Analysis of xx-top500-486-base.sdk
Contents
Original Sudoku
level: medium
position: ..35...........2.6.81......56..2...........1.7...........1...8....3.6...4.....7.. initial
Autosolve
position: ..35..1.89..8132.6.81...35.56..218.383.....1.71..38.6.3..1..68.1.83.6.2.4.6.8.731 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H1: 4,7 => CTR => H1: 9 * DIS # H1: 4,7 => CTR => H1: 9 * DIS # H4: 9 => CTR => H4: 4,7 * DIS # C5: 4,9 => CTR => C5: 2 * DIS # D4: 4,9 => CTR => D4: 7 * DIS # D4: 4,9 => CTR => D4: 7 * PRF # D5: 4,9 => SOL * DIS # E5: 4,9 => CTR => E5: 5,6,7 * DIS # G6: 4,9 => CTR => G6: 5 * DIS # I6: 4,9 => CTR => I6: 2,5 * DIS # I5: 4,9 => CTR => I5: 2,7 * DIS # G6: 4,9 => CTR => G6: 5 * DIS # I6: 4,9 => CTR => I6: 2,5 * DIS # C5: 4,9 => CTR => C5: 2 * PRF # D5: 4,9 => SOL * DIS # E5: 4,9 => CTR => E5: 5,6,7 * DIS # G8: 5 => CTR => G8: 4,9 * DIS # B7: 5,7 => CTR => B7: 2,9 * DIS # D3: 2,9 => CTR => D3: 4,6,7 * CNT 19 HDP CHAINS / 64 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H1: 4,7 => CTR => H1: 9 * DIS H1: 9 # B2: 5 => CTR => B2: 4,7 * PRF H1: 9 + B2: 4,7 # F1: 2 => SOL * STA H1: 9 + B2: 4,7 + F1: 2 * CNT 3 HDP CHAINS / 9 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..35...........2.6.81......56..2...........1.7...........1...8....3.6...4.....7.. | initial |
| ..35..1.89..8132.6.81...35.56..218.383.....1.71..38.6.3..1..68.1.83.6.2.4.6.8.731 | autosolve |
| 673542198945813276281697354569721843832465917714938562327154689198376425456289731 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) A1: 2,6 B1: 4,7 C2: 5,7 A3: 2,6 H2: 4,7 C4: 4,9 D6: 4,9 G5: 4,9 C7: 5,7 D9: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,A3: 2.. / A1 = 2 => 8 pairs (_) / A3 = 2 => 9 pairs (_) C5,C6: 2.. / C5 = 2 => 12 pairs (_) / C6 = 2 => 0 pairs (X) I5,I6: 2.. / I5 = 2 => 0 pairs (X) / I6 = 2 => 12 pairs (_) B7,B9: 2.. / B7 = 2 => 11 pairs (_) / B9 = 2 => 0 pairs (X) A1,F1: 2.. / A1 = 2 => 8 pairs (_) / F1 = 2 => 9 pairs (_) C5,I5: 2.. / C5 = 2 => 12 pairs (_) / I5 = 2 => 0 pairs (X) C6,I6: 2.. / C6 = 2 => 0 pairs (X) / I6 = 2 => 12 pairs (_) B7,F7: 2.. / B7 = 2 => 11 pairs (_) / F7 = 2 => 0 pairs (X) D3,D9: 2.. / D3 = 2 => 0 pairs (X) / D9 = 2 => 11 pairs (_) B1,B2: 4.. / B1 = 4 => 12 pairs (_) / B2 = 4 => 13 pairs (_) B2,H2: 4.. / B2 = 4 => 13 pairs (_) / H2 = 4 => 12 pairs (_) B2,C2: 5.. / B2 = 5 => 12 pairs (_) / C2 = 5 => 11 pairs (_) E5,F5: 5.. / E5 = 5 => 10 pairs (_) / F5 = 5 => 16 pairs (_) G6,I6: 5.. / G6 = 5 => 11 pairs (_) / I6 = 5 => 0 pairs (X) B9,F9: 5.. / B9 = 5 => 17 pairs (_) / F9 = 5 => 11 pairs (_) C2,C7: 5.. / C2 = 5 => 11 pairs (_) / C7 = 5 => 12 pairs (_) G6,G8: 5.. / G6 = 5 => 11 pairs (_) / G8 = 5 => 0 pairs (X) A1,A3: 6.. / A1 = 6 => 9 pairs (_) / A3 = 6 => 8 pairs (_) D5,E5: 6.. / D5 = 6 => 10 pairs (_) / E5 = 6 => 0 pairs (*) A1,E1: 6.. / A1 = 6 => 9 pairs (_) / E1 = 6 => 8 pairs (_) D3,D5: 6.. / D3 = 6 => 0 pairs (*) / D5 = 6 => 0 pairs (X) H4,I5: 7.. / H4 = 7 => 0 pairs (X) / I5 = 7 => 14 pairs (_) D4,H4: 7.. / D4 = 7 => 14 pairs (_) / H4 = 7 => 0 pairs (X) B8,E8: 7.. / B8 = 7 => 13 pairs (_) / E8 = 7 => 12 pairs (_) C2,C7: 7.. / C2 = 7 => 12 pairs (_) / C7 = 7 => 11 pairs (_) I3,I5: 7.. / I3 = 7 => 0 pairs (X) / I5 = 7 => 14 pairs (_) H1,I3: 9.. / H1 = 9 => 12 pairs (_) / I3 = 9 => 0 pairs (X) H1,H4: 9.. / H1 = 9 => 12 pairs (_) / H4 = 9 => 0 pairs (X) * DURATION: 0:00:45.225522 START: 19:14:34.300287 END: 19:15:19.525809 2017-05-04 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B1,C2,C4,C7,D6,D9,G5,H2) * ..35..1.89..8132.6.81...35.56..218.383.....1.71..38.6.3..1..68.1.83.6.2.4.6.8.731 * PAIR B1: 4,7 BLK 1 B2: 4,7,5 # reduction candidate for 4,7 B2: 5 # 12 pairs B2: 4,7 # 11 pairs * PAIR B1: 4,7 ROW 1 E1: 4,7,6,9 # reduction candidate for 4,7 E1: 4,7 # 12 pairs F1: 4,7,2,9 # reduction candidate for 4,7 F1: 4,7 # 11 pairs H1: 4,7,9 # reduction candidate for 4,7 H1: 4,7 => CTR * ..35.21.89..8132.62816..3595647218938329654177194385623..1..68.1.83.692.4.6.8.731 H1: 9 # 12 pairs * PAIR C2: 5,7 BLK 1 B2: 5,7,4 # reduction candidate for 5,7 B2: 4 # 13 pairs B2: 5,7 # 12 pairs * PAIR A3: 2,6 ROW 3 D3: 2,6,4,7,9 # reduction candidate for 2,6 D3: 2,6 # 12 pairs D3: 4,7,9 # 11 pairs * PAIR H2: 4,7 BLK 3 H1: 4,7,9 # reduction candidate for 4,7 H1: 4,7 => CTR * ..35.21.89..8132.62816..3595647218938329654177194385623..1..68.1.83.692.4.6.8.731 H1: 9 # 12 pairs I3: 4,7,9 # reduction candidate for 4,7 I3: 4,7 # 12 pairs * PAIR H2: 4,7 ROW 2 B2: 4,7,5 # reduction candidate for 4,7 B2: 5 # 12 pairs B2: 4,7 # 11 pairs * PAIR H2: 4,7 COL H H4: 4,7,9 # reduction candidate for 4,7 H4: 9 => CTR * ..35.21.89..8132.62816..3595647218938329654177194385623..1..68.1.83.692.4.6.8.731 H4: 4,7 # 12 pairs * PAIR C4: 4,9 BLK 4 C5: 4,9,2 # reduction candidate for 4,9 C5: 4,9 => CTR * 6.35.21989.58132462816..35756..2187383.765.12712.38.6.3271..68.198376.2.456289731 C5: 2 # 12 pairs C6: 4,9,2 # reduction candidate for 4,9 C6: 4,9 # 12 pairs * PAIR C4: 4,9 ROW 4 D4: 4,9,7 # reduction candidate for 4,9 D4: 4,9 => CTR * 6435721989758132462816..35756..2187383.765.1.71..38.6.3271..68.1983.6.2.456289731 D4: 7 # 14 pairs H4: 4,9,7 # reduction candidate for 4,9 H4: 4,9 # 14 pairs * PAIR D6: 4,9 BLK 5 D4: 4,9,7 # reduction candidate for 4,9 D4: 4,9 => CTR * 6435721989758132462816..35756..2187383.765.1.71..38.6.3271..68.1983.6.2.456289731 D4: 7 # 14 pairs D5: 4,9,6,7 # reduction candidate for 4,9 D5: 4,9 => SOLVED * 673542198945813276281697354569721843832465917714938562327154689198376425456289731 D5: 6,7 # 11 pairs E5: 4,9,5,6,7 # reduction candidate for 4,9 E5: 4,9 => CTR * ..35..1.89.58132.6.81..735456.72184383264591771493856232715468919837642545628.731 E5: 5,6,7 # 10 pairs F5: 4,9,5,7 # reduction candidate for 4,9 F5: 4,9 # 15 pairs * PAIR D6: 4,9 ROW 6 C6: 4,9,2 # reduction candidate for 4,9 C6: 4,9 # 12 pairs G6: 4,9,5 # reduction candidate for 4,9 G6: 4,9 => CTR * 6.35.21989.58132462816..35756..2187383.765.12712.38.6532715.68.198376524456289731 G6: 5 # 11 pairs I6: 4,9,2,5 # reduction candidate for 4,9 I6: 4,9 => CTR * 6.35.21989.58132462816..35756..2187383.765.12712.3856.3271..68.198376425456289731 I6: 2,5 # 11 pairs * PAIR D6: 4,9 COL D D3: 4,9,2,6,7 # reduction candidate for 4,9 D3: 4,9 # 18 pairs D3: 2,6,7 # 10 pairs * PAIR G5: 4,9 BLK 6 H4: 4,9,7 # reduction candidate for 4,9 H4: 4,9 # 14 pairs I5: 4,9,2,7 # reduction candidate for 4,9 I5: 4,9 => CTR * 6.35.21989.58132462816..35756..21873832765.1.71..385623271..68.198376425456289731 I5: 2,7 # 11 pairs G6: 4,9,5 # reduction candidate for 4,9 G6: 4,9 => CTR * 6.35.21989.58132462816..35756..2187383.765.12712.38.6532715.68.198376524456289731 G6: 5 # 11 pairs I6: 4,9,2,5 # reduction candidate for 4,9 I6: 4,9 => CTR * 6.35.21989.58132462816..35756..2187383.765.12712.3856.3271..68.198376425456289731 I6: 2,5 # 11 pairs * PAIR G5: 4,9 ROW 5 C5: 4,9,2 # reduction candidate for 4,9 C5: 4,9 => CTR * 6.35.21989.58132462816..35756..2187383.765.12712.38.6.3271..68.198376.2.456289731 C5: 2 # 12 pairs D5: 4,9,6,7 # reduction candidate for 4,9 D5: 4,9 => SOLVED * 673542198945813276281697354569721843832465917714938562327154689198376425456289731 D5: 6,7 # 11 pairs E5: 4,9,5,6,7 # reduction candidate for 4,9 E5: 4,9 => CTR * ..35..1.89.58132.6.81..735456.72184383264591771493856232715468919837642545628.731 E5: 5,6,7 # 10 pairs F5: 4,9,5,7 # reduction candidate for 4,9 F5: 4,9 # 15 pairs * PAIR G5: 4,9 COL G G8: 4,9,5 # reduction candidate for 4,9 G8: 5 => CTR * 6.35.21989.58132462816..35756..2187383.765.12712.38.6532715.68.198376524456289731 G8: 4,9 # 11 pairs * PAIR C7: 5,7 BLK 7 B7: 5,7,2,9 # reduction candidate for 5,7 B7: 5,7 => CTR * 2.356.1.89..8132.66812..35.56..218.383.65941771.438.623..1.26891983.6.2.426985731 B7: 2,9 # 11 pairs B8: 5,7,9 # reduction candidate for 5,7 B8: 5,7 # 13 pairs * PAIR C7: 5,7 ROW 7 E7: 5,7,4,9 # reduction candidate for 5,7 E7: 5,7 # 14 pairs F7: 5,7,2,4,9 # reduction candidate for 5,7 F7: 5,7 # 15 pairs * PAIR D9: 2,9 BLK 8 F7: 2,9,4,5,7 # reduction candidate for 2,9 F7: 2,9 # 16 pairs F9: 2,9,5 # reduction candidate for 2,9 F9: 2,9 # 17 pairs * PAIR D9: 2,9 ROW 9 B9: 2,9,5 # reduction candidate for 2,9 B9: 5 # 17 pairs B9: 2,9 # 11 pairs * PAIR D9: 2,9 COL D D3: 2,9,4,6,7 # reduction candidate for 2,9 D3: 2,9 => CTR * 2.35691.89..8132.6.812..3595647218938326..41771943856239.1.268.1.83.692.426985731 D3: 4,6,7 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-486-base-pr-000.dot * REASONING * DIS # H1: 4,7 => CTR => H1: 9 * DIS # H1: 4,7 => CTR => H1: 9 * DIS # H4: 9 => CTR => H4: 4,7 * DIS # C5: 4,9 => CTR => C5: 2 * DIS # D4: 4,9 => CTR => D4: 7 * DIS # D4: 4,9 => CTR => D4: 7 * PRF # D5: 4,9 => SOL * DIS # E5: 4,9 => CTR => E5: 5,6,7 * DIS # G6: 4,9 => CTR => G6: 5 * DIS # I6: 4,9 => CTR => I6: 2,5 * DIS # I5: 4,9 => CTR => I5: 2,7 * DIS # G6: 4,9 => CTR => G6: 5 * DIS # I6: 4,9 => CTR => I6: 2,5 * DIS # C5: 4,9 => CTR => C5: 2 * PRF # D5: 4,9 => SOL * DIS # E5: 4,9 => CTR => E5: 5,6,7 * DIS # G8: 5 => CTR => G8: 4,9 * DIS # B7: 5,7 => CTR => B7: 2,9 * DIS # D3: 2,9 => CTR => D3: 4,6,7 * CNT 19 HDP CHAINS / 64 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B1,C2,C4,C7,D6,D9,G5,H2) * ..35..1.89..8132.6.81...35.56..218.383.....1.71..38.6.3..1..68.1.83.6.2.4.6.8.731 * PAIR B1: 4,7 BLK 1 B2: 4,7,5 # reduction candidate for 4,7 B2: 5 # 12 pairs B2: 4,7 # 11 pairs * PAIR B1: 4,7 ROW 1 E1: 4,7,6,9 # reduction candidate for 4,7 E1: 4,7 # 12 pairs F1: 4,7,2,9 # reduction candidate for 4,7 F1: 4,7 # 11 pairs H1: 4,7,9 # reduction candidate for 4,7 H1: 4,7 => CTR * ..35.21.89..8132.62816..3595647218938329654177194385623..1..68.1.83.692.4.6.8.731 * PAIR RESTART * PAIR B1: 4,7 BLK 1 B2: 4,7,5 # reduction candidate for 4,7 B2: 5 => CTR * .435..198957813246.81...35756..2187383.765.1.71..38.6.3.51..68.1.8356.2.4.6.8.731 * PAIR B1: 4,7 ROW 1 F1: 4,7,2 # reduction candidate for 4,7 F1: 2 => SOLVED * 673542198945813276281697354569721843832465917714938562327154689198376425456289731 * DURATION: 0:00:09.343570 START: 19:16:16.113013 END: 19:16:25.456583 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-486-base-pr-001.dot * REASONING * DIS # H1: 4,7 => CTR => H1: 9 * DIS H1: 9 # B2: 5 => CTR => B2: 4,7 * PRF H1: 9 + B2: 4,7 # F1: 2 => SOL * STA H1: 9 + B2: 4,7 + F1: 2 * CNT 3 HDP CHAINS / 9 HYP OPENED
