Analysis of xx-top500-338-base.sdk
Contents
Original Sudoku
level: medium
position: .2.4...6.1...8..........5..5..6.2...7.....1.....3.........1.7...3.....2..6....... initial
Autosolve
position: .2.4.7.611...8.......1..5..5136.2...7.....13....3.1.5.....1.7...317...2..67....1. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A6: 4,9 => CTR => A6: 2,6,8 * DIS # B7: 4,9 => CTR => B7: 5,8 * DIS # C6: 2,6 => CTR => C6: 4,8,9 * DIS # I6: 2,6 => CTR => I6: 4,7,9 * DIS # F3: 3,6 => CTR => F3: 9 * CNT 5 HDP CHAINS / 19 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A6: 4,9 => CTR => A6: 2,6,8 * DIS A6: 2,6,8 # B7: 4,9 => CTR => B7: 5,8 * DIS A6: 2,6,8 + B7: 5,8 # C6: 2,6 => CTR => C6: 4,8,9 * DIS A6: 2,6,8 + B7: 5,8 + C6: 4,8,9 # I6: 2,6 => CTR => I6: 4,7,9 * DIS A6: 2,6,8 + B7: 5,8 + C6: 4,8,9 + I6: 4,7,9 # F3: 3,6 => CTR => F3: 9 * DIS A6: 2,6,8 + B7: 5,8 + C6: 4,8,9 + I6: 4,7,9 + F3: 9 # F2: 6 => CTR => F2: 3,5 * PRF A6: 2,6,8 + B7: 5,8 + C6: 4,8,9 + I6: 4,7,9 + F3: 9 + F2: 3,5 # B6: 4,9 => SOL * STA A6: 2,6,8 + B7: 5,8 + C6: 4,8,9 + I6: 4,7,9 + F3: 9 + F2: 3,5 + B6: 4,9 * CNT 7 HDP CHAINS / 27 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .2.4...6.1...8..........5..5..6.2...7.....1.....3.........1.7...3.....2..6....... | initial |
| .2.4.7.611...8.......1..5..5136.2...7.....13....3.1.5.....1.7...317...2..67....1. | autosolve |
| 925437861176285394384169572513672489742958136698341257259816743831794625467523918 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) B5: 4,9 C5: 2,6 I5: 2,6 F7: 3,6 I7: 3,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D2,E3: 2.. / D2 = 2 => 16 pairs (_) / E3 = 2 => 0 pairs (X) E3,I3: 2.. / E3 = 2 => 0 pairs (X) / I3 = 2 => 16 pairs (_) C5,I5: 2.. / C5 = 2 => 16 pairs (_) / I5 = 2 => 0 pairs (X) E3,E9: 2.. / E3 = 2 => 0 pairs (X) / E9 = 2 => 16 pairs (_) G2,G6: 2.. / G2 = 2 => 0 pairs (X) / G6 = 2 => 16 pairs (_) A1,A3: 3.. / A1 = 3 => 0 pairs (X) / A3 = 3 => 16 pairs (_) F7,I7: 3.. / F7 = 3 => 0 pairs (X) / I7 = 3 => 16 pairs (_) B7,C7: 5.. / B7 = 5 => 5 pairs (_) / C7 = 5 => 0 pairs (X) I8,I9: 5.. / I8 = 5 => 5 pairs (_) / I9 = 5 => 5 pairs (_) C1,E1: 5.. / C1 = 5 => 6 pairs (_) / E1 = 5 => 0 pairs (X) B2,B7: 5.. / B2 = 5 => 0 pairs (X) / B7 = 5 => 5 pairs (_) C2,F2: 6.. / C2 = 6 => 16 pairs (_) / F2 = 6 => 0 pairs (X) C5,I5: 6.. / C5 = 6 => 0 pairs (X) / I5 = 6 => 16 pairs (_) F7,I7: 6.. / F7 = 6 => 16 pairs (_) / I7 = 6 => 0 pairs (X) A3,A6: 6.. / A3 = 6 => 0 pairs (X) / A6 = 6 => 16 pairs (_) E3,E8: 6.. / E3 = 6 => 16 pairs (_) / E8 = 6 => 0 pairs (X) G6,G8: 6.. / G6 = 6 => 0 pairs (X) / G8 = 6 => 16 pairs (_) B2,B3: 7.. / B2 = 7 => 6 pairs (_) / B3 = 7 => 5 pairs (_) E4,E6: 7.. / E4 = 7 => 7 pairs (_) / E6 = 7 => 6 pairs (_) E6,I6: 7.. / E6 = 7 => 6 pairs (_) / I6 = 7 => 7 pairs (_) D5,F5: 8.. / D5 = 8 => 6 pairs (_) / F5 = 8 => 6 pairs (_) * DURATION: 0:00:39.546059 START: 14:18:36.892585 END: 14:19:16.438644 2017-05-04 * CP COUNT: (21) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,C5,F7,I5,I7) * .2.4.7.611...8.......1..5..5136.2...7.....13....3.1.5.....1.7...317...2..67....1. * PAIR B5: 4,9 BLK 4 A6: 4,9,2,6,8 # reduction candidate for 4,9 A6: 4,9 => CTR * 32.4.7.611...862.36..1..5..5136.2...7.....13....3.165.....137.6.3176..2..67....1. A6: 2,6,8 # 5 pairs B6: 4,9,8 # reduction candidate for 4,9 B6: 4,9 # 9 pairs C6: 4,9,2,6,8 # reduction candidate for 4,9 C6: 4,9 # 7 pairs * PAIR B5: 4,9 ROW 5 E5: 4,9,5 # reduction candidate for 4,9 E5: 4,9 # 10 pairs F5: 4,9,5,8 # reduction candidate for 4,9 F5: 4,9 # 8 pairs * PAIR B5: 4,9 COL B B2: 4,9,5,7 # reduction candidate for 4,9 B2: 4,9 # 6 pairs B3: 4,9,7,8 # reduction candidate for 4,9 B3: 4,9 # 7 pairs B7: 4,9,5,8 # reduction candidate for 4,9 B7: 4,9 => CTR * .2.457.6115.28....67.1395.25136.2...7.....13..8.3.165...5.137.6.3176..2..67.2..1. B7: 5,8 # 6 pairs * PAIR C5: 2,6 BLK 4 A6: 2,6,4,8,9 # reduction candidate for 2,6 A6: 2,6 # 6 pairs C6: 2,6,4,8,9 # reduction candidate for 2,6 C6: 2,6 => CTR * 32.4.7.611...86...6..1395.25136.2...7.....13....3.1.5.....137.6.3176..2..67....1. C6: 4,8,9 # 6 pairs * PAIR I5: 2,6 BLK 6 G6: 2,6,4,9 # reduction candidate for 2,6 G6: 2,6 # 6 pairs I6: 2,6,4,7,9 # reduction candidate for 2,6 I6: 2,6 => CTR * .2.4.7.611...8.2.....12.5..5136.2...7.....13....371.5.....167.3.317..62..67....1. I6: 4,7,9 # 6 pairs * PAIR F7: 3,6 COL F F2: 3,6,5,9 # reduction candidate for 3,6 F2: 3,6 # 8 pairs F3: 3,6,9 # reduction candidate for 3,6 F3: 3,6 => CTR * .2.4.7.611.6.8.......1..5..5136.2...7.2...1366..3.1.5.....167.3.317..62..67.3..1. F3: 9 # 7 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-338-base-pr-000.dot * REASONING * DIS # A6: 4,9 => CTR => A6: 2,6,8 * DIS # B7: 4,9 => CTR => B7: 5,8 * DIS # C6: 2,6 => CTR => C6: 4,8,9 * DIS # I6: 2,6 => CTR => I6: 4,7,9 * DIS # F3: 3,6 => CTR => F3: 9 * CNT 5 HDP CHAINS / 19 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,C5,F7,I5,I7) * .2.4.7.611...8.......1..5..5136.2...7.....13....3.1.5.....1.7...317...2..67....1. * PAIR B5: 4,9 BLK 4 A6: 4,9,2,6,8 # reduction candidate for 4,9 A6: 4,9 => CTR * 32.4.7.611...862.36..1..5..5136.2...7.....13....3.165.....137.6.3176..2..67....1. B6: 4,9,8 # reduction candidate for 4,9 B6: 4,9 # 9 pairs C6: 4,9,2,6,8 # reduction candidate for 4,9 C6: 4,9 # 7 pairs * PAIR B5: 4,9 ROW 5 E5: 4,9,5 # reduction candidate for 4,9 E5: 4,9 # 10 pairs F5: 