Analysis of xx-top500-027-base.sdk
Contents
Original Sudoku
level: medium
position: 8.....3.5....67......4......7..1..6.5.....8............6.3.5.....2....1....8..... initial
Autosolve
position: 846192375.3.56748.7.5483..6.73.185645...3.8..68..5..3.168375.4.352.4.718497821653 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C5: 1,9 => SOL * DIS # G3: 1,2 => CTR => G3: 9 * PRF # G3: 9 => SOL * DIS # G3: 1,2 => CTR => G3: 9 * PRF # G3: 9 => SOL * DIS # I5: 1,2 => CTR => I5: 7,9 * PRF # I6: 1,2 => SOL * PRF # G3: 2,9 => SOL * DIS # G3: 1 => CTR => G3: 2,9 * DIS # I5: 1,2 => CTR => I5: 7,9 * DIS # D5: 2,9 => CTR => D5: 6,7 * PRF # F5: 4,9 => SOL * DIS # C6: 1 => CTR => C6: 4,9 * DIS # I5: 2,9 => CTR => I5: 1,7 * DIS # G6: 2,9 => CTR => G6: 1 * PRF # G6: 1 => SOL * PRF # I6: 2,9 => SOL * DIS # D5: 2,9 => CTR => D5: 6,7 * PRF # D5: 6,9 => SOL * PRF # F5: 4 => SOL * PRF # G3: 2,9 => SOL * DIS # G3: 1 => CTR => G3: 2,9 * DIS # G6: 2,9 => CTR => G6: 1 * PRF # G6: 1 => SOL * DIS # I5: 2,9 => CTR => I5: 1,7 * PRF # I6: 2,9 => SOL * CNT 26 HDP CHAINS / 42 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C5: 1,9 => SOL * STA C5: 1,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 8.....3.5....67......4......7..1..6.5.....8............6.3.5.....2....1....8..... | initial |
| 846192375.3.56748.7.5483..6.73.185645...3.8..68..5..3.168375.4.352.4.718497821653 | autosolve |
| 846192375239567481715483926973218564521634897684759132168375249352946718497821653 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) A2: 2,9 C2: 1,9 B3: 1,2 I2: 1,2 H3: 2,9 A4: 2,9 B5: 1,2 D4: 2,9 F6: 4,9 H5: 2,9 D8: 6,9 F8: 6,9 G7: 2,9 I7: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,B3: 1.. / C2 = 1 => 0 pairs (X) / B3 = 1 => 0 pairs (_) I2,G3: 1.. / I2 = 1 => 0 pairs (*) / G3 = 1 => 0 pairs (X) C2,I2: 1.. / C2 = 1 => 0 pairs (X) / I2 = 1 => 0 pairs (_) B3,G3: 1.. / B3 = 1 => 0 pairs (*) / G3 = 1 => 0 pairs (X) B3,B5: 1.. / B3 = 1 => 0 pairs (*) / B5 = 1 => 0 pairs (X) G3,G6: 1.. / G3 = 1 => 0 pairs (X) / G6 = 1 => 0 pairs (_) A2,B3: 2.. / A2 = 2 => 0 pairs (*) / B3 = 2 => 0 pairs (X) A4,B5: 2.. / A4 = 2 => 0 pairs (X) / B5 = 2 => 0 pairs (_) G7,I7: 2.. / G7 = 2 => 16 pairs (_) / I7 = 2 => 0 pairs (X) A2,I2: 2.. / A2 = 2 => 0 pairs (*) / I2 = 2 => 0 pairs (X) A4,D4: 2.. / A4 = 2 => 0 pairs (X) / D4 = 2 => 0 pairs (_) A2,A4: 2.. / A2 = 2 => 0 pairs (*) / A4 = 2 => 0 pairs (X) B3,B5: 2.. / B3 = 2 => 0 pairs (X) / B5 = 2 => 0 pairs (_) H3,H5: 2.. / H3 = 2 => 0 pairs (*) / H5 = 2 => 0 pairs (X) C5,C6: 4.. / C5 = 4 => 15 pairs (_) / C6 = 4 => 0 pairs (*) F5,F6: 4.. / F5 = 4 => 0 pairs (*) / F6 = 4 => 0 pairs (X) C5,F5: 4.. / C5 = 4 => 15 pairs (_) / F5 = 4 => 0 pairs (*) C6,F6: 4.. / C6 = 4 => 0 pairs (*) / F6 = 4 => 0 pairs (X) D5,F5: 6.. / D5 = 6 => 0 pairs (*) / F5 = 6 => 0 pairs (X) D8,F8: 6.. / D8 = 6 => 12 pairs (_) / F8 = 6 => 0 pairs (*) D5,D8: 6.. / D5 = 6 => 0 pairs (*) / D8 = 6 => 0 pairs (X) F5,F8: 6.. / F5 = 6 => 12 pairs (_) / F8 = 6 => 0 pairs (*) D5,D6: 7.. / D5 = 7 => 14 pairs (_) / D6 = 7 => 0 pairs (*) I5,I6: 7.. / I5 = 7 => 0 pairs (*) / I6 = 7 => 0 pairs (X) D5,I5: 7.. / D5 = 7 => 14 pairs (_) / I5 = 7 => 0 pairs (*) D6,I6: 7.. / D6 = 7 => 0 pairs (*) / I6 = 7 => 0 pairs (X) A2,C2: 9.. / A2 = 9 => 0 pairs (X) / C2 = 9 => 0 pairs (_) G3,H3: 9.. / G3 = 9 => 0 pairs (*) / H3 = 9 => 0 pairs (X) D8,F8: 9.. / D8 = 9 => 0 pairs (*) / F8 = 9 => 0 pairs (X) G7,I7: 9.. / G7 = 9 => 0 pairs (X) / I7 = 9 => 16 pairs (_) A4,D4: 9.. / A4 = 9 => 0 pairs (*) / D4 = 9 => 0 pairs (X) A2,A4: 9.. / A2 = 9 => 0 pairs (X) / A4 = 9 => 0 pairs (_) H3,H5: 9.. / H3 = 9 => 0 pairs (X) / H5 = 9 => 0 pairs (_) * DURATION: 0:01:05.472914 START: 03:31:55.763773 END: 03:33:01.236687 2017-05-04 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,B3,B5,C2,D4,D8,F6,F8,G7,H3,H5,I2,I7) * 846192375.3.56748.7.5483..6.73.185645...3.8..68..5..3.168375.4.352.4.718497821653 * PAIR C2: 1,9 COL C C5: 1,9,4 # reduction candidate for 1,9 C5: 1,9 => SOLVED * 846192375239567481715483926973218564521634897684759132168375249352946718497821653 C5: 4 # 15 pairs C6: 1,9,4 # reduction candidate for 1,9 C6: 1,9 # 15 pairs * PAIR B3: 1,2 ROW 3 G3: 1,2,9 # reduction candidate for 1,2 G3: 1,2 => CTR * 846192375.3.56748.72548319627391856451.73682968.25..37168375.4.352.4.718497821653 G3: 9 => SOLVED * 846192375239567481715483926973218564521634897684759132168375249352946718497821653 * PAIR I2: 1,2 BLK 3 G3: 1,2,9 # reduction candidate for 1,2 G3: 1,2 => CTR * 846192375.3.56748.72548319627391856451.73682968.25..37168375.4.352.4.718497821653 G3: 9 => SOLVED * 846192375239567481715483926973218564521634897684759132168375249352946718497821653 * PAIR I2: 1,2 COL I I5: 1,2,7,9 # reduction candidate for 1,2 I5: 1,2 => CTR * 846192375.3.56748.7.5483926.73.1856452473689168..54.37168375249352649718497821653 I5: 7,9 # 20 pairs I6: 1,2,7,9 # reduction candidate for 1,2 I6: 1,2 => SOLVED * 846192375239567481715483926973218564521634897684759132168375249352946718497821653 I6: 7,9 # 15 pairs * PAIR H3: 2,9 BLK 3 G3: 2,9,1 # reduction candidate for 2,9 G3: 2,9 => SOLVED * 846192375239567481715483926973218564521634897684759132168375249352946718497821653 G3: 1 => CTR * 846192375.3.56748.7.5483196.73.1856451..3.82.68.25.93.168375.4.352.4.718497821653 * PAIR B5: 1,2 ROW 5 I5: 1,2,7,9 # reduction candidate for 1,2 I5: 1,2 => CTR * 846192375.3.56748.7.5483926.73.1856452473689168..54.37168375249352649718497821653 I5: 7,9 # 20 pairs * PAIR D4: 2,9 BLK 5 D5: 2,9,6,7 # reduction candidate for 2,9 D5: 2,9 => CTR * 846192375.3.56748.7.5483..6.73.18564514.368.7689754.3.168375.49352649718497821653 D5: 6,7 # 15 pairs D6: 2,9,7 # reduction candidate for 2,9 D6: 2,9 # 14 pairs * PAIR F6: 4,9 BLK 5 F5: 4,9,6 # reduction candidate for 4,9 F5: 4,9 => SOLVED * 846192375239567481715483926973218564521634897684759132168375249352946718497821653 F5: 6 # 12 pairs * PAIR F6: 4,9 ROW 6 C6: 4,9,1 # reduction candidate for 4,9 C6: 1 => CTR * 846192375.39567481715483..6973218564524.3.897681.54.3.168375.4.352.4.718497821653 C6: 4,9 # 19 pairs * PAIR H5: 2,9 BLK 6 I5: 2,9,1,7 # reduction candidate for 2,9 I5: 2,9 => CTR * 846192375.3.567481715483..6.73.1856452.7368..68..54.37168375.4.352649718497821653 I5: 1,7 # 15 pairs G6: 2,9,1 # reduction candidate for 2,9 G6: 2,9 => CTR * 846192375.3.56748.7.5483196.73.1856451..3.82.68.25.93.168375.4.352.4.718497821653 G6: 1 => SOLVED * 846192375239567481715483926973218564521634897684759132168375249352946718497821653 I6: 2,9,1,7 # reduction candidate for 2,9 I6: 2,9 => SOLVED * 846192375239567481715483926973218564521634897684759132168375249352946718497821653 I6: 1,7 # 15 pairs * PAIR H5: 2,9 ROW 5 D5: 2,9,6,7 # reduction candidate for 2,9 D5: 2,9 => CTR * 846192375.3.56748.7.5483..6.73.18564514.368.7689754.3.168375.49352649718497821653 D5: 6,7 # 15 pairs * PAIR D8: 6,9 COL D D5: 6,9,2,7 # reduction candidate for 6,9 D5: 6,9 => SOLVED * 846192375239567481715483926973218564521634897684759132168375249352946718497821653 D5: 2,7 # 14 pairs * PAIR F8: 6,9 COL F F5: 6,9,4 # reduction candidate for 6,9 F5: 4 => SOLVED * 846192375239567481715483926973218564521634897684759132168375249352946718497821653 F5: 6,9 # 15 pairs * PAIR G7: 2,9 COL G G3: 2,9,1 # reduction candidate for 2,9 G3: 2,9 => SOLVED * 846192375239567481715483926973218564521634897684759132168375249352946718497821653 G3: 1 => CTR * 846192375.3.56748.7.5483196.73.1856451..3.82.68.25.93.168375.4.352.4.718497821653 G6: 2,9,1 # reduction candidate for 2,9 G6: 2,9 => CTR * 846192375.3.56748.7.5483196.73.1856451..3.82.68.25.93.168375.4.352.4.718497821653 G6: 1 => SOLVED * 846192375239567481715483926973218564521634897684759132168375249352946718497821653 * PAIR I7: 2,9 COL I I5: 2,9,1,7 # reduction candidate for 2,9 I5: 2,9 => CTR * 846192375.3.567481715483..6.73.1856452.7368..68..54.37168375.4.352649718497821653 I5: 1,7 # 15 pairs I6: 2,9,1,7 # reduction candidate for 2,9 I6: 2,9 => SOLVED * 846192375239567481715483926973218564521634897684759132168375249352946718497821653 I6: 1,7 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-027-base-pr-000.dot * REASONING * PRF # C5: 1,9 => SOL * DIS # G3: 1,2 => CTR => G3: 9 * PRF # G3: 9 => SOL * DIS # G3: 1,2 => CTR => G3: 9 * PRF # G3: 9 => SOL * DIS # I5: 1,2 => CTR => I5: 7,9 * PRF # I6: 1,2 => SOL * PRF # G3: 2,9 => SOL * DIS # G3: 1 => CTR => G3: 2,9 * DIS # I5: 1,2 => CTR => I5: 7,9 * DIS # D5: 2,9 => CTR => D5: 6,7 * PRF # F5: 4,9 => SOL * DIS # C6: 1 => CTR => C6: 4,9 * DIS # I5: 2,9 => CTR => I5: 1,7 * DIS # G6: 2,9 => CTR => G6: 1 * PRF # G6: 1 => SOL * PRF # I6: 2,9 => SOL * DIS # D5: 2,9 => CTR => D5: 6,7 * PRF # D5: 6,9 => SOL * PRF # F5: 4 => SOL * PRF # G3: 2,9 => SOL * DIS # G3: 1 => CTR => G3: 2,9 * DIS # G6: 2,9 => CTR => G6: 1 * PRF # G6: 1 => SOL * DIS # I5: 2,9 => CTR => I5: 1,7 * PRF # I6: 2,9 => SOL * CNT 26 HDP CHAINS / 42 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,B3,B5,C2,D4,D8,F6,F8,G7,H3,H5,I2,I7) * 846192375.3.56748.7.5483..6.73.185645...3.8..68..5..3.168375.4.352.4.718497821653 * PAIR C2: 1,9 COL C C5: 1,9,4 # reduction candidate for 1,9 C5: 1,9 => SOLVED * 846192375239567481715483926973218564521634897684759132168375249352946718497821653 * DURATION: 0:00:02.186436 START: 03:33:54.399244 END: 03:33:56.585680 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-027-base-pr-001.dot * REASONING * PRF # C5: 1,9 => SOL * STA C5: 1,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 027 solution: 846192375239567481715483926973218564521634897684759132168375249352946718497821653 info: 1323 FNBTWXY S8.f 38008 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 846192375239567481715483926973218564521634897684759132168375249352946718497821653 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 # C5: 1,9 => SOL * INC # C5: 4 => UNS * INC # C6: 1,9 => UNS * DIS # G3: 1,2 => CTR => G3: 9 * PRF # G3: 9 => SOL * DIS # G3: 1,2 => CTR => G3: 9 * PRF # G3: 9 => SOL * DIS # I5: 1,2 => CTR => I5: 7,9 * INC # I5: 7,9 => UNS * PRF # I6: 1,2 => SOL * INC # I6: 7,9 => UNS * PRF # G3: 2,9 => SOL * DIS # G3: 1 => CTR => G3: 2,9 * DIS # I5: 1,2 => CTR => I5: 7,9 * INC # I5: 7,9 => UNS * DIS # D5: 2,9 => CTR => D5: 6,7 * INC # D5: 6,7 => UNS * INC # D6: 2,9 => UNS * PRF # F5: 4,9 => SOL * INC # F5: 6 => UNS * INC # C6: 4,9 => UNS * DIS # C6: 1 => CTR => C6: 4,9 * DIS # I5: 2,9 => CTR => I5: 1,7 * INC # I5: 1,7 => UNS * DIS # G6: 2,9 => CTR => G6: 1 * PRF # G6: 1 => SOL * PRF # I6: 2,9 => SOL * INC # I6: 1,7 => UNS * DIS # D5: 2,9 => CTR => D5: 6,7 * INC # D5: 6,7 => UNS * PRF # D5: 6,9 => SOL * INC # D5: 2,7 => UNS * INC # F5: 6,9 => UNS * PRF # F5: 4 => SOL * PRF # G3: 2,9 => SOL * DIS # G3: 1 => CTR => G3: 2,9 * DIS # G6: 2,9 => CTR => G6: 1 * PRF # G6: 1 => SOL * DIS # I5: 2,9 => CTR => I5: 1,7 * INC # I5: 1,7 => UNS * PRF # I6: 2,9 => SOL * INC # I6: 1,7 => UNS * CNT 42 HDP CHAINS / 42 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C5: 1,9 => SOL * STA C5: 1,9 * CNT 1 HDP CHAINS / 1 HYP OPENED