Analysis of xx-top500-180-base.sdk
Contents
Original Sudoku
level: medium
position: 3.....56....7.1....4.......2......815.7.3..............812.........5.3........... initial
Autosolve
position: 31948256782576143974639512823457..815.71382..1.8.24753.81243.75.7285.31..53.178.2 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A8: 6,9 => SOL * DIS # A8: 4 => CTR => A8: 6,9 * DIS # A9: 6,9 => CTR => A9: 4 * PRF # A9: 4 => SOL * PRF # A8: 6,9 => SOL * DIS # A8: 4 => CTR => A8: 6,9 * DIS # A9: 6,9 => CTR => A9: 4 * PRF # A9: 4 => SOL * PRF # A8: 4,6 => SOL * DIS # A8: 9 => CTR => A8: 4,6 * PRF # A9: 4,9 => SOL * DIS # A9: 6 => CTR => A9: 4,9 * CNT 12 HDP CHAINS / 12 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A8: 6,9 => SOL * STA A8: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 3.....56....7.1....4.......2......815.7.3..............812.........5.3........... | initial |
| 31948256782576143974639512823457..815.71382..1.8.24753.81243.75.7285.31..53.178.2 | autosolve |
| 319482567825761439746395128234576981597138246168924753981243675672859314453617892 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) B5: 6,9 B6: 6,9 F4: 6,9 D6: 6,9 G4: 6,9 H5: 4,9 I5: 4,6 A7: 6,9 F8: 6,9 D9: 6,9 G7: 6,9 I8: 4,6 H9: 4,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H5,I5: 4.. / H5 = 4 => 0 pairs (*) / I5 = 4 => 0 pairs (X) A8,A9: 4.. / A8 = 4 => 0 pairs (X) / A9 = 4 => 0 pairs (_) I8,H9: 4.. / I8 = 4 => 0 pairs (*) / H9 = 4 => 0 pairs (X) A8,I8: 4.. / A8 = 4 => 0 pairs (X) / I8 = 4 => 0 pairs (_) A9,H9: 4.. / A9 = 4 => 0 pairs (*) / H9 = 4 => 0 pairs (X) H5,H9: 4.. / H5 = 4 => 0 pairs (*) / H9 = 4 => 0 pairs (X) I5,I8: 4.. / I5 = 4 => 0 pairs (X) / I8 = 4 => 0 pairs (_) B5,B6: 6.. / B5 = 6 => 0 pairs (X) / B6 = 6 => 0 pairs (_) F4,D6: 6.. / F4 = 6 => 0 pairs (*) / D6 = 6 => 0 pairs (X) G4,I5: 6.. / G4 = 6 => 0 pairs (X) / I5 = 6 => 0 pairs (_) F8,D9: 6.. / F8 = 6 => 0 pairs (X) / D9 = 6 => 0 pairs (_) G7,I8: 6.. / G7 = 6 => 0 pairs (*) / I8 = 6 => 0 pairs (X) F4,G4: 6.. / F4 = 6 => 0 pairs (*) / G4 = 6 => 0 pairs (X) B5,I5: 6.. / B5 = 6 => 0 pairs (X) / I5 = 6 => 0 pairs (_) B6,D6: 6.. / B6 = 6 => 0 pairs (*) / D6 = 6 => 0 pairs (X) A7,G7: 6.. / A7 = 6 => 0 pairs (X) / G7 = 6 => 0 pairs (_) A9,D9: 6.. / A9 = 6 => 0 pairs (X) / D9 = 6 => 0 pairs (_) D6,D9: 6.. / D6 = 6 => 0 pairs (X) / D9 = 6 => 0 pairs (_) F4,F8: 6.. / F4 = 6 => 0 pairs (*) / F8 = 6 => 0 pairs (X) G4,G7: 6.. / G4 = 6 => 0 pairs (X) / G7 = 6 => 0 pairs (_) I5,I8: 6.. / I5 = 6 => 0 pairs (*) / I8 = 6 => 0 pairs (X) B5,B6: 9.. / B5 = 9 => 0 pairs (*) / B6 = 9 => 0 pairs (X) F4,D6: 9.. / F4 = 9 => 0 pairs (X) / D6 = 9 => 0 pairs (_) G4,H5: 9.. / G4 = 9 => 0 pairs (*) / H5 = 9 => 0 pairs (X) F8,D9: 9.. / F8 = 9 => 0 pairs (*) / D9 = 9 => 0 pairs (X) G7,H9: 9.. / G7 = 9 => 0 pairs (X) / H9 = 9 => 0 pairs (_) F4,G4: 9.. / F4 = 9 => 0 pairs (X) / G4 = 9 => 0 pairs (_) B5,H5: 9.. / B5 = 9 => 0 pairs (*) / H5 = 9 => 0 pairs (X) B6,D6: 9.. / B6 = 9 => 0 pairs (X) / D6 = 9 => 0 pairs (_) A7,G7: 9.. / A7 = 9 => 0 pairs (*) / G7 = 9 => 0 pairs (X) A8,F8: 9.. / A8 = 9 => 0 pairs (X) / F8 = 9 => 0 pairs (_) D6,D9: 9.. / D6 = 9 => 0 pairs (*) / D9 = 9 => 0 pairs (X) F4,F8: 9.. / F4 = 9 => 0 pairs (X) / F8 = 9 => 0 pairs (_) G4,G7: 9.. / G4 = 9 => 0 pairs (*) / G7 = 9 => 0 pairs (X) H5,H9: 9.. / H5 = 9 => 0 pairs (X) / H9 = 9 => 0 pairs (_) * DURATION: 0:01:03.015909 START: 08:51:05.830627 END: 08:52:08.846536 2017-05-04 