Header Info
Top 500 Minimum 17 486 solution: 673542198945813276281697354569721843832465917714938562327154689198376425456289731 info: 96136 FNBXK S8.f 13519 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 673542198945813276281697354569721843832465917714938562327154689198376425456289731 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 # B2: 4,7 => UNS * INC # B2: 5 => UNS * INC # E1: 4,7 => UNS * INC # F1: 4,7 => UNS * DIS # H1: 4,7 => CTR => H1: 9 * INC # H1: 9 => UNS * INC # B2: 5,7 => UNS * INC # B2: 4 => UNS * INC # D3: 2,6 => UNS * INC # D3: 4,7,9 => UNS * DIS # H1: 4,7 => CTR => H1: 9 * INC # H1: 9 => UNS * INC # I3: 4,7 => UNS * INC # B2: 4,7 => UNS * INC # B2: 5 => UNS * INC # H4: 4,7 => UNS * DIS # H4: 9 => CTR => H4: 4,7 * DIS # C5: 4,9 => CTR => C5: 2 * INC # C5: 2 => UNS * INC # C6: 4,9 => UNS * DIS # D4: 4,9 => CTR => D4: 7 * INC # D4: 7 => UNS * INC # H4: 4,9 => UNS * DIS # D4: 4,9 => CTR => D4: 7 * INC # D4: 7 => UNS * PRF # D5: 4,9 => SOL * INC # D5: 6,7 => UNS * DIS # E5: 4,9 => CTR => E5: 5,6,7 * INC # E5: 5,6,7 => UNS * INC # F5: 4,9 => UNS * INC # C6: 4,9 => UNS * DIS # G6: 4,9 => CTR => G6: 5 * INC # G6: 5 => UNS * DIS # I6: 4,9 => CTR => I6: 2,5 * INC # I6: 2,5 => UNS * INC # D3: 4,9 => UNS * INC # D3: 2,6,7 => UNS * INC # H4: 4,9 => UNS * DIS # I5: 4,9 => CTR => I5: 2,7 * INC # I5: 2,7 => UNS * DIS # G6: 4,9 => CTR => G6: 5 * INC # G6: 5 => UNS * DIS # I6: 4,9 => CTR => I6: 2,5 * INC # I6: 2,5 => UNS * DIS # C5: 4,9 => CTR => C5: 2 * INC # C5: 2 => UNS * PRF # D5: 4,9 => SOL * INC # D5: 6,7 => UNS * DIS # E5: 4,9 => CTR => E5: 5,6,7 * INC # E5: 5,6,7 => UNS * INC # F5: 4,9 => UNS * INC # G8: 4,9 => UNS * DIS # G8: 5 => CTR => G8: 4,9 * DIS # B7: 5,7 => CTR => B7: 2,9 * INC # B7: 2,9 => UNS * INC # B8: 5,7 => UNS * INC # E7: 5,7 => UNS * INC # F7: 5,7 => UNS * INC # F7: 2,9 => UNS * INC # F9: 2,9 => UNS * INC # B9: 2,9 => UNS * INC # B9: 5 => UNS * DIS # D3: 2,9 => CTR => D3: 4,6,7 * INC # D3: 4,6,7 => UNS * CNT 64 HDP CHAINS / 64 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 4,7 => UNS * INC # B2: 5 => UNS * INC # E1: 4,7 => UNS * INC # F1: 4,7 => UNS * DIS # H1: 4,7 => CTR => H1: 9 * INC H1: 9 # B2: 4,7 => UNS * DIS H1: 9 # B2: 5 => CTR => B2: 4,7 * INC H1: 9 + B2: 4,7 # F1: 4,7 => UNS * PRF H1: 9 + B2: 4,7 # F1: 2 => SOL * STA H1: 9 + B2: 4,7 + F1: 2 * CNT 9 HDP CHAINS / 9 HYP OPENED