Analysis of xx-top500-177-base.sdk
Contents
Original Sudoku
level: medium
position: 3.9..45.....61..7..........5...39....7.....6...........6.2.....8.....3.....7..... initial
Autosolve
position: 3.98745.6...61.9736.739....5.6.397...73528.69.9..67.3576.2.3.9.8..9.63.793.7.16.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B3: 1,2 => SOL * DIS # B3: 5 => CTR => B3: 1,2 * DIS # B2: 2,4 => CTR => B2: 5,8 * DIS # C2: 2,4 => CTR => C2: 5,8 * DIS # A6: 1 => CTR => A6: 2,4 * DIS # B2: 2,5 => CTR => B2: 4,8 * PRF # C2: 2,5 => SOL * DIS # B3: 2,5 => CTR => B3: 1 * PRF # B3: 1 => SOL * DIS # H3: 1,2 => CTR => H3: 4,8 * DIS # I3: 1,2 => CTR => I3: 4,8 * DIS # H4: 1,2 => CTR => H4: 4,8 * DIS # A6: 1,4 => CTR => A6: 2 * PRF # A6: 2 => SOL * DIS # A6: 1,4 => CTR => A6: 2 * PRF # A6: 2 => SOL * PRF # G6: 1,4 => SOL * PRF # G6: 1,4 => SOL * DIS # G3: 1,4 => CTR => G3: 2,8 * DIS # C8: 4,5 => CTR => C8: 1,2 * DIS # H8: 4,5 => CTR => H8: 1,2 * CNT 21 HDP CHAINS / 44 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # B3: 1,2 => SOL * STA B3: 1,2 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 3.9..45.....61..7..........5...39....7.....6...........6.2.....8.....3.....7..... | initial |
| 3.98745.6...61.9736.739....5.6.397...73528.69.9..67.3576.2.3.9.8..9.63.793.7.16.. | autosolve |
| 329874516485612973617395248546139782173528469298467135764253891851946327932781654 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) B1: 1,2 A2: 2,4 F2: 2,5 F3: 2,5 H1: 1,2 A5: 1,4 D4: 1,4 D6: 1,4 G5: 1,4 E8: 4,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,B3: 1.. / B1 = 1 => 0 pairs (X) / B3 = 1 => 0 pairs (_) A5,A6: 1.. / A5 = 1 => 10 pairs (_) / A6 = 1 => 0 pairs (X) D4,D6: 1.. / D4 = 1 => 11 pairs (_) / D6 = 1 => 10 pairs (_) C7,C8: 1.. / C7 = 1 => 0 pairs (X) / C8 = 1 => 11 pairs (_) B1,H1: 1.. / B1 = 1 => 0 pairs (X) / H1 = 1 => 0 pairs (_) A5,G5: 1.. / A5 = 1 => 10 pairs (_) / G5 = 1 => 0 pairs (X) C8,H8: 1.. / C8 = 1 => 11 pairs (_) / H8 = 1 => 0 pairs (X) F2,F3: 2.. / F2 = 2 => 0 pairs (*) / F3 = 2 => 0 pairs (X) B1,H1: 2.. / B1 = 2 => 0 pairs (*) / H1 = 2 => 0 pairs (X) A2,A6: 2.. / A2 = 2 => 0 pairs (X) / A6 = 2 => 0 pairs (_) G3,G6: 2.. / G3 = 2 => 0 pairs (*) / G6 = 2 => 0 pairs (X) D4,D6: 4.. / D4 = 4 => 10 pairs (_) / D6 = 4 => 11 pairs (_) A5,G5: 4.. / A5 = 4 => 0 pairs (X) / G5 = 4 => 10 pairs (_) F2,F3: 5.. / F2 = 5 => 0 pairs (X) / F3 = 5 => 0 pairs (_) H8,H9: 5.. / H8 = 5 => 0 pairs (X) / H9 = 5 => 12 pairs (_) B3,F3: 5.. / B3 = 5 => 0 pairs (X) / F3 = 5 => 0 pairs (_) C7,E7: 5.. / C7 = 5 => 13 pairs (_) / E7 = 5 => 0 pairs (*) B2,C2: 8.. / B2 = 8 => 11 pairs (_) / C2 = 8 => 0 pairs (X) B4,C6: 8.. / B4 = 8 => 0 pairs (X) / C6 = 8 => 11 pairs (_) E7,E9: 8.. / E7 = 8 => 19 pairs (_) / E9 = 8 => 12 pairs (_) C6,G6: 8.. / C6 = 8 => 11 pairs (_) / G6 = 8 => 0 pairs (X) B2,B4: 8.. / B2 = 8 => 11 pairs (_) / B4 = 8 => 0 pairs (X) C2,C6: 8.. / C2 = 8 => 0 pairs (X) / C6 = 8 => 11 pairs (_) * DURATION: 0:00:39.884824 START: 08:44:35.406768 END: 08:45:15.291592 2017-05-04 * CP COUNT: (23) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,B1,D4,D6,E8,F2,F3,G5,H1) * 3.98745.6...61.9736.739....5.6.397...73528.69.9..67.3576.2.3.9.8..9.63.793.7.16.. * PAIR B1: 1,2 BLK 1 B3: 1,2,5 # reduction candidate for 1,2 B3: 1,2 => SOLVED * 329874516485612973617395248546139782173528469298467135764253891851946327932781654 B3: 5 => CTR * 3198745262..615973657392...526.397...73528.69.98.6723576.2.3.9.8429563179357.16.2 * PAIR A2: 2,4 BLK 1 B2: 2,4,5,8 # reduction candidate for 2,4 B2: 2,4 => CTR * 3.98745.6..8615973657392...586.397...73528.69.9..67.3576.2.3.9.8..9.63.793.7.16.. B2: 5,8 # 11 pairs C2: 2,4,5,8 # reduction candidate for 2,4 C2: 2,4 => CTR * 319874526284615973657392...526.397...73528.69.98.6723576.2.3.9.8429563179357.16.2 C2: 5,8 # 11 pairs * PAIR A2: 2,4 COL A A6: 2,4,1 # reduction candidate for 2,4 A6: 1 => CTR * 3198745262..615973657392...5261397..47352816919846723576.2.3.9.8429563179357.16.2 A6: 2,4 # 10 pairs * PAIR F2: 2,5 ROW 2 B2: 2,5,4,8 # reduction candidate for 2,5 B2: 2,5 => CTR * 3.98745.64.861.9736.739.284586.39742173528.69.9..6783576.2.3.9.84.9563.793.7.165. B2: 4,8 # 11 pairs C2: 2,5,4,8 # reduction candidate for 2,5 C2: 2,5 => SOLVED * 329874516485612973617395248546139782173528469298467135764253891851946327932781654 C2: 4,8 # 12 pairs * PAIR F3: 2,5 ROW 3 B3: 2,5,1 # reduction candidate for 2,5 B3: 2,5 => CTR * 3198745262..615973657392...526.397...73528.69.98.6723576.2.3.9.8429563179357.16.2 B3: 1 => SOLVED * 329874516485612973617395248546139782173528469298467135764253891851946327932781654 * PAIR H1: 1,2 BLK 3 G3: 1,2,4,8 # reduction candidate for 1,2 G3: 1,2 # 13 pairs H3: 1,2,4,8 # reduction candidate for 1,2 H3: 1,2 => CTR * 3.98745.62..615973657392.1.526.397...73528.69.98.6723576.2.3.9.8419563.793.7.16.2 H3: 4,8 # 11 pairs I3: 1,2,4,8 # reduction candidate for 1,2 I3: 1,2 => CTR * 3.98745.62..615973657392..1526.397...73528.69.98.6723576.2.3.9.84.9563.793.7.1652 I3: 4,8 # 11 pairs * PAIR H1: 1,2 COL H H4: 1,2,4,8 # reduction candidate for 1,2 H4: 1,2 => CTR * 319874526...61.9736.739....5.6.397...73528.69.9..67.3576.2.3.9.8219.63.793.7.16.2 H4: 4,8 # 11 pairs H8: 1,2,4,5 # reduction candidate for 1,2 H8: 1,2 # 15 pairs * PAIR A5: 1,4 BLK 4 A6: 1,4,2 # reduction candidate for 1,4 A6: 1,4 => CTR * 3198745262..615973657392...526.397...73528.69.98.6723576.2.3.9.8429563179357.16.2 A6: 2 => SOLVED * 329874516485612973617395248546139782173528469298467135764253891851946327932781654 * PAIR D4: 1,4 ROW 4 H4: 1,4,2,8 # reduction candidate for 1,4 H4: 1,4 # 14 pairs I4: 1,4,2,8 # reduction candidate for 1,4 I4: 1,4 # 14 pairs * PAIR D6: 1,4 ROW 6 A6: 1,4,2 # reduction candidate for 1,4 A6: 1,4 => CTR * 3198745262..615973657392...526.397...73528.69.98.6723576.2.3.9.8429563179357.16.2 A6: 2 => SOLVED * 329874516485612973617395248546139782173528469298467135764253891851946327932781654 G6: 1,4,2,8 # reduction candidate for 1,4 G6: 1,4 => SOLVED * 329874516485612973617395248546139782173528469298467135764253891851946327932781654 G6: 2,8 # 11 pairs * PAIR G5: 1,4 BLK 6 H4: 1,4,2,8 # reduction candidate for 1,4 H4: 1,4 # 14 pairs I4: 1,4,2,8 # reduction candidate for 1,4 I4: 1,4 # 14 pairs G6: 1,4,2,8 # reduction candidate for 1,4 G6: 1,4 => SOLVED * 329874516485612973617395248546139782173528469298467135764253891851946327932781654 G6: 2,8 # 11 pairs * PAIR G5: 1,4 COL G G3: 1,4,2,8 # reduction candidate for 1,4 G3: 1,4 => CTR * 3.98745.62..615973657392...526.397...73528.69.98.6723576.2.389.84.9563.793.78165. G3: 2,8 # 11 pairs G7: 1,4,8 # reduction candidate for 1,4 G7: 1,4 # 13 pairs * PAIR E8: 4,5 BLK 8 E7: 4,5,8 # reduction candidate for 4,5 E7: 4,5 # 12 pairs E9: 4,5,8 # reduction candidate for 4,5 E9: 4,5 # 19 pairs * PAIR E8: 4,5 ROW 8 B8: 4,5,2 # reduction candidate for 4,5 B8: 4,5 # 18 pairs C8: 4,5,1,2 # reduction candidate for 4,5 C8: 4,5 => CTR * 319874526...61.9736.739....526.397...73528.69.98.67235761253.9.85.946317934781652 C8: 1,2 # 11 pairs H8: 4,5,1,2 # reduction candidate for 4,5 H8: 4,5 => CTR * 319874526...61.973657392...5.6.397.2.73528.69.9..67.3576.2.3.9.8219.63.793.7.16.. H8: 1,2 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-177-base-pr-000.dot * REASONING * PRF # B3: 1,2 => SOL * DIS # B3: 5 => CTR => B3: 1,2 * DIS # B2: 2,4 => CTR => B2: 5,8 * DIS # C2: 2,4 => CTR => C2: 5,8 * DIS # A6: 1 => CTR => A6: 2,4 * DIS # B2: 2,5 => CTR => B2: 4,8 * PRF # C2: 2,5 => SOL * DIS # B3: 2,5 => CTR => B3: 1 * PRF # B3: 1 => SOL * DIS # H3: 1,2 => CTR => H3: 4,8 * DIS # I3: 1,2 => CTR => I3: 4,8 * DIS # H4: 1,2 => CTR => H4: 4,8 * DIS # A6: 1,4 => CTR => A6: 2 * PRF # A6: 2 => SOL * DIS # A6: 1,4 => CTR => A6: 2 * PRF # A6: 2 => SOL * PRF # G6: 1,4 => SOL * PRF # G6: 1,4 => SOL * DIS # G3: 1,4 => CTR => G3: 2,8 * DIS # C8: 4,5 => CTR => C8: 1,2 * DIS # H8: 4,5 => CTR => H8: 1,2 * CNT 21 HDP CHAINS / 44 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,B1,D4,D6,E8,F2,F3,G5,H1) * 3.98745.6...61.9736.739....5.6.397...73528.69.9..67.3576.2.3.9.8..9.63.793.7.16.. * PAIR B1: 1,2 BLK 1 B3: 1,2,5 # reduction candidate for 1,2 B3: 1,2 => SOLVED * 329874516485612973617395248546139782173528469298467135764253891851946327932781654 * DURATION: 0:00:02.129791 START: 08:45:55.768623 END: 08:45:57.898414 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-177-base-pr-001.dot * REASONING * PRF # B3: 1,2 => SOL * STA B3: 1,2 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 177 solution: 329874516485612973617395248546139782173528469298467135764253891851946327932781654 info: 1827 FNBTWY S8.f 29889 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 329874516485612973617395248546139782173528469298467135764253891851946327932781654 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:
* PRF # B3: 1,2 => SOL * DIS # B3: 5 => CTR => B3: 1,2 * DIS # B2: 2,4 => CTR => B2: 5,8 * INC # B2: 5,8 => UNS * DIS # C2: 2,4 => CTR => C2: 5,8 * INC # C2: 5,8 => UNS * INC # A6: 2,4 => UNS * DIS # A6: 1 => CTR => A6: 2,4 * DIS # B2: 2,5 => CTR => B2: 4,8 * INC # B2: 4,8 => UNS * PRF # C2: 2,5 => SOL * INC # C2: 4,8 => UNS * DIS # B3: 2,5 => CTR => B3: 1 * PRF # B3: 1 => SOL * INC # G3: 1,2 => UNS * DIS # H3: 1,2 => CTR => H3: 4,8 * INC # H3: 4,8 => UNS * DIS # I3: 1,2 => CTR => I3: 4,8 * INC # I3: 4,8 => UNS * DIS # H4: 1,2 => CTR => H4: 4,8 * INC # H4: 4,8 => UNS * INC # H8: 1,2 => UNS * DIS # A6: 1,4 => CTR => A6: 2 * PRF # A6: 2 => SOL * INC # H4: 1,4 => UNS * INC # I4: 1,4 => UNS * DIS # A6: 1,4 => CTR => A6: 2 * PRF # A6: 2 => SOL * PRF # G6: 1,4 => SOL * INC # G6: 2,8 => UNS * INC # H4: 1,4 => UNS * INC # I4: 1,4 => UNS * PRF # G6: 1,4 => SOL * INC # G6: 2,8 => UNS * DIS # G3: 1,4 => CTR => G3: 2,8 * INC # G3: 2,8 => UNS * INC # G7: 1,4 => UNS * INC # E7: 4,5 => UNS * INC # E9: 4,5 => UNS * INC # B8: 4,5 => UNS * DIS # C8: 4,5 => CTR => C8: 1,2 * INC # C8: 1,2 => UNS * DIS # H8: 4,5 => CTR => H8: 1,2 * INC # H8: 1,2 => UNS * CNT 44 HDP CHAINS / 44 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # B3: 1,2 => SOL * STA B3: 1,2 * CNT 1 HDP CHAINS / 1 HYP OPENED