Analysis of xx-top500-384-base.sdk
Contents
Original Sudoku
level: medium
position: .61...8.....39..............89..1...5.......3.......2.2..43.......2...6.......1.. initial
Autosolve
position: 961..283....39.6.1...16.29.389.214.65......131....3.2821.436.89...21.36.6.....1.2 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B8: 4,7 => CTR => B8: 5,9 * DIS # E6: 4 => CTR => E6: 5,7 * PRF # D5: 8 => SOL * CNT 3 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 # B8: 4,7 => CTR => B8: 5,9 * DIS B8: 5,9 # E6: 4 => CTR => E6: 5,7 * PRF B8: 5,9 + E6: 5,7 # D5: 8 => SOL * STA B8: 5,9 + E6: 5,7 + D5: 8 * CNT 3 HDP CHAINS / 26 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .61...8.....39..............89..1...5.......3.......2.2..43.......2...6.......1.. | initial |
| 961..283....39.6.1...16.29.389.214.65......131....3.2821.436.89...21.36.6.....1.2 | autosolve |
| 961572834852394671743168295389721456526849713174653928217436589498215367635987142 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) D1: 5,7 B6: 4,7 D4: 5,7 D6: 6,9 H4: 5,7 G5: 7,9 C7: 5,7 D9: 8,9 G7: 5,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,C2: 2.. / B2 = 2 => 12 pairs (_) / C2 = 2 => 9 pairs (_) B5,C5: 2.. / B5 = 2 => 9 pairs (_) / C5 = 2 => 12 pairs (_) B2,B5: 2.. / B2 = 2 => 12 pairs (_) / B5 = 2 => 9 pairs (_) C2,C5: 2.. / C2 = 2 => 9 pairs (_) / C5 = 2 => 12 pairs (_) B3,C3: 3.. / B3 = 3 => 9 pairs (_) / C3 = 3 => 10 pairs (_) B9,C9: 3.. / B9 = 3 => 10 pairs (_) / C9 = 3 => 9 pairs (_) B3,B9: 3.. / B3 = 3 => 9 pairs (_) / B9 = 3 => 10 pairs (_) C3,C9: 3.. / C3 = 3 => 10 pairs (_) / C9 = 3 => 9 pairs (_) I8,H9: 4.. / I8 = 4 => 20 pairs (_) / H9 = 4 => 11 pairs (_) E1,I1: 4.. / E1 = 4 => 13 pairs (_) / I1 = 4 => 22 pairs (_) H2,H9: 4.. / H2 = 4 => 20 pairs (_) / H9 = 4 => 11 pairs (_) D4,E6: 5.. / D4 = 5 => 10 pairs (_) / E6 = 5 => 20 pairs (_) H4,G6: 5.. / H4 = 5 => 20 pairs (_) / G6 = 5 => 10 pairs (_) D4,H4: 5.. / D4 = 5 => 10 pairs (_) / H4 = 5 => 20 pairs (_) E6,G6: 5.. / E6 = 5 => 20 pairs (_) / G6 = 5 => 10 pairs (_) C7,G7: 5.. / C7 = 5 => 10 pairs (_) / G7 = 5 => 20 pairs (_) D1,D4: 5.. / D1 = 5 => 20 pairs (_) / D4 = 5 => 10 pairs (_) G6,G7: 5.. / G6 = 5 => 10 pairs (_) / G7 = 5 => 20 pairs (_) C5,C6: 6.. / C5 = 6 => 16 pairs (_) / C6 = 6 => 9 pairs (_) D5,D6: 6.. / D5 = 6 => 9 pairs (_) / D6 = 6 => 16 pairs (_) C5,D5: 6.. / C5 = 6 => 16 pairs (_) / D5 = 6 => 9 pairs (_) C6,D6: 6.. / C6 = 6 => 9 pairs (_) / D6 = 6 => 16 pairs (_) D4,H4: 7.. / D4 = 7 => 20 pairs (_) / H4 = 7 => 10 pairs (_) C7,G7: 7.. / C7 = 7 => 20 pairs (_) / G7 = 7 => 10 pairs (_) D1,D4: 7.. / D1 = 7 => 10 pairs (_) / D4 = 7 => 20 