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B5,B6,D6,D9,F4,F8,G4,G7,H5,H9,I5,I8) * 31948256782576143974639512823457..815.71382..1.8.24753.81243.75.7285.31..53.178.2 * PAIR A7: 6,9 BLK 7 A8: 6,9,4 # reduction candidate for 6,9 A8: 6,9 => SOLVED * 319482567825761439746395128234576981597138246168924753981243675672859314453617892 A8: 4 => CTR * 31948256782576143974639512823457..815.71382..1.8.24753.81243.75472859316.53617842 A9: 6,9,4 # reduction candidate for 6,9 A9: 6,9 => CTR * 31948256782576143974639512823457..815.71382..1.8.24753.81243.75472859316.53617842 A9: 4 => SOLVED * 319482567825761439746395128234576981597138246168924753981243675672859314453617892 * PAIR F8: 6,9 ROW 8 A8: 6,9,4 # reduction candidate for 6,9 A8: 6,9 => SOLVED * 319482567825761439746395128234576981597138246168924753981243675672859314453617892 A8: 4 => CTR * 31948256782576143974639512823457..815.71382..1.8.24753.81243.75472859316.53617842 * PAIR D9: 6,9 ROW 9 A9: 6,9,4 # reduction candidate for 6,9 A9: 6,9 => CTR * 31948256782576143974639512823457..815.71382..1.8.24753.81243.75472859316.53617842 A9: 4 => SOLVED * 319482567825761439746395128234576981597138246168924753981243675672859314453617892 * PAIR I8: 4,6 ROW 8 A8: 4,6,9 # reduction candidate for 4,6 A8: 4,6 => SOLVED * 319482567825761439746395128234576981597138246168924753981243675672859314453617892 A8: 9 => CTR * 31948256782576143974639512823457..815.71382..1.8.24753.81243.75972856314.53.178.2 * PAIR H9: 4,9 ROW 9 A9: 4,9,6 # reduction candidate for 4,9 A9: 4,9 => SOLVED * 319482567825761439746395128234576981597138246168924753981243675672859314453617892 A9: 6 => CTR * 31948256782576143974639512823457..815.71382..1.8.24753.81243.75472859316.53.178.2 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-180-base-pr-000.dot * REASONING * PRF # A8: 6,9 => SOL * DIS # A8: 4 => CTR => A8: 6,9 * DIS # A9: 6,9 => CTR => A9: 4 * PRF # A9: 4 => SOL * PRF # A8: 6,9 => SOL * DIS # A8: 4 => CTR => A8: 6,9 * DIS # A9: 6,9 => CTR => A9: 4 * PRF # A9: 4 => SOL * PRF # A8: 4,6 => SOL * DIS # A8: 9 => CTR => A8: 4,6 * PRF # A9: 4,9 => SOL * DIS # A9: 6 => CTR => A9: 4,9 * CNT 12 HDP CHAINS / 12 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B5,B6,D6,D9,F4,F8,G4,G7,H5,H9,I5,I8) * 31948256782576143974639512823457..815.71382..1.8.24753.81243.75.7285.31..53.178.2 * PAIR A7: 6,9 BLK 7 A8: 6,9,4 # reduction candidate for 6,9 A8: 6,9 => SOLVED * 319482567825761439746395128234576981597138246168924753981243675672859314453617892 * DURATION: 0:00:02.078161 START: 08:52:24.390593 END: 08:52:26.468754 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-180-base-pr-001.dot * REASONING * PRF # A8: 6,9 => SOL * STA A8: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 180 solution: 319482567825761439746395128234576981597138246168924753981243675672859314453617892 info: 1828 FNTWX S8.f 28927 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 319482567825761439746395128234576981597138246168924753981243675672859314453617892 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 # A8: 6,9 => SOL * DIS # A8: 4 => CTR => A8: 6,9 * DIS # A9: 6,9 => CTR => A9: 4 * PRF # A9: 4 => SOL * PRF # A8: 6,9 => SOL * DIS # A8: 4 => CTR => A8: 6,9 * DIS # A9: 6,9 => CTR => A9: 4 * PRF # A9: 4 => SOL * PRF # A8: 4,6 => SOL * DIS # A8: 9 => CTR => A8: 4,6 * PRF # A9: 4,9 => SOL * DIS # A9: 6 => CTR => A9: 4,9 * CNT 12 HDP CHAINS / 12 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A8: 6,9 => SOL * STA A8: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED