Analysis of xx-top500-413-base.sdk
Contents
Original Sudoku
level: medium
position: ...35.9..6.....4....1......2..8......3.9............6.....46.1.39.......7........ initial
Autosolve
position: 84.3519.66.329.4.19.16.4.3.26.813.9443.96.1..1.94...635..74631939.1.....71.539... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B3: 5 => CTR => B3: 2,7 * DIS # B3: 2 => CTR => B3: 5,7 * PRF # H2: 8 => SOL * DIS # H2: 5 => CTR => H2: 7,8 * DIS # C5: 8 => CTR => C5: 5,7 * PRF # F6: 2,7 => SOL * PRF # G6: 5,7 => SOL * CNT 7 HDP CHAINS / 39 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B3: 5 => CTR => B3: 2,7 * DIS B3: 2,7 # G3: 7,8 => CTR => G3: 2,5 * DIS B3: 2,7 + G3: 2,5 # I3: 7,8 => CTR => I3: 2,5 * PRF B3: 2,7 + G3: 2,5 + I3: 2,5 => SOL * STA B3: 2,7 + G3: 2,5 + I3: 2,5 * CNT 4 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...35.9..6.....4....1......2..8......3.9............6.....46.1.39.......7........ | initial |
| 84.3519.66.329.4.19.16.4.3.26.813.9443.96.1..1.94...635..74631939.1.....71.539... | autosolve |
| 842351976653297481971684235265813794437965128189472563528746319394128657716539842 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) C1: 2,7 B2: 5,7 F2: 7,8 E3: 7,8 H1: 2,7 C4: 5,7 B6: 7,8 E6: 2,7 G4: 5,7 B7: 2,8 C7: 2,8 C8: 4,6 C9: 4,6 E8: 2,8 F8: 2,8 I8: 5,7 I9: 2,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,B3: 2.. / C1 = 2 => 16 pairs (_) / B3 = 2 => 0 pairs (X) B7,C7: 2.. / B7 = 2 => 16 pairs (_) / C7 = 2 => 0 pairs (X) E8,F8: 2.. / E8 = 2 => 0 pairs (*) / F8 = 2 => 0 pairs (X) C1,H1: 2.. / C1 = 2 => 16 pairs (_) / H1 = 2 => 0 pairs (X) B3,B7: 2.. / B3 = 2 => 0 pairs (X) / B7 = 2 => 16 pairs (_) C1,C7: 2.. / C1 = 2 => 16 pairs (_) / C7 = 2 => 0 pairs (X) E6,E8: 2.. / E6 = 2 => 17 pairs (_) / E8 = 2 => 0 pairs (*) C8,C9: 4.. / C8 = 4 => 17 pairs (_) / C9 = 4 => 20 pairs (_) H8,H9: 4.. / H8 = 4 => 20 pairs (_) / H9 = 4 => 17 pairs (_) C8,H8: 4.. / C8 = 4 => 17 pairs (_) / H8 = 4 => 20 pairs (_) C9,H9: 4.. / C9 = 4 => 20 pairs (_) / H9 = 4 => 17 pairs (_) B2,B3: 5.. / B2 = 5 => 18 pairs (_) / B3 = 5 => 0 pairs (X) C4,C5: 5.. / C4 = 5 => 17 pairs (_) / C5 = 5 => 18 pairs (_) F5,F6: 5.. / F5 = 5 => 0 pairs (*) / F6 = 5 => 0 pairs (X) B2,H2: 5.. / B2 = 5 => 18 pairs (_) / H2 = 5 => 0 pairs (X) C4,G4: 5.. / C4 = 5 => 17 pairs (_) / G4 = 5 => 18 pairs (_) F6,G6: 5.. / F6 = 5 => 18 pairs (_) / G6 = 5 => 0 pairs (*) C8,C9: 6.. / C8 = 6 => 20 pairs (_) / C9 = 6 => 17 pairs (_) G8,G9: 6.. / G8 = 6 => 17 pairs (_) / G9 = 6 => 20 pairs (_) C8,G8: 6.. / C8 = 6 => 20 pairs (_) / G8 = 6 => 17 pairs (_) C9,G9: 6.. / C9 = 6 => 17 pairs (_) / G9 = 6 => 20 pairs (_) F2,E3: 7.. / F2 = 7 => 0 pairs (*) / E3 = 7 => 0 pairs (X) C1,H1: 7.. / C1 = 7 => 0 pairs (X) / H1 = 7 => 16 pairs (_) C4,G4: 7.. / C4 = 7 => 18 pairs (_) / G4 = 7 => 17 pairs (_) E3,E6: 7.. / E3 = 7 => 17 pairs (_) / E6 = 7 => 0 pairs (*) F2,E3: 8.. / F2 = 8 => 17 pairs (_) / E3 = 8 => 0 pairs (*) C5,B6: 8.. / C5 = 8 => 0 pairs (X) / B6 = 8 => 16 pairs (_) B7,C7: 8.. / B7 = 8 => 0 pairs (X) / C7 = 8 => 16 pairs (_) E8,F8: 8.. / E8 = 8 => 17 pairs (_) / F8 = 8 => 0 pairs (*) F2,H2: 8.. / F2 = 8 => 17 pairs (_) / H2 = 8 => 0 pairs (*) B6,G6: 8.. / B6 = 8 => 16 pairs (_) / G6 = 8 => 0 pairs (X) B6,B7: 8.. / B6 = 8 => 16 pairs (_) / B7 = 8 => 0 pairs (X) C5,C7: 8.. / C5 = 8 => 0 pairs (X) / C7 = 8 => 16 pairs (_) E3,E8: 8.. / E3 = 8 => 0 pairs (*) / E8 = 8 => 0 pairs (X) F2,F8: 8.. / F2 = 8 => 17 pairs (_) / F8 = 8 => 0 pairs (*) * DURATION: 0:01:08.931361 START: 16:54:23.455963 END: 16:55:32.387324 2017-05-04 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B6,B7,C1,C4,C7,C8,C9,E3,E6,E8,F2,F8,G4,H1,I8,I9) * 84.3519.66.329.4.19.16.4.3.26.813.9443.96.1..1.94...635..74631939.1.....71.539... * PAIR C1: 2,7 BLK 1 B3: 2,7,5 # reduction candidate for 2,7 B3: 5 => CTR * 842351976673298451951674.3.26.813.9443.96.1..18942..6352874631939.182.4.7145396.. B3: 2,7 # 18 pairs * PAIR B2: 5,7 BLK 1 B3: 5,7,2 # reduction candidate for 5,7 B3: 2 => CTR * 84.3519.665329.4.19216.4.3.26.813.9443.96.1..17942586358274631939.182...71.5392.8 B3: 5,7 # 16 pairs * PAIR B2: 5,7 ROW 2 H2: 5,7,8 # reduction candidate for 5,7 H2: 8 => SOLVED * 842351976653297481971684235265813794437965128189472563528746319394128657716539842 H2: 5,7 # 17 pairs * PAIR F2: 7,8 ROW 2 H2: 7,8,5 # reduction candidate for 7,8 H2: 5 => CTR * 842351976673298451951674.3.26.813.9443.96.1..18942..6352874631939.182.4.7145396.. H2: 7,8 # 18 pairs * PAIR E3: 7,8 ROW 3 G3: 7,8,2,5 # reduction candidate for 7,8 G3: 7,8 # 20 pairs I3: 7,8,2,5 # reduction candidate for 7,8 I3: 7,8 # 20 pairs * PAIR H1: 2,7 BLK 3 G3: 2,7,5,8 # reduction candidate for 2,7 G3: 2,7 # 20 pairs I3: 2,7,5,8 # reduction candidate for 2,7 I3: 2,7 # 20 pairs * PAIR H1: 2,7 COL H H5: 2,7,5,8 # reduction candidate for 2,7 H5: 2,7 # 21 pairs H5: 5,8 # 18 pairs * PAIR C4: 5,7 BLK 4 C5: 5,7,8 # reduction candidate for 5,7 C5: 8 => CTR * 84735192665329847192167453826581379443896715217942586358274631939.182...71.539... C5: 5,7 # 16 pairs * PAIR B6: 7,8 BLK 4 C5: 7,8,5 # reduction candidate for 7,8 C5: 5 # 18 pairs C5: 7,8 # 17 pairs * PAIR B6: 7,8 ROW 6 G6: 7,8,2,5 # reduction candidate for 7,8 G6: 2,5 # 18 pairs G6: 7,8 # 17 pairs * PAIR E6: 2,7 BLK 5 F5: 2,7,5 # reduction candidate for 2,7 F5: 2,7 # 18 pairs F6: 2,7,5 # reduction candidate for 2,7 F6: 2,7 => SOLVED * 842351976653297481971684235265813794437965128189472563528746319394128657716539842 F6: 5 # 18 pairs * PAIR E6: 2,7 ROW 6 G6: 2,7,5,8 # reduction candidate for 2,7 G6: 5,8 # 19 pairs G6: 2,7 # 18 pairs * PAIR G4: 5,7 BLK 6 H5: 5,7,2,8 # reduction candidate for 5,7 H5: 5,7 # 22 pairs I5: 5,7,2,8 # reduction candidate for 5,7 I5: 5,7 # 22 pairs G6: 5,7,2,8 # reduction candidate for 5,7 G6: 5,7 => SOLVED * 842351976653297481971684235265813794437965128189472563528746319394128657716539842 G6: 2,8 # 19 pairs * PAIR G4: 5,7 COL G G3: 5,7,2,8 # reduction candidate for 5,7 G3: 5,7 # 20 pairs G8: 5,7,6 # reduction candidate for 5,7 G8: 5,7 # 20 pairs * PAIR I8: 5,7 BLK 9 G8: 5,7,6 # reduction candidate for 5,7 G8: 5,7 # 20 pairs H8: 5,7,4 # reduction candidate for 5,7 H8: 5,7 # 17 pairs * PAIR I8: 5,7 COL I I3: 5,7,2,8 # reduction candidate for 5,7 I3: 5,7 # 19 pairs I5: 5,7,2,8 # reduction candidate for 5,7 I5: 5,7 # 22 pairs * PAIR I9: 2,8 BLK 9 G9: 2,8,6 # reduction candidate for 2,8 G9: 2,8 # 17 pairs H9: 2,8,4 # reduction candidate for 