pairs (_) F2,F3: 8.. / F2 = 8 => 10 pairs (_) / F3 = 8 => 10 pairs (_) D5,E5: 8.. / D5 = 8 => 0 pairs (*) / E5 = 8 => 0 pairs (X) A8,C8: 8.. / A8 = 8 => 13 pairs (_) / C8 = 8 => 10 pairs (_) D9,E9: 8.. / D9 = 8 => 11 pairs (_) / E9 = 8 => 0 pairs (*) D5,D9: 8.. / D5 = 8 => 0 pairs (*) / D9 = 8 => 0 pairs (X) E5,E9: 8.. / E5 = 8 => 11 pairs (_) / E9 = 8 => 0 pairs (*) G5,G6: 9.. / G5 = 9 => 9 pairs (_) / G6 = 9 => 16 pairs (_) B8,B9: 9.. / B8 = 9 => 10 pairs (_) / B9 = 9 => 14 pairs (_) D6,G6: 9.. / D6 = 9 => 9 pairs (_) / G6 = 9 => 16 pairs (_) B8,F8: 9.. / B8 = 9 => 10 pairs (_) / F8 = 9 => 14 pairs (_) * DURATION: 0:01:03.069172 START: 15:58:09.729248 END: 15:59:12.798420 2017-05-04 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,C7,D1,D4,D6,D9,G5,G7,H4) * 961..283....39.6.1...16.29.389.214.65......131....3.2821.436.89...21.36.6.....1.2 * PAIR D1: 5,7 BLK 2 E1: 5,7,4 # reduction candidate for 5,7 E1: 5,7 # 22 pairs F2: 5,7,4,8 # reduction candidate for 5,7 F2: 5,7 # 15 pairs F3: 5,7,4,8 # reduction candidate for 5,7 F3: 5,7 # 15 pairs * PAIR D1: 5,7 ROW 1 I1: 5,7,4 # reduction candidate for 5,7 I1: 4 # 22 pairs I1: 5,7 # 13 pairs * PAIR B6: 4,7 BLK 4 B5: 4,7,2 # reduction candidate for 4,7 B5: 4,7 # 12 pairs C5: 4,7,2,6 # reduction candidate for 4,7 C5: 4,7 # 10 pairs C6: 4,7,6 # reduction candidate for 4,7 C6: 4,7 # 16 pairs * PAIR B6: 4,7 ROW 6 E6: 4,7,5 # reduction candidate for 4,7 E6: 5 # 20 pairs E6: 4,7 # 10 pairs * PAIR B6: 4,7 COL B B2: 4,7,2,5 # reduction candidate for 4,7 B2: 4,7 # 15 pairs B3: 4,7,3,5 # reduction candidate for 4,7 B3: 4,7 # 18 pairs B8: 4,7,5,9 # reduction candidate for 4,7 B8: 4,7 => CTR * 961..283..5239.671.3.16.29.38972145652..84.131...53.2821.436.89...21936.6938..142 B8: 5,9 # 10 pairs B9: 4,7,3,5,9 # reduction candidate for 4,7 B9: 4,7 # 13 pairs * PAIR D4: 5,7 BLK 5 E6: 5,7,4 # reduction candidate for 5,7 E6: 4 => CTR * 961752834...39.651.5316.2973895214765..687913176943528215436789...21.36563.87.1.2 E6: 5,7 # 13 pairs * PAIR D6: 6,9 BLK 5 D5: 6,9,8 # reduction candidate for 6,9 D5: 8 => SOLVED * 961572834852394671743168295389721456526849713174653928217436589498215367635987142 D5: 6,9 # 11 pairs * PAIR H4: 5,7 BLK 6 G6: 5,7,9 # reduction candidate for 5,7 G6: 9 # 16 pairs G6: 5,7 # 9 pairs * PAIR H4: 5,7 COL H H2: 5,7,4 # reduction candidate for 5,7 H2: 5,7 # 11 pairs H9: 5,7,4 # reduction candidate for 5,7 H9: 5,7 # 20 pairs * PAIR G5: 7,9 BLK 6 G6: 7,9,5 # reduction candidate for 7,9 G6: 7,9 # 20 pairs G6: 5 # 10 pairs * PAIR G5: 7,9 ROW 5 F5: 7,9,4 # reduction candidate for 7,9 F5: 7,9 # 22 pairs F5: 4 # 13 pairs * PAIR C7: 5,7 BLK 7 B8: 5,7,4,9 # reduction candidate for 5,7 B8: 5,7 # 17 pairs C8: 5,7,4,8 # reduction candidate for 5,7 C8: 5,7 # 19 pairs B9: 5,7,3,4,9 # reduction candidate for 5,7 B9: 5,7 # 15 pairs C9: 5,7,3,4 # reduction candidate for 5,7 C9: 5,7 # 17 pairs * PAIR C7: 5,7 COL C C2: 5,7,2,4,8 # reduction candidate for 5,7 C2: 5,7 # 15 pairs C3: 5,7,3,4,8 # reduction candidate for 5,7 C3: 5,7 # 12 pairs * PAIR D9: 8,9 COL D D5: 8,9,6 # reduction candidate for 8,9 D5: 8,9 # 16 pairs D5: 6 # 9 pairs * PAIR G7: 5,7 BLK 9 I8: 5,7,4 # reduction candidate for 5,7 I8: 5,7 # 11 pairs H9: 5,7,4 # reduction candidate for 5,7 H9: 5,7 # 20 pairs * PAIR G7: 5,7 COL G G6: 5,7,9 # reduction candidate for 5,7 G6: 9 # 16 pairs G6: 5,7 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-384-base-pr-000.dot * REASONING * DIS # B8: 4,7 => CTR => B8: 5,9 * DIS # E6: 4 => CTR => E6: 5,7 * PRF # D5: 8 => SOL * CNT 3 HDP CHAINS / 39 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,C7,D1,D4,D6,D9,G5,G7,H4) * 961..283....39.6.1...16.29.389.214.65......131....3.2821.436.89...21.36.6.....1.2 * PAIR D1: 5,7 BLK 2 E1: 5,7,4 # reduction candidate for 5,7 E1: 5,7 # 22 pairs F2: 5,7,4,8 # reduction candidate for 5,7 F2: 5,7 # 15 pairs F3: 5,7,4,8 # reduction candidate for 5,7 F3: 5,7 # 15 pairs * PAIR D1: 5,7 ROW 1 I1: 5,7,4 # reduction candidate for 5,7 I1: 4 # 22 pairs I1: 5,7 # 13 pairs * PAIR B6: 4,7 BLK 4 B5: 4,7,2 # reduction candidate for 4,7 B5: 4,7 # 12 pairs C5: 4,7,2,6 # reduction candidate for 4,7 C5: 4,7 # 10 pairs C6: 4,7,6 # reduction candidate for 4,7 C6: 4,7 # 16 pairs * PAIR B6: 4,7 ROW 6 E6: 4,7,5 # reduction candidate for 4,7 E6: 5 # 20 pairs E6: 4,7 # 10 pairs * PAIR B6: 4,7 COL B B2: 4,7,2,5 # reduction candidate for 4,7 B2: 4,7 # 15 pairs B3: 4,7,3,5 # reduction candidate for 4,7 B3: 4,7 # 18 pairs B8: 4,7,5,9 # reduction candidate for 4,7 B8: 4,7 => CTR * 961..283..5239.671.3.16.29.38972145652..84.131...53.2821.436.89...21936.6938..142 B9: 4,7,3,5,9 # reduction candidate for 4,7 B9: 4,7 # 13 pairs * PAIR RESTART * PAIR B6: 4,7 BLK 4 B5: 4,7,2 # reduction candidate for 4,7 B5: 4,7 # 12 pairs C5: 4,7,2,6 # reduction candidate for 4,7 C5: 4,7 # 11 pairs C6: 4,7,6 # reduction candidate for 4,7 C6: 4,7 # 17 pairs * PAIR B6: 4,7 ROW 6 E6: 4,7,5 # reduction candidate for 4,7 E6: 5 # 21 pairs E6: 4,7 # 11 pairs * PAIR B6: 4,7 COL B B2: 4,7,2,5 # reduction candidate for 4,7 B2: 4,7 # 15 pairs B3: 4,7,3,5 # reduction candidate for 4,7 B3: 4,7 # 18 pairs B9: 4,7,3,5,9 # reduction candidate for 4,7 B9: 4,7 # 13 pairs * PAIR D4: 5,7 BLK 5 E6: 5,7,4 # reduction candidate for 5,7 E6: 4 => CTR * 961752834...39.651...16.29.3895214765.....9131..943528215436789.9.21.36.6..8.91.2 * PAIR D6: 6,9 BLK 5 D5: 6,9,8 # reduction candidate for 6,9 D5: 8 => SOLVED * 961572834852394671743168295389721456526849713174653928217436589498215367635987142 * DURATION: 0:00:27.530519 START: 15:59:52.175658 END: 16:00:19.706177 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-384-base-pr-001.dot * REASONING * DIS # B8: 4,7 => CTR => B8: 5,9 * DIS B8: 5,9 # E6: 4 => CTR => E6: 5,7 * PRF B8: 5,9 + E6: 5,7 # D5: 8 => SOL * STA B8: 5,9 + E6: 5,7 + D5: 8 * CNT 3 HDP CHAINS / 26 HYP OPENED
Header Info
Top 500 Minimum 17 384 solution: 961572834852394671743168295389721456526849713174653928217436589498215367635987142 info: 33592 FNBTXYO S8.f 21752 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 961572834852394671743168295389721456526849713174653928217436589498215367635987142 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 # E1: 5,7 => UNS * INC # F2: 5,7 => UNS * INC # F3: 5,7 => UNS * INC # I1: 5,7 => UNS * INC # I1: 4 => UNS * INC # B5: 4,7 => UNS * INC # C5: 4,7 => UNS * INC # C6: 4,7 => UNS * INC # E6: 4,7 => UNS * INC # E6: 5 => UNS * INC # B2: 4,7 => UNS * INC # B3: 4,7 => UNS * DIS # B8: 4,7 => CTR => B8: 5,9 * INC # B8: 5,9 => UNS * INC # B9: 4,7 => UNS * INC # E6: 5,7 => UNS * DIS # E6: 4 => CTR => E6: 5,7 * INC # D5: 6,9 => UNS * PRF # D5: 8 => SOL * INC # G6: 5,7 => UNS * INC # G6: 9 => UNS * INC # H2: 5,7 => UNS * INC # H9: 5,7 => UNS * INC # G6: 7,9 => UNS * INC # G6: 5 => UNS * INC # F5: 7,9 => UNS * INC # F5: 4 => UNS * INC # B8: 5,7 => UNS * INC # C8: 5,7 => UNS * INC # B9: 5,7 => UNS * INC # C9: 5,7 => UNS * INC # C2: 5,7 => UNS * INC # C3: 5,7 => UNS * INC # D5: 8,9 => UNS * INC # D5: 6 => UNS * INC # I8: 5,7 => UNS * INC # H9: 5,7 => UNS * INC # G6: 5,7 => UNS * INC # G6: 9 => UNS * CNT 39 HDP CHAINS / 39 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E1: 5,7 => UNS * INC # F2: 5,7 => UNS * INC # F3: 5,7 => UNS * INC # I1: 5,7 => UNS * INC # I1: 4 => UNS * INC # B5: 4,7 => UNS * INC # C5: 4,7 => UNS * INC # C6: 4,7 => UNS * INC # E6: 4,7 => UNS * INC # E6: 5 => UNS * INC # B2: 4,7 => UNS * INC # B3: 4,7 => UNS * DIS # B8: 4,7 => CTR => B8: 5,9 * INC B8: 5,9 # B9: 4,7 => UNS * INC B8: 5,9 # B5: 4,7 => UNS * INC B8: 5,9 # C5: 4,7 => UNS * INC B8: 5,9 # C6: 4,7 => UNS * INC B8: 5,9 # E6: 4,7 => UNS * INC B8: 5,9 # E6: 5 => UNS * INC B8: 5,9 # B2: 4,7 => UNS * INC B8: 5,9 # B3: 4,7 => UNS * INC B8: 5,9 # B9: 4,7 => UNS * INC B8: 5,9 # E6: 5,7 => UNS * DIS B8: 5,9 # E6: 4 => CTR => E6: 5,7 * INC B8: 5,9 + E6: 5,7 # D5: 6,9 => UNS * PRF B8: 5,9 + E6: 5,7 # D5: 8 => SOL * STA B8: 5,9 + E6: 5,7 + D5: 8 * CNT 26 HDP CHAINS / 26 HYP OPENED