4,9,5,8 # reduction candidate for 4,9 F5: 4,9 # 8 pairs * PAIR B5: 4,9 COL B B2: 4,9,5,7 # reduction candidate for 4,9 B2: 4,9 # 8 pairs B3: 4,9,7,8 # reduction candidate for 4,9 B3: 4,9 # 9 pairs B7: 4,9,5,8 # reduction candidate for 4,9 B7: 4,9 => CTR * .2.457.6115..8.....7.16.5.25136.2...7.2...13668.3.125...5.167...317..62..67....1. * PAIR RESTART * PAIR B5: 4,9 BLK 4 B6: 4,9,8 # reduction candidate for 4,9 B6: 4,9 # 9 pairs C6: 4,9,2,6,8 # reduction candidate for 4,9 C6: 4,9 # 7 pairs * PAIR B5: 4,9 ROW 5 E5: 4,9,5 # reduction candidate for 4,9 E5: 4,9 # 11 pairs F5: 4,9,5,8 # reduction candidate for 4,9 F5: 4,9 # 8 pairs * PAIR B5: 4,9 COL B B2: 4,9,5,7 # reduction candidate for 4,9 B2: 4,9 # 8 pairs B3: 4,9,7,8 # reduction candidate for 4,9 B3: 4,9 # 9 pairs * PAIR C5: 2,6 BLK 4 A6: 2,6,8 # reduction candidate for 2,6 A6: 2,6 # 7 pairs C6: 2,6,4,8,9 # reduction candidate for 2,6 C6: 2,6 => CTR * 32.4.7.611...86...6..1395.25136.2...7.....13.8..3.1.5.....137.6.3176..2..67....1. * RESTART * PAIR I5: 2,6 BLK 6 G6: 2,6,4,9 # reduction candidate for 2,6 G6: 2,6 # 8 pairs I6: 2,6,4,7,9 # reduction candidate for 2,6 I6: 2,6 => CTR * .2.4.7.611...8.2.....12.5..5136.2...7.....13....371.5.....167.3.317..62..67....1. * RESTART * PAIR F7: 3,6 COL F F2: 3,6,5,9 # reduction candidate for 3,6 F2: 3,6 # 11 pairs F3: 3,6,9 # reduction candidate for 3,6 F3: 3,6 => CTR * .2.4.7.611.6.8.......1..5..5136.2...7.2...1366..3.125.....167.3.317..62..67.3..1. * RESTART * PAIR F7: 3,6 COL F F2: 3,6,5 # reduction candidate for 3,6 F2: 5 # 16 pairs F2: 3,6 # 11 pairs * PAIR RESTART * PAIR F7: 3,6 COL F F2: 3,6,5 # reduction candidate for 3,6 F2: 5 # 16 pairs F2: 3,6 # 11 pairs * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A6,B5,B7,C5,D2,E1,F7,G6,I5,I7) * .2.4.7.611...8.......1.95..5136.2...7.....13....3.1.5.....1.7...317...2..67....1. * PAIR E1: 3,5 BLK 2 F2: 3,5,6 # reduction candidate for 3,5 F2: 6 => CTR * .2.4.7.611...862.36..1.95..5136.2...7.6...1322..3.165...2.137.6.3176..2..67....1. * PAIR B5: 4,9 BLK 4 B6: 4,9,8 # reduction candidate for 4,9 B6: 4,9 => SOLVED * 925437861176285394384169572513672489742958136698341257259816743831794625467523918 * DURATION: 0:00:29.134344 START: 14:19:33.725448 END: 14:20:02.859792 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-338-base-pr-001.dot * REASONING * DIS # A6: 4,9 => CTR => A6: 2,6,8 * DIS A6: 2,6,8 # B7: 4,9 => CTR => B7: 5,8 * DIS A6: 2,6,8 + B7: 5,8 # C6: 2,6 => CTR => C6: 4,8,9 * DIS A6: 2,6,8 + B7: 5,8 + C6: 4,8,9 # I6: 2,6 => CTR => I6: 4,7,9 * DIS A6: 2,6,8 + B7: 5,8 + C6: 4,8,9 + I6: 4,7,9 # F3: 3,6 => CTR => F3: 9 * DIS A6: 2,6,8 + B7: 5,8 + C6: 4,8,9 + I6: 4,7,9 + F3: 9 # F2: 6 => CTR => F2: 3,5 * PRF A6: 2,6,8 + B7: 5,8 + C6: 4,8,9 + I6: 4,7,9 + F3: 9 + F2: 3,5 # B6: 4,9 => SOL * STA A6: 2,6,8 + B7: 5,8 + C6: 4,8,9 + I6: 4,7,9 + F3: 9 + F2: 3,5 + B6: 4,9 * CNT 7 HDP CHAINS / 27 HYP OPENED
Header Info
Top 500 Minimum 17 338 solution: 925437861176285394384169572513672489742958136698341257259816743831794625467523918 info: 3118 FNBHWXY S8.f 16758 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 925437861176285394384169572513672489742958136698341257259816743831794625467523918 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:
* DIS # A6: 4,9 => CTR => A6: 2,6,8 * INC # A6: 2,6,8 => UNS * INC # B6: 4,9 => UNS * INC # C6: 4,9 => UNS * INC # E5: 4,9 => UNS * INC # F5: 4,9 => UNS * INC # B2: 4,9 => UNS * INC # B3: 4,9 => UNS * DIS # B7: 4,9 => CTR => B7: 5,8 * INC # B7: 5,8 => UNS * INC # A6: 2,6 => UNS * DIS # C6: 2,6 => CTR => C6: 4,8,9 * INC # C6: 4,8,9 => UNS * INC # G6: 2,6 => UNS * DIS # I6: 2,6 => CTR => I6: 4,7,9 * INC # I6: 4,7,9 => UNS * INC # F2: 3,6 => UNS * DIS # F3: 3,6 => CTR => F3: 9 * INC # F3: 9 => UNS * CNT 19 HDP CHAINS / 19 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A6: 4,9 => CTR => A6: 2,6,8 * INC A6: 2,6,8 # B6: 4,9 => UNS * INC A6: 2,6,8 # C6: 4,9 => UNS * INC A6: 2,6,8 # E5: 4,9 => UNS * INC A6: 2,6,8 # F5: 4,9 => UNS * INC A6: 2,6,8 # B2: 4,9 => UNS * INC A6: 2,6,8 # B3: 4,9 => UNS * DIS A6: 2,6,8 # B7: 4,9 => CTR => B7: 5,8 * INC A6: 2,6,8 + B7: 5,8 # B6: 4,9 => UNS * INC A6: 2,6,8 + B7: 5,8 # C6: 4,9 => UNS * INC A6: 2,6,8 + B7: 5,8 # E5: 4,9 => UNS * INC A6: 2,6,8 + B7: 5,8 # F5: 4,9 => UNS * INC A6: 2,6,8 + B7: 5,8 # B2: 4,9 => UNS * INC A6: 2,6,8 + B7: 5,8 # B3: 4,9 => UNS * INC A6: 2,6,8 + B7: 5,8 # A6: 2,6 => UNS * DIS A6: 2,6,8 + B7: 5,8 # C6: 2,6 => CTR => C6: 4,8,9 * INC A6: 2,6,8 + B7: 5,8 + C6: 4,8,9 # G6: 2,6 => UNS * DIS A6: 2,6,8 + B7: 5,8 + C6: 4,8,9 # I6: 2,6 => CTR => I6: 4,7,9 * INC A6: 2,6,8 + B7: 5,8 + C6: 4,8,9 + I6: 4,7,9 # F2: 3,6 => UNS * DIS A6: 2,6,8 + B7: 5,8 + C6: 4,8,9 + I6: 4,7,9 # F3: 3,6 => CTR => F3: 9 * INC A6: 2,6,8 + B7: 5,8 + C6: 4,8,9 + I6: 4,7,9 + F3: 9 # F2: 3,6 => UNS * INC A6: 2,6,8 + B7: 5,8 + C6: 4,8,9 + I6: 4,7,9 + F3: 9 # F2: 5 => UNS * INC A6: 2,6,8 + B7: 5,8 + C6: 4,8,9 + I6: 4,7,9 + F3: 9 # F2: 3,6 => UNS * INC A6: 2,6,8 + B7: 5,8 + C6: 4,8,9 + I6: 4,7,9 + F3: 9 # F2: 5 => UNS * INC A6: 2,6,8 + B7: 5,8 + C6: 4,8,9 + I6: 4,7,9 + F3: 9 # F2: 3,5 => UNS * DIS A6: 2,6,8 + B7: 5,8 + C6: 4,8,9 + I6: 4,7,9 + F3: 9 # F2: 6 => CTR => F2: 3,5 * PRF A6: 2,6,8 + B7: 5,8 + C6: 4,8,9 + I6: 4,7,9 + F3: 9 + F2: 3,5 # B6: 4,9 => SOL * STA A6: 2,6,8 + B7: 5,8 + C6: 4,8,9 + I6: 4,7,9 + F3: 9 + F2: 3,5 + B6: 4,9 * CNT 27 HDP CHAINS / 27 HYP OPENED