2,8 H9: 2,8 # 20 pairs * PAIR I9: 2,8 COL I I3: 2,8,5,7 # reduction candidate for 2,8 I3: 2,8 # 22 pairs I5: 2,8,5,7 # reduction candidate for 2,8 I5: 2,8 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-413-base-pr-000.dot * REASONING * DIS # B3: 5 => CTR => B3: 2,7 * DIS # B3: 2 => CTR => B3: 5,7 * PRF # H2: 8 => SOL * DIS # H2: 5 => CTR => H2: 7,8 * DIS # C5: 8 => CTR => C5: 5,7 * PRF # F6: 2,7 => SOL * PRF # G6: 5,7 => SOL * CNT 7 HDP CHAINS / 39 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B6,B7,C1,C4,C7,C8,C9,E3,E6,E8,F2,F8,G4,H1,I8,I9) * 84.3519.66.329.4.19.16.4.3.26.813.9443.96.1..1.94...635..74631939.1.....71.539... * PAIR C1: 2,7 BLK 1 B3: 2,7,5 # reduction candidate for 2,7 B3: 5 => CTR * 842351976673298451951674.3.26.813.9443.96.1..18942..6352874631939.182.4.7145396.. * PAIR E3: 7,8 ROW 3 G3: 7,8,2,5 # reduction candidate for 7,8 G3: 7,8 => CTR * 84.35192665329.4.19216.4.3526.813.9443.96.1..17942586358274631939.18...771.539... I3: 7,8,2,5 # reduction candidate for 7,8 I3: 7,8 => CTR * 84.35192665329.4.19216.453.26581379443.96.1..1794258635827463193941826..716539248 I3: 2,5 => SOLVED * 842351976653297481971684235265813794437965128189472563528746319394128657716539842 * DURATION: 0:00:05.426608 START: 16:56:14.130527 END: 16:56:19.557135 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-413-base-pr-001.dot * REASONING * DIS # B3: 5 => CTR => B3: 2,7 * DIS B3: 2,7 # G3: 7,8 => CTR => G3: 2,5 * DIS B3: 2,7 + G3: 2,5 # I3: 7,8 => CTR => I3: 2,5 * PRF B3: 2,7 + G3: 2,5 + I3: 2,5 => SOL * STA B3: 2,7 + G3: 2,5 + I3: 2,5 * CNT 4 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 413 solution: 842351976653297481971684235265813794437965128189472563528746319394128657716539842 info: 95044 FNBXK S8.f 42362 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 842351976653297481971684235265813794437965128189472563528746319394128657716539842 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:
* INC # B3: 2,7 => UNS * DIS # B3: 5 => CTR => B3: 2,7 * INC # B3: 5,7 => UNS * DIS # B3: 2 => CTR => B3: 5,7 * INC # H2: 5,7 => UNS * PRF # H2: 8 => SOL * INC # H2: 7,8 => UNS * DIS # H2: 5 => CTR => H2: 7,8 * INC # G3: 7,8 => UNS * INC # I3: 7,8 => UNS * INC # G3: 2,7 => UNS * INC # I3: 2,7 => UNS * INC # H5: 2,7 => UNS * INC # H5: 5,8 => UNS * INC # C5: 5,7 => UNS * DIS # C5: 8 => CTR => C5: 5,7 * INC # C5: 7,8 => UNS * INC # C5: 5 => UNS * INC # G6: 7,8 => UNS * INC # G6: 2,5 => UNS * INC # F5: 2,7 => UNS * PRF # F6: 2,7 => SOL * INC # F6: 5 => UNS * INC # G6: 2,7 => UNS * INC # G6: 5,8 => UNS * INC # H5: 5,7 => UNS * INC # I5: 5,7 => UNS * PRF # G6: 5,7 => SOL * INC # G6: 2,8 => UNS * INC # G3: 5,7 => UNS * INC # G8: 5,7 => UNS * INC # G8: 5,7 => UNS * INC # H8: 5,7 => UNS * INC # I3: 5,7 => UNS * INC # I5: 5,7 => UNS * INC # G9: 2,8 => UNS * INC # H9: 2,8 => UNS * INC # I3: 2,8 => UNS * INC # I5: 2,8 => UNS * CNT 39 HDP CHAINS / 39 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B3: 2,7 => UNS * DIS # B3: 5 => CTR => B3: 2,7 * DIS B3: 2,7 # G3: 7,8 => CTR => G3: 2,5 * DIS B3: 2,7 + G3: 2,5 # I3: 7,8 => CTR => I3: 2,5 * PRF B3: 2,7 + G3: 2,5 + I3: 2,5 => SOL * STA B3: 2,7 + G3: 2,5 + I3: 2,5 * CNT 5 HDP CHAINS / 4 HYP OPENED