => 0 pairs (_) D8,D9: 8.. / D8 = 8 => 0 pairs (*) / D9 = 8 => 0 pairs (X) H7,I7: 8.. / H7 = 8 => 0 pairs (*) / I7 = 8 => 0 pairs (X) B8,D8: 8.. / B8 = 8 => 0 pairs (X) / D8 = 8 => 0 pairs (_) B9,D9: 8.. / B9 = 8 => 0 pairs (*) / D9 = 8 => 0 pairs (X) H5,H7: 8.. / H5 = 8 => 0 pairs (X) / H7 = 8 => 0 pairs (_) I5,I7: 8.. / I5 = 8 => 0 pairs (*) / I7 = 8 => 0 pairs (X) D2,F2: 9.. / D2 = 9 => 22 pairs (_) / F2 = 9 => 0 pairs (X) G3,I3: 9.. / G3 = 9 => 0 pairs (X) / I3 = 9 => 0 pairs (_) C4,B5: 9.. / C4 = 9 => 0 pairs (X) / B5 = 9 => 0 pairs (_) I5,G6: 9.. / I5 = 9 => 0 pairs (X) / G6 = 9 => 0 pairs (_) B8,C8: 9.. / B8 = 9 => 0 pairs (X) / C8 = 9 => 0 pairs (_) E7,F7: 9.. / E7 = 9 => 0 pairs (X) / F7 = 9 => 0 pairs (_) C4,E4: 9.. / C4 = 9 => 0 pairs (X) / E4 = 9 => 0 pairs (_) B5,I5: 9.. / B5 = 9 => 0 pairs (*) / I5 = 9 => 0 pairs (X) B5,B8: 9.. / B5 = 9 => 0 pairs (*) / B8 = 9 => 0 pairs (X) C4,C8: 9.. / C4 = 9 => 0 pairs (X) / C8 = 9 => 0 pairs (_) D2,D6: 9.. / D2 = 9 => 22 pairs (_) / D6 = 9 => 0 pairs (X) E4,E7: 9.. / E4 = 9 => 0 pairs (*) / E7 = 9 => 0 pairs (X) G3,G6: 9.. / G3 = 9 => 0 pairs (X) / G6 = 9 => 0 pairs (_) I3,I5: 9.. / I3 = 9 => 0 pairs (*) / I5 = 9 => 0 pairs (X) * DURATION: 0:01:28.619643 START: 15:15:03.816217 END: 15:16:32.435860 2017-05-04 * CP COUNT: (48) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B5,B9,C1,C4,C8,D2,D8,D9,E4,E7,F2,F8,F9,G3,G6,H5,H7,I3,I8,I9) * 9..283475475.1.823832574.1.25.1.87341.74352..348.2..515243..1..7...5.34.6.3.4.59. * PAIR D2: 6,9 COL D D6: 6,9,7 # reduction candidate for 6,9 D6: 6,9 => SOLVED * 961283475475916823832574619256198734197435268348627951524369187719852346683741592 D6: 7 => CTR * 9..283475475916823832574.1.25.168734167435289348729651524397168791.5.34.6.3.4.59. * PAIR F2: 6,9 COL F F6: 6,9,7 # reduction candidate for 6,9 F6: 6,9 => CTR * 9..283475475916823832574.1.25.1687341674352893487296515243971687...5.34.6.384.597 F6: 7 => SOLVED * 961283475475916823832574619256198734197435268348627951524369187719852346683741592 F7: 6,9,7 # reduction candidate for 6,9 F7: 6,9 => SOLVED * 961283475475916823832574619256198734197435268348627951524369187719852346683741592 F7: 7 => CTR * 9..283475475916823832574.1.2591687341674352..348.2..515243971..7..65.3426.3842597 * PAIR I3: 6,9 COL I I5: 6,9,8 # reduction candidate for 6,9 I5: 6,9 => CTR * 9..283475475916823832574.1.25.1687341674352893487296515243971687..65.3426.3842597 I5: 8 => SOLVED * 961283475475916823832574619256198734197435268348627951524369187719852346683741592 * PAIR B5: 6,9 ROW 5 I5: 6,9,8 # reduction candidate for 6,9 I5: 6,9 => CTR * 9..283475475916823832574.1.25.1687341674352893487296515243971687..65.3426.3842597 I5: 8 => SOLVED * 961283475475916823832574619256198734197435268348627951524369187719852346683741592 * PAIR E4: 6,9 BLK 5 D6: 6,9,7 # reduction candidate for 6,9 D6: 6,9 => SOLVED * 961283475475916823832574619256198734197435268348627951524369187719852346683741592 D6: 7 => CTR * 9..283475475916823832574.1.25.168734167435289348729651524397168791.5.34.6.3.4.59. F6: 6,9,7 # reduction candidate for 6,9 F6: 6,9 => CTR * 9..283475475916823832574.1.25.1687341674352893487296515243971687...5.34.6.384.597 F6: 7 => SOLVED * 961283475475916823832574619256198734197435268348627951524369187719852346683741592 * PAIR H5: 6,8 BLK 6 I5: 6,8,9 # reduction candidate for 6,8 I5: 6,8 => SOLVED * 961283475475916823832574619256198734197435268348627951524369187719852346683741592 I5: 9 => CTR * 9..283475475.1.823832574.1.25.1.87341.7435289348.2.6515243..168791.5.34.6.3.4.59. * PAIR G6: 6,9 BLK 6 I5: 6,9,8 # reduction candidate for 6,9 I5: 6,9 => CTR * 9..283475475916823832574.1.25.1687341674352893487296515243971687..65.3426.3842597 I5: 8 => SOLVED * 961283475475916823832574619256198734197435268348627951524369187719852346683741592 * PAIR G6: 6,9 ROW 6 D6: 6,9,7 # reduction candidate for 6,9 D6: 6,9 => SOLVED * 961283475475916823832574619256198734197435268348627951524369187719852346683741592 D6: 7 => CTR * 9..283475475916823832574.1.25.168734167435289348729651524397168791.5.34.6.3.4.59. F6: 6,9,7 # reduction candidate for 6,9 F6: 6,9 => CTR * 9..283475475916823832574.1.25.1687341674352893487296515243971687...5.34.6.384.597 F6: 7 => SOLVED * 961283475475916823832574619256198734197435268348627951524369187719852346683741592 * PAIR C8: 1,9 BLK 7 B8: 1,9,8 # reduction candidate for 1,9 B8: 1,9 => SOLVED * 961283475475916823832574619256198734197435268348627951524369187719852346683741592 B8: 8 => CTR * 9..283475475.1.823832574.1.25.1.87341974352..348.2.9515243..1..789651342613842597 * PAIR B9: 1,8 BLK 7 B8: 1,8,9 # reduction candidate for 1,8 B8: 1,8 => SOLVED * 961283475475916823832574619256198734197435268348627951524369187719852346683741592 B8: 9 => CTR * 916283475475.1.82383257461925916873416743528.348.2..515243..1..791852346683741592 * PAIR E7: 6,9 BLK 8 F7: 6,9,7 # reduction candidate for 6,9 F7: 6,9 => SOLVED * 961283475475916823832574619256198734197435268348627951524369187719852346683741592 F7: 7 => CTR * 9..283475475916823832574.1.2591687341674352..348.2..515243971..7..65.3426.3842597 * PAIR H7: 6,8 BLK 9 I7: 6,8,7 # reduction candidate for 6,8 I7: 6,8 => CTR * 9..283475475.1.823832574.1.25.1.87341.74352..34872..515243971..789651342613842597 I7: 7 => SOLVED * 961283475475916823832574619256198734197435268348627951524369187719852346683741592 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-364-base-pr-000.dot * REASONING * PRF # D6: 