Analysis of xx-top500-497-base.sdk
Contents
Original Sudoku
level: medium
position: .....87..2...1....1.4.........26.3...5....6..8.........3.6........4...2........1. initial
Autosolve
position: ....287412...14.6.1.4..623....26.3...5.18.6..8...4.1...3.6........4...2....8...1. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 6,9 => CTR => A1: 3,5 * DIS # B6: 6,9 => CTR => B6: 2,7 * DIS # B8: 6,9 => CTR => B8: 1,7,8 * DIS # B9: 6,9 => CTR => B9: 2,4,7 * DIS # H4: 7,9 => CTR => H4: 5,8 * DIS # I4: 7,9 => CTR => I4: 4,5,8 * DIS # I5: 7,9 => CTR => I5: 2,4 * PRF # I6: 7,9 => SOL * DIS # A5: 7,9 => CTR => A5: 3,4 * DIS # C5: 7,9 => CTR => C5: 2,3 * PRF # F8: 5,9 => SOL * DIS # F9: 5,9 => CTR => F9: 2,7 * DIS # G7: 5,9 => CTR => G7: 4,8 * DIS # H7: 5,9 => CTR => H7: 7,8 * DIS # I7: 5,9 => CTR => I7: 7,8 * DIS # G7: 5,9 => CTR => G7: 4,8 * DIS # H7: 5,9 => CTR => H7: 7,8 * DIS # I7: 5,9 => CTR => I7: 7,8 * DIS # C8: 5,9 => CTR => C8: 1,6,7,8 * PRF # F8: 5,9 => SOL * DIS # G2: 5,9 => CTR => G2: 8 * CNT 21 HDP CHAINS / 55 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 6,9 => CTR => A1: 3,5 * DIS A1: 3,5 # B6: 6,9 => CTR => B6: 2,7 * PRF A1: 3,5 + B6: 2,7 # I6: 7,9 => SOL * STA A1: 3,5 + B6: 2,7 + I6: 7,9 * CNT 3 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .....87..2...1....1.4.........26.3...5....6..8.........3.6........4...2........1. | initial |
| ....287412...14.6.1.4..623....26.3...5.18.6..8...4.1...3.6........4...2....8...1. | autosolve |
| 369528741275314869184796235791265384453187692826943157932651478618479523547832916 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) B1: 6,9 H5: 7,9 C7: 1,2 E7: 5,9 F7: 1,2 G8: 5,9 I8: 3,6 I9: 3,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B4,C4: 1.. / B4 = 1 => 0 pairs (X) / C4 = 1 => 0 pairs (_) F7,F8: 1.. / F7 = 1 => 0 pairs (*) / F8 = 1 => 0 pairs (X) C7,F7: 1.. / C7 = 1 => 0 pairs (X) / F7 = 1 => 0 pairs (_) B4,B8: 1.. / B4 = 1 => 0 pairs (X) / B8 = 1 => 0 pairs (_) I5,I6: 2.. / I5 = 2 => 0 pairs (*) / I6 = 2 => 0 pairs (X) F7,F9: 2.. / F7 = 2 => 0 pairs (X) / F9 = 2 => 0 pairs (_) C5,I5: 2.. / C5 = 2 => 0 pairs (X) / I5 = 2 => 0 pairs (_) C7,F7: 2.. / C7 = 2 => 0 pairs (*) / F7 = 2 => 0 pairs (X) B6,B9: 2.. / B6 = 2 => 0 pairs (*) / B9 = 2 => 0 pairs (X) D1,D2: 3.. / D1 = 3 => 0 pairs (X) / D2 = 3 => 10 pairs (_) F5,F6: 3.. / F5 = 3 => 0 pairs (X) / F6 = 3 => 12 pairs (_) E8,E9: 3.. / E8 = 3 => 6 pairs (_) / E9 = 3 => 6 pairs (_) I8,I9: 3.. / I8 = 3 => 6 pairs (_) / I9 = 3 => 6 pairs (_) C2,D2: 3.. / C2 = 3 => 0 pairs (X) / D2 = 3 => 10 pairs (_) C6,F6: 3.. / C6 = 3 => 0 pairs (X) / F6 = 3 => 12 pairs (_) E8,I8: 3.. / E8 = 3 => 6 pairs (_) / I8 = 3 => 6 pairs (_) E9,I9: 3.. / E9 = 3 => 6 pairs (_) / I9 = 3 => 6 pairs (_) A1,A5: 3.. / A1 = 3 => 12 pairs (_) / A5 = 3 => 0 pairs (X) I4,I5: 4.. / I4 = 4 => 0 pairs (*) / I5 = 4 => 0 pairs (X) G7,G9: 4.. / G7 = 4 => 16 pairs (_) / G9 = 4 => 0 pairs (X) A5,I5: 4.. / A5 = 4 => 0 pairs (*) / I5 = 4 => 0 pairs (X) A7,G7: 4.. / A7 = 4 => 0 pairs (X) / G7 = 4 => 16 pairs (_) B4,B9: 4.. / B4 = 4 => 0 pairs (X) / B9 = 4 => 0 pairs (_) B6,C6: 6.. / B6 = 6 => 0 pairs (X) / C6 = 6 => 12 pairs (_) I8,I9: 6.. / I8 = 6 => 6 pairs (_) / I9 = 6 => 6 pairs (_) H7,I7: 7.. / H7 = 7 => 12 pairs (_) / I7 = 7 => 8 pairs (_) H4,I4: 8.. / H4 = 8 => 8 pairs (_) / I4 = 8 => 0 pairs (X) B8,C8: 8.. / B8 = 8 => 0 pairs (X) / C8 = 8 => 8 pairs (_) B3,I3: 8.. / B3 = 8 => 10 pairs (_) / I3 = 8 => 0 pairs (X) C2,C8: 8.. / C2 = 8 => 0 pairs (X) / C8 = 8 => 8 pairs (_) G2,G7: 8.. / G2 = 8 => 14 pairs (_) / G7 = 8 => 0 pairs (X) H4,H7: 8.. / H4 = 8 => 8 pairs (_) / H7 = 8 => 0 pairs (X) * DURATION: 0:00:54.133842 START: 19:41:09.511211 END: 19:42:03.645053 2017-05-04 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,C7,E7,F7,G8,H5,I8,I9) * ....287412...14.6.1.4..623....26.3...5.18.6..8...4.1...3.6........4...2....8...1. * PAIR B1: 6,9 BLK 1 A1: 6,9,3,5 # reduction candidate for 6,9 A1: 6,9 => CTR * ....287412...14.6.1.4..623..4126.3..35.18.6.48...431.2.3.6........4...2..2.8...1. A1: 3,5 # 9 pairs C1: 6,9,3,5 # reduction candidate for 6,9 C1: 6,9 # 15 pairs * PAIR B1: 6,9 COL B B6: 6,9,2,7 # reduction candidate for 6,9 B6: 6,9 => CTR * ....287412...14.6.1.4..623..4126.3...5.18.6..8...4.1...3.6........4...2..2.8...1. B6: 2,7 # 14 pairs B8: 6,9,1,7,8 # reduction candidate for 6,9 B8: 6,9 => CTR * 36..2874127.31486.1847.623.91726538445318.6.2826.431.7.316.2478.984.152..428..91. B8: 1,7,8 # 8 pairs B9: 6,9,2,4,7 # reduction candidate for 6,9 B9: 6,9 => CTR * ....287412...14.6.1.4..623..4126.3...5.18.6.4826.431...326.1....184...2....8.2.1. B9: 2,4,7 # 8 pairs * PAIR H5: 7,9 BLK 6 H4: 7,9,5,8 # reduction candidate for 7,9 H4: 7,9 => CTR * ....287412...1486.184..623..4126.3.8.5.18.6.48...4.1.2.3.6...87...4...2..2.8...1. H4: 5,8 # 9 pairs I4: 7,9,4,5,8 # reduction candidate for 7,9 I4: 7,9 => CTR * ....287412...14.6.1.4..623..4126.38..5.18.6.48...4.1.2.3.6........4...2..2.8...1. I4: 4,5,8 # 8 pairs I5: 7,9,2,4 # reduction candidate for 7,9 I5: 7,9 => CTR * ....287412...14.6.1.4..623....26.3.44521836..8.3.4.1.2.316........4...2....8...1. I5: 2,4 # 9 pairs H6: 7,9,5 # reduction candidate for 7,9 H6: 7,9 # 14 pairs I6: 7,9,2,5 # reduction candidate for 7,9 I6: 7,9 => SOLVED * 369528741275314869184796235791265384453187692826943157932651478618479523547832916 I6: 2,5 # 9 pairs * PAIR H5: 7,9 ROW 5 A5: 7,9,3,4 # reduction candidate for 7,9 A5: 7,9 => CTR * 3...287412..314.6.1.4..623..4126.3...5.18.6.48...4.1.2.3.6........4...2..2.8...1. A5: 3,4 # 9 pairs C5: 7,9,2,3 # reduction candidate for 7,9 C5: 7,9 => CTR * ....287412...14.6.1.4..623....26.3.445.1836.28.3.4.1...3.6..4.....4...2..4.8...1. C5: 2,3 # 9 pairs F5: 7,9,3 # reduction candidate for 7,9 F5: 7,9 # 12 pairs * PAIR H5: 7,9 COL H H7: 7,9,5,8 # reduction candidate for 7,9 H7: 5,8 # 12 pairs H7: 7,9 # 11 pairs * PAIR E7: 5,9 BLK 8 E8: 5,9,3,7 # reduction candidate for 5,9 E8: 5,9 # 15 pairs F8: 5,9,1,7 # reduction candidate for 5,9 F8: 5,9 => SOLVED * 369528741275314869184796235791265384453187692826943157932651478618479523547832916 F8: 1,7 # 9 pairs E9: 5,9,3,7 # reduction candidate for 5,9 E9: 5,9 # 14 pairs F9: 5,9,2,7 # reduction candidate for 5,9 F9: 5,9 => CTR * 3695287412753148691847962359172653844531876928269431575316.2478..84.1.2..428.951. F9: 2,7 # 9 pairs * PAIR E7: 5,9 ROW 7 A7: 5,9,4 # reduction candidate for 5,9 A7: 5,9 # 16 pairs G7: 5,9,4,8 # reduction candidate for 5,9 G7: 5,9 => CTR * ....287412...1486.184..623..4126.3...5.18.6.48...4.1.24326.1....184...2....8.241. G7: 4,8 # 9 pairs H7: 5,9,7,8 # reduction candidate for 5,9 H7: 5,9 => CTR * ....287412...14.6.1.4..623..4126.38..5.18.6.48...4.1.24326.18.7.184...2....8.241. H7: 7,8 # 10 pairs I7: 5,9,7,8 # reduction candidate for 5,9 I7: 5,9 => CTR * ....287412...14.6.1.4..623..41265387.5.18.6948...4.1524326.187..184...2....8.241. I7: 7,8 # 9 pairs * PAIR E7: 5,9 COL E E3: 5,9,7 # reduction candidate for 5,9 E3: 7 # 15 pairs E3: 5,9 # 12 pairs * PAIR G8: 5,9 BLK 9 G7: 5,9,4,8 # reduction candidate for 5,9 G7: 5,9 => CTR * ....287412...1486.184..623..4126.3...5.18.6.48...4.1.24326.1....184...2....8.241. G7: 4,8 # 9 pairs H7: 5,9,7,8 # reduction candidate for 5,9 H7: 5,9 => CTR * ....287412...14.6.1.4..623..4126.38..5.18.6.48...4.1.24326.18.7.184...2....8.241. H7: 7,8 # 10 pairs I7: 5,9,7,8 # reduction candidate for 5,9 I7: 5,9 => CTR * ....287412...14.6.1.4..623..41265387.5.18.6948...4.1524326.187..184...2....8.241. I7: 7,8 # 9 pairs G9: 5,9,4 # reduction candidate for 5,9 G9: 5,9 # 16 pairs * PAIR G8: 5,9 ROW 8 A8: 5,9,6,7 # reduction candidate for 5,9 A8: 5,9 # 11 pairs C8: 5,9,1,6,7,8 # reduction candidate for 5,9 C8: 5,9 => CTR * ....287412.8314.6.1.4..6238...26.38..5.18.6..8...4.1...3.6..8...8.4.1.2....8..41. C8: 1,6,7,8 # 8 pairs E8: 5,9,3,7 # reduction candidate for 5,9 E8: 5,9 # 15 pairs F8: 5,9,1,7 # reduction candidate for 5,9 F8: 5,9 => SOLVED * 369528741275314869184796235791265384453187692826943157932651478618479523547832916 F8: 1,7 # 9 pairs * PAIR G8: 5,9 COL G G2: 5,9,8 # reduction candidate for 5,9 G2: 5,9 => CTR * ....287412...14.6.1.4..623..4126.38..5.18.6.48...4.1.24326.18...184...2....8.241. G2: 8 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-497-base-pr-000.dot * REASONING * DIS # A1: 6,9 => CTR => A1: 3,5 * DIS # B6: 6,9 => CTR => B6: 2,7 * DIS # B8: 6,9 => CTR => B8: 1,7,8 * DIS # B9: 6,9 => CTR => B9: 2,4,7 * DIS # H4: 7,9 => CTR => H4: 5,8 * DIS # I4: 7,9 => CTR => I4: 4,5,8 * DIS # I5: 7,9 => CTR => I5: 2,4 * PRF # I6: 7,9 => SOL * DIS # A5: 7,9 => CTR => A5: 3,4 * DIS # C5: 7,9 => CTR => C5: 2,3 * PRF # F8: 5,9 => SOL * DIS # F9: 5,9 => CTR => F9: 2,7 * DIS # G7: 5,9 => CTR => G7: 4,8 * DIS # H7: 5,9 => CTR => H7: 7,8 * DIS # I7: 5,9 => CTR => I7: 7,8 * DIS # G7: 5,9 => CTR => G7: 4,8 * DIS # H7: 5,9 => CTR => H7: 7,8 * DIS # I7: 5,9 => CTR => I7: 7,8 * DIS # C8: 5,9 => CTR => C8: 1,6,7,8 * PRF # F8: 5,9 => SOL * DIS # G2: 5,9 => CTR => G2: 8 * CNT 21 HDP CHAINS / 55 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,C7,E7,F7,G8,H5,I8,I9) * ....287412...14.6.1.4..623....26.3...5.18.6..8...4.1...3.6........4...2....8...1. * PAIR B1: 6,9 BLK 1 A1: 6,9,3,5 # reduction candidate for 6,9 A1: 6,9 => CTR * ....287412...14.6.1.4..623..4126.3..35.18.6.48...431.2.3.6........4...2..2.8...1. C1: 6,9,3,5 # reduction candidate for 6,9 C1: 6,9 # 15 pairs * RESTART * PAIR B1: 6,9 BLK 1 C1: 6,9,3,5 # reduction candidate for 6,9 C1: 3,5 # 18 pairs C1: 6,9 # 15 pairs * PAIR B1: 6,9 COL B B6: 6,9,2,7 # reduction candidate for 6,9 B6: 6,9 => CTR * ....287412...14.6.1.4..623..4126.3...5.18.6..8...4.1...3.6........4...2..2.8...1. * PAIR RESTART * PAIR H5: 7,9 BLK 6 H6: 7,9,5 # reduction candidate for 7,9 H6: 7,9 # 19 pairs I6: 7,9,2,5 # reduction candidate for 7,9 I6: 7,9 => SOLVED * 369528741275314869184796235791265384453187692826943157932651478618479523547832916 * DURATION: 0:00:09.620163 START: 19:42:51.086016 END: 19:43:00.706179 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-497-base-pr-001.dot * REASONING * DIS # A1: 6,9 => CTR => A1: 3,5 * DIS A1: 3,5 # B6: 6,9 => CTR => B6: 2,7 * PRF A1: 3,5 + B6: 2,7 # I6: 7,9 => SOL * STA A1: 3,5 + B6: 2,7 + I6: 7,9 * CNT 3 HDP CHAINS / 7 HYP OPENED
Header Info
Top 500 Minimum 17 497 solution: 369528741275314869184796235791265384453187692826943157932651478618479523547832916 info: 96592 FNBHYK S8.f 2530 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 369528741275314869184796235791265384453187692826943157932651478618479523547832916 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 # A1: 6,9 => CTR => A1: 3,5 * INC # A1: 3,5 => UNS * INC # C1: 6,9 => UNS * DIS # B6: 6,9 => CTR => B6: 2,7 * INC # B6: 2,7 => UNS * DIS # B8: 6,9 => CTR => B8: 1,7,8 * INC # B8: 1,7,8 => UNS * DIS # B9: 6,9 => CTR => B9: 2,4,7 * INC # B9: 2,4,7 => UNS * DIS # H4: 7,9 => CTR => H4: 5,8 * INC # H4: 5,8 => UNS * DIS # I4: 7,9 => CTR => I4: 4,5,8 * INC # I4: 4,5,8 => UNS * DIS # I5: 7,9 => CTR => I5: 2,4 * INC # I5: 2,4 => UNS * INC # H6: 7,9 => UNS * PRF # I6: 7,9 => SOL * INC # I6: 2,5 => UNS * DIS # A5: 7,9 => CTR => A5: 3,4 * INC # A5: 3,4 => UNS * DIS # C5: 7,9 => CTR => C5: 2,3 * INC # C5: 2,3 => UNS * INC # F5: 7,9 => UNS * INC # H7: 7,9 => UNS * INC # H7: 5,8 => UNS * INC # E8: 5,9 => UNS * PRF # F8: 5,9 => SOL * INC # F8: 1,7 => UNS * INC # E9: 5,9 => UNS * DIS # F9: 5,9 => CTR => F9: 2,7 * INC # F9: 2,7 => UNS * INC # A7: 5,9 => UNS * DIS # G7: 5,9 => CTR => G7: 4,8 * INC # G7: 4,8 => UNS * DIS # H7: 5,9 => CTR => H7: 7,8 * INC # H7: 7,8 => UNS * DIS # I7: 5,9 => CTR => I7: 7,8 * INC # I7: 7,8 => UNS * INC # E3: 5,9 => UNS * INC # E3: 7 => UNS * DIS # G7: 5,9 => CTR => G7: 4,8 * INC # G7: 4,8 => UNS * DIS # H7: 5,9 => CTR => H7: 7,8 * INC # H7: 7,8 => UNS * DIS # I7: 5,9 => CTR => I7: 7,8 * INC # I7: 7,8 => UNS * INC # G9: 5,9 => UNS * INC # A8: 5,9 => UNS * DIS # C8: 5,9 => CTR => C8: 1,6,7,8 * INC # C8: 1,6,7,8 => UNS * INC # E8: 5,9 => UNS * PRF # F8: 5,9 => SOL * INC # F8: 1,7 => UNS * DIS # G2: 5,9 => CTR => G2: 8 * INC # G2: 8 => UNS * CNT 55 HDP CHAINS / 55 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 6,9 => CTR => A1: 3,5 * INC A1: 3,5 # C1: 6,9 => UNS * INC A1: 3,5 # C1: 6,9 => UNS * INC A1: 3,5 # C1: 3,5 => UNS * DIS A1: 3,5 # B6: 6,9 => CTR => B6: 2,7 * INC A1: 3,5 + B6: 2,7 # H6: 7,9 => UNS * PRF A1: 3,5 + B6: 2,7 # I6: 7,9 => SOL * STA A1: 3,5 + B6: 2,7 + I6: 7,9 * CNT 7 HDP CHAINS / 7 HYP OPENED