Analysis of xx-top500-376-base.sdk
Contents
Original Sudoku
level: medium
position: 5....64.....3................2.4.8...3.25.....9.......7....4...1......2........39 initial
Autosolve
position: 52..964.39..3.52..3..4.29..6.2.4389.83.259.4.49....3.27.3924...1.9.3..242......39 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C6: 1,7 => SOL * PRF # I4: 1,7 => SOL * DIS # I5: 7 => CTR => I5: 1,6 * DIS # F9: 7,8 => CTR => F9: 1 * DIS # F6: 1 => CTR => F6: 7,8 * CNT 5 HDP CHAINS / 32 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C6: 1,7 => SOL * STA C6: 1,7 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 5....64.....3................2.4.8...3.25.....9.......7....4...1......2........39 | initial |
| 52..964.39..3.52..3..4.29..6.2.4389.83.259.4.49....3.27.3924...1.9.3..242......39 | autosolve |
| 528796413974315268316482975652143897837259146491678352763924581189537624245861739 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) C5: 1,7 D4: 1,7 G5: 1,6 B7: 5,6 F8: 7,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F6,F9: 1.. / F6 = 1 => 0 pairs (X) / F9 = 1 => 6 pairs (_) G5,G7: 1.. / G5 = 1 => 11 pairs (_) / G7 = 1 => 11 pairs (_) B2,C2: 4.. / B2 = 4 => 8 pairs (_) / C2 = 4 => 5 pairs (_) B9,C9: 4.. / B9 = 4 => 5 pairs (_) / C9 = 4 => 8 pairs (_) B2,B9: 4.. / B2 = 4 => 8 pairs (_) / B9 = 4 => 5 pairs (_) C2,C9: 4.. / C2 = 4 => 5 pairs (_) / C9 = 4 => 8 pairs (_) H3,I3: 5.. / H3 = 5 => 7 pairs (_) / I3 = 5 => 0 pairs (*) B4,C6: 5.. / B4 = 5 => 0 pairs (*) / C6 = 5 => 0 pairs (X) I4,H6: 5.. / I4 = 5 => 7 pairs (_) / H6 = 5 => 0 pairs (*) D8,D9: 5.. / D8 = 5 => 8 pairs (_) / D9 = 5 => 8 pairs (_) B4,I4: 5.. / B4 = 5 => 0 pairs (*) / I4 = 5 => 0 pairs (X) C6,H6: 5.. / C6 = 5 => 7 pairs (_) / H6 = 5 => 0 pairs (*) B7,G7: 5.. / B7 = 5 => 10 pairs (_) / G7 = 5 => 12 pairs (_) C6,C9: 5.. / C6 = 5 => 7 pairs (_) / C9 = 5 => 0 pairs (*) H3,H6: 5.. / H3 = 5 => 7 pairs (_) / H6 = 5 => 0 pairs (*) I3,I4: 5.. / I3 = 5 => 0 pairs (*) / I4 = 5 => 0 pairs (X) D6,E6: 6.. / D6 = 6 => 6 pairs (_) / E6 = 6 => 7 pairs (_) G5,I5: 6.. / G5 = 6 => 11 pairs (_) / I5 = 6 => 11 pairs (_) E6,E9: 6.. / E6 = 6 => 7 pairs (_) / E9 = 6 => 6 pairs (_) G8,G9: 7.. / G8 = 7 => 15 pairs (_) / G9 = 7 => 7 pairs (_) C5,I5: 7.. / C5 = 7 => 10 pairs (_) / I5 = 7 => 0 pairs (X) H7,I7: 8.. / H7 = 8 => 7 pairs (_) / I7 = 8 => 6 pairs (_) * DURATION: 0:00:37.876072 START: 15:44:40.360078 END: 15:45:18.236150 2017-05-04 * CP COUNT: (22) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,C5,D4,F8,G5) * 52..964.39..3.52..3..4.29..6.2.4389.83.259.4.49....3.27.3924...1.9.3..242......39 * PAIR C5: 1,7 BLK 4 B4: 1,7,5 # reduction candidate for 1,7 B4: 1,7 # 7 pairs C6: 1,7,5 # reduction candidate for 1,7 C6: 1,7 => SOLVED * 528796413974315268316482975652143897837259146491678352763924581189537624245861739 C6: 5 # 7 pairs * PAIR C5: 1,7 ROW 5 I5: 1,7,6 # reduction candidate for 1,7 I5: 6 # 11 pairs I5: 1,7 # 11 pairs * PAIR C5: 1,7 COL C C1: 1,7,8 # reduction candidate for 1,7 C1: 1,7 # 9 pairs C2: 1,7,4,6,8 # reduction candidate for 1,7 C2: 1,7 # 14 pairs C3: 1,7,6,8 # reduction candidate for 1,7 C3: 1,7 # 15 pairs * PAIR D4: 1,7 BLK 5 D6: 1,7,6,8 # reduction candidate for 1,7 D6: 1,7 # 18 pairs E6: 1,7,6,8 # reduction candidate for 1,7 E6: 1,7 # 9 pairs F6: 1,7,8 # reduction candidate for 1,7 F6: 1,7 # 8 pairs * PAIR D4: 1,7 ROW 4 B4: 1,7,5 # reduction candidate for 1,7 B4: 1,7 # 7 pairs I4: 1,7,5 # reduction candidate for 1,7 I4: 1,7 => SOLVED * 528796413974315268316482975652143897837259146491678352763924581189537624245861739 I4: 5 # 7 pairs * PAIR D4: 1,7 COL D D1: 1,7,8 # reduction candidate for 1,7 D1: 1,7 # 7 pairs D9: 1,7,5,6,8 # reduction candidate for 1,7 D9: 1,7 # 20 pairs * PAIR G5: 1,6 BLK 6 I5: 1,6,7 # reduction candidate for 1,6 I5: 7 => CTR * 52..964.39..3.52..3..4.29..672143895831259647495...3127539241..1.9.3..242....1.39 I5: 1,6 # 10 pairs * PAIR G5: 1,6 COL G G7: 1,6,5 # reduction candidate for 1,6 G7: 5 # 12 pairs G7: 1,6 # 10 pairs * PAIR B7: 5,6 BLK 7 B8: 5,6,8 # reduction candidate for 5,6 B8: 5,6 # 11 pairs B9: 5,6,4,8 # reduction candidate for 5,6 B9: 5,6 # 12 pairs C9: 5,6,4,8 # reduction candidate for 5,6 C9: 5,6 # 9 pairs * PAIR B7: 5,6 ROW 7 G7: 5,6,1 # reduction candidate for 5,6 G7: 5,6 # 11 pairs G7: 1 # 11 pairs * PAIR F8: 7,8 BLK 8 D8: 7,8,5,6 # reduction candidate for 7,8 D8: 7,8 # 13 pairs D9: 7,8,1,5,6 # reduction candidate for 7,8 D9: 7,8 # 10 pairs E9: 7,8,1,6 # reduction candidate for 7,8 E9: 7,8 # 10 pairs F9: 7,8,1 # reduction candidate for 7,8 F9: 7,8 => CTR * 52..964739.43.52..3.64.29.5652743891831259647497..13527.3924...1.9.3..242.5....39 F9: 1 # 6 pairs * PAIR F8: 7,8 COL F F6: 7,8,1 # reduction candidate for 7,8 F6: 1 => CTR * 52..964739.43.52..3.64.29.5652743891831259647497..13527.3924...1.9.3..242.5....39 F6: 7,8 # 6 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-376-base-pr-000.dot * REASONING * PRF # C6: 1,7 => SOL * PRF # I4: 1,7 => SOL * DIS # I5: 7 => CTR => I5: 1,6 * DIS # F9: 7,8 => CTR => F9: 1 * DIS # F6: 1 => CTR => F6: 7,8 * CNT 5 HDP CHAINS / 32 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,C5,D4,F8,G5) * 52..964.39..3.52..3..4.29..6.2.4389.83.259.4.49....3.27.3924...1.9.3..242......39 * PAIR C5: 1,7 BLK 4 B4: 1,7,5 # reduction candidate for 1,7 B4: 1,7 # 7 pairs C6: 1,7,5 # reduction candidate for 1,7 C6: 1,7 => SOLVED * 528796413974315268316482975652143897837259146491678352763924581189537624245861739 * DURATION: 0:00:03.214843 START: 15:45:49.206105 END: 15:45:52.420948 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-376-base-pr-001.dot * REASONING * PRF # C6: 1,7 => SOL * STA C6: 1,7 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 376 solution: 528796413974315268316482975652143897837259146491678352763924581189537624245861739 info: 17695 FNBXK S8.f 41972 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 528796413974315268316482975652143897837259146491678352763924581189537624245861739 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 # B4: 1,7 => UNS * PRF # C6: 1,7 => SOL * INC # C6: 5 => UNS * INC # I5: 1,7 => UNS * INC # I5: 6 => UNS * INC # C1: 1,7 => UNS * INC # C2: 1,7 => UNS * INC # C3: 1,7 => UNS * INC # D6: 1,7 => UNS * INC # E6: 1,7 => UNS * INC # F6: 1,7 => UNS * INC # B4: 1,7 => UNS * PRF # I4: 1,7 => SOL * INC # I4: 5 => UNS * INC # D1: 1,7 => UNS * INC # D9: 1,7 => UNS * INC # I5: 1,6 => UNS * DIS # I5: 7 => CTR => I5: 1,6 * INC # G7: 1,6 => UNS * INC # G7: 5 => UNS * INC # B8: 5,6 => UNS * INC # B9: 5,6 => UNS * INC # C9: 5,6 => UNS * INC # G7: 5,6 => UNS * INC # G7: 1 => UNS * INC # D8: 7,8 => UNS * INC # D9: 7,8 => UNS * INC # E9: 7,8 => UNS * DIS # F9: 7,8 => CTR => F9: 1 * INC # F9: 1 => UNS * INC # F6: 7,8 => UNS * DIS # F6: 1 => CTR => F6: 7,8 * CNT 32 HDP CHAINS / 32 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B4: 1,7 => UNS * PRF # C6: 1,7 => SOL * STA C6: 1,7 * CNT 2 HDP CHAINS / 2 HYP OPENED