6,9 => SOL * DIS # D6: 7 => CTR => D6: 6,9 * DIS # F6: 6,9 => CTR => F6: 7 * PRF # F6: 7 => SOL * PRF # F7: 6,9 => SOL * DIS # F7: 7 => CTR => F7: 6,9 * DIS # I5: 6,9 => CTR => I5: 8 * PRF # I5: 8 => SOL * DIS # I5: 6,9 => CTR => I5: 8 * PRF # I5: 8 => SOL * PRF # D6: 6,9 => SOL * DIS # D6: 7 => CTR => D6: 6,9 * DIS # F6: 6,9 => CTR => F6: 7 * PRF # F6: 7 => SOL * PRF # I5: 6,8 => SOL * DIS # I5: 9 => CTR => I5: 6,8 * DIS # I5: 6,9 => CTR => I5: 8 * PRF # I5: 8 => SOL * PRF # D6: 6,9 => SOL * DIS # D6: 7 => CTR => D6: 6,9 * DIS # F6: 6,9 => CTR => F6: 7 * PRF # F6: 7 => SOL * PRF # B8: 1,9 => SOL * DIS # B8: 8 => CTR => B8: 1,9 * PRF # B8: 1,8 => SOL * DIS # B8: 9 => CTR => B8: 1,8 * PRF # F7: 6,9 => SOL * DIS # F7: 7 => CTR => F7: 6,9 * DIS # I7: 6,8 => CTR => I7: 7 * PRF # I7: 7 => SOL * CNT 30 HDP CHAINS / 30 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B5,B9,C1,C4,C8,D2,D8,D9,E4,E7,F2,F8,F9,G3,G6,H5,H7,I3,I8,I9) * 9..283475475.1.823832574.1.25.1.87341.74352..348.2..515243..1..7...5.34.6.3.4.59. * PAIR D2: 6,9 COL D D6: 6,9,7 # reduction candidate for 6,9 D6: 6,9 => SOLVED * 961283475475916823832574619256198734197435268348627951524369187719852346683741592 * DURATION: 0:00:02.187607 START: 15:17:10.359358 END: 15:17:12.546965 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-364-base-pr-001.dot * REASONING * PRF # D6: 6,9 => SOL * STA D6: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 364 solution: 961283475475916823832574619256198734197435268348627951524369187719852346683741592 info: 4952 FNBHWY S8.f 48881 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 961283475475916823832574619256198734197435268348627951524369187719852346683741592 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:
* PRF # D6: 6,9 => SOL * DIS # D6: 7 => CTR => D6: 6,9 * DIS # F6: 6,9 => CTR => F6: 7 * PRF # F6: 7 => SOL * PRF # F7: 6,9 => SOL * DIS # F7: 7 => CTR => F7: 6,9 * DIS # I5: 6,9 => CTR => I5: 8 * PRF # I5: 8 => SOL * DIS # I5: 6,9 => CTR => I5: 8 * PRF # I5: 8 => SOL * PRF # D6: 6,9 => SOL * DIS # D6: 7 => CTR => D6: 6,9 * DIS # F6: 6,9 => CTR => F6: 7 * PRF # F6: 7 => SOL * PRF # I5: 6,8 => SOL * DIS # I5: 9 => CTR => I5: 6,8 * DIS # I5: 6,9 => CTR => I5: 8 * PRF # I5: 8 => SOL * PRF # D6: 6,9 => SOL * DIS # D6: 7 => CTR => D6: 6,9 * DIS # F6: 6,9 => CTR => F6: 7 * PRF # F6: 7 => SOL * PRF # B8: 1,9 => SOL * DIS # B8: 8 => CTR => B8: 1,9 * PRF # B8: 1,8 => SOL * DIS # B8: 9 => CTR => B8: 1,8 * PRF # F7: 6,9 => SOL * DIS # F7: 7 => CTR => F7: 6,9 * DIS # I7: 6,8 => CTR => I7: 7 * PRF # I7: 7 => SOL * CNT 30 HDP CHAINS / 30 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # D6: 6,9 => SOL * STA D6: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED