Analysis of xx-top500-077-base.sdk
Contents
Original Sudoku
level: medium
position: 5..1...6.....3.7..8........4..5.6....7....2.....8......32.7...........51......... initial
Autosolve
position: 5.71.28632..6387.586375.12.4..5.6937.75...2..3..8.75..1324756..7..2...51.5...1.72 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E5: 4,9 => CTR => E5: 1 * DIS # F5: 4,9 => CTR => F5: 3 * PRF # F5: 3 => SOL * DIS # B4: 2 => CTR => B4: 1,8 * DIS # C6: 1 => CTR => C6: 6,9 * DIS # E6: 1,2 => CTR => E6: 4,9 * PRF # F5: 3,9 => SOL * DIS # F5: 4 => CTR => F5: 3,9 * DIS # H5: 1,4 => CTR => H5: 8 * PRF # H5: 8 => SOL * PRF # E6: 1,4 => SOL * PRF # I5: 4,6 => SOL * DIS # I5: 8 => CTR => I5: 4,6 * PRF # C9: 6,9 => SOL * PRF # F5: 3,9 => SOL * DIS # F5: 4 => CTR => F5: 3,9 * PRF # C9: 6,8 => SOL * DIS # C9: 4,9 => CTR => C9: 6,8 * CNT 18 HDP CHAINS / 36 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E5: 4,9 => CTR => E5: 1 * DIS E5: 1 # F5: 4,9 => CTR => F5: 3 * PRF E5: 1 + F5: 3 => SOL * STA E5: 1 + F5: 3 * CNT 3 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 5..1...6.....3.7..8........4..5.6....7....2.....8......32.7...........51......... | initial |
| 5.71.28632..6387.586375.12.4..5.6937.75...2..3..8.75..1324756..7..2...51.5...1.72 | autosolve |
| 547192863291638745863754129418526937675913284329847516132475698784269351956381472 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (20) B1: 4,9 E1: 4,9 F3: 4,9 H2: 4,9 I3: 4,9 C4: 1,8 A5: 6,9 E4: 1,2 D5: 3,9 H6: 1,4 I6: 4,6 A9: 6,9 E8: 6,8 F8: 3,9 D9: 3,9 E9: 6,8 H7: 8,9 I7: 8,9 G8: 3,4 G9: 3,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,C2: 1.. / B2 = 1 => 23 pairs (_) / C2 = 1 => 22 pairs (_) H5,H6: 1.. / H5 = 1 => 0 pairs (X) / H6 = 1 => 22 pairs (_) E5,H5: 1.. / E5 = 1 => 22 pairs (_) / H5 = 1 => 0 pairs (X) B4,B6: 2.. / B4 = 2 => 0 pairs (X) / B6 = 2 => 21 pairs (_) E4,E6: 2.. / E4 = 2 => 21 pairs (_) / E6 = 2 => 0 pairs (X) B4,E4: 2.. / B4 = 2 => 0 pairs (X) / E4 = 2 => 21 pairs (_) B6,E6: 2.. / B6 = 2 => 21 pairs (_) / E6 = 2 => 0 pairs (X) D5,F5: 3.. / D5 = 3 => 0 pairs (X) / F5 = 3 => 0 pairs (_) F8,D9: 3.. / F8 = 3 => 0 pairs (X) / D9 = 3 => 0 pairs (_) G8,G9: 3.. / G8 = 3 => 0 pairs (*) / G9 = 3 => 0 pairs (X) F8,G8: 3.. / F8 = 3 => 0 pairs (X) / G8 = 3 => 0 pairs (_) D9,G9: 3.. / D9 = 3 => 0 pairs (*) / G9 = 3 => 0 pairs (X) D5,D9: 3.. / D5 = 3 => 0 pairs (X) / D9 = 3 => 0 pairs (_) F5,F8: 3.. / F5 = 3 => 0 pairs (*) / F8 = 3 => 0 pairs (X) E1,F3: 4.. / E1 = 4 => 0 pairs (X) / F3 = 4 => 0 pairs (_) H2,I3: 4.. / H2 = 4 => 0 pairs (*) / I3 = 4 => 0 pairs (X) G8,G9: 4.. / G8 = 4 => 0 pairs (X) / G9 = 4 => 0 pairs (_) B1,E1: 4.. / B1 = 4 => 0 pairs (*) / E1 = 4 => 0 pairs (X) F3,I3: 4.. / F3 = 4 => 0 pairs (*) / I3 = 4 => 0 pairs (X) C9,G9: 4.. / C9 = 4 => 0 pairs (X) / G9 = 4 => 0 pairs (_) F3,F5: 4.. / F3 = 4 => 0 pairs (*) / F5 = 4 => 0 pairs (X) A5,C6: 6.. / A5 = 6 => 0 pairs (*) / C6 = 6 => 0 pairs (X) I5,I6: 6.. / I5 = 6 => 0 pairs (X) / I6 = 6 => 0 pairs (_) E8,E9: 6.. / E8 = 6 => 18 pairs (_) / E9 = 6 => 0 pairs (X) A5,I5: 6.. / A5 = 6 => 0 pairs (*) / I5 = 6 => 0 pairs (X) C6,I6: 6.. / C6 = 6 => 0 pairs (X) / I6 = 6 => 0 pairs (_) C8,E8: 6.. / C8 = 6 => 0 pairs (X) / E8 = 6 => 18 pairs (_) A5,A9: 6.. / A5 = 6 => 0 pairs (*) / A9 = 6 => 0 pairs (X) B4,C4: 8.. / B4 = 8 => 22 pairs (_) / C4 = 8 => 20 pairs (_) H5,I5: 8.. / H5 = 8 => 0 pairs (*) / I5 = 8 => 0 pairs (X) E8,E9: 8.. / E8 = 8 => 0 pairs (X) / E9 = 8 => 18 pairs (_) H7,I7: 8.. / H7 = 8 => 0 pairs (X) / I7 = 8 => 0 pairs (_) C9,E9: 8.. / C9 = 8 => 0 pairs (X) / E9 = 8 => 18 pairs (_) B4,B8: 8.. / B4 = 8 => 22 pairs (_) / B8 = 8 => 20 pairs (_) H5,H7: 8.. / H5 = 8 => 0 pairs (*) / H7 = 8 => 0 pairs (X) I5,I7: 8.. / I5 = 8 => 0 pairs (X) / I7 = 8 => 0 pairs (_) E1,F3: 9.. / E1 = 9 => 0 pairs (*) / F3 = 9 => 0 pairs (X) H2,I3: 9.. / H2 = 9 => 0 pairs (X) / I3 = 9 => 0 pairs (_) F8,D9: 9.. / F8 = 9 => 0 pairs (*) / D9 = 9 => 0 pairs (X) H7,I7: 9.. / H7 = 9 => 0 pairs (*) / I7 = 9 => 0 pairs (X) B1,E1: 9.. / B1 = 9 => 0 pairs (X) / E1 = 9 => 0 pairs (_) F3,I3: 9.. / F3 = 9 => 0 pairs (X) / I3 = 9 => 0 pairs (_) A5,A9: 9.. / A5 = 9 => 0 pairs (X) / A9 = 9 => 0 pairs (_) D5,D9: 9.. / D5 = 9 => 0 pairs (*) / D9 = 9 => 0 pairs (X) H2,H7: 9.. / H2 = 9 => 0 pairs (X) / H7 = 9 => 0 pairs (_) I3,I7: 9.. / I3 = 9 => 0 pairs (*) / I7 = 9 => 0 pairs (X) * DURATION: 0:01:43.348916 START: 05:21:18.738353 END: 05:23:02.087269 2017-05-04 * CP COUNT: (46) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A9,B1,C4,D5,D9,E1,E4,E8,E9,F3,F8,G8,G9,H2,H6,H7,I3,I6,I7) * 5.71.28632..6387.586375.12.4..5.6937.75...2..3..8.75..1324756..7..2...51.5...1.72 * PAIR B1: 4,9 BLK 1 B2: 4,9,1 # reduction candidate for 4,9 B2: 4,9 # 22 pairs C2: 4,9,1 # reduction candidate for 4,9 C2: 4,9 # 23 pairs * PAIR B1: 4,9 COL B B8: 4,9,8 # reduction candidate for 4,9 B8: 4,9 # 22 pairs B8: 8 # 20 pairs * PAIR E1: 4,9 COL E E5: 4,9,1 # reduction candidate for 4,9 E5: 4,9 => CTR * 5.71.28632..6387958637591244..5.6937675..42183..8.75461324756897..2.345195...1.72 E5: 1 # 22 pairs E6: 4,9,1,2 # reduction candidate for 4,9 E6: 4,9 # 22 pairs * PAIR F3: 4,9 COL F F5: 4,9,3 # reduction candidate for 4,9 F5: 4,9 => CTR * 5.71.28632..6387.586375.12.4..5.69379753.42.63.68975.41324756.87..263451654981372 F5: 3 => SOLVED * 547192863291638745863754129418526937675913284329847516132475698784269351956381472 * PAIR H2: 4,9 ROW 2 B2: 4,9,1 # reduction candidate for 4,9 B2: 4,9 # 22 pairs C2: 4,9,1 # reduction candidate for 4,9 C2: 4,9 # 23 pairs * PAIR C4: 1,8 BLK 4 B4: 1,8,2 # reduction candidate for 1,8 B4: 2 => CTR * 5.71.28632..638795863759124428516937675.942183..82754613247568978.26..51.56.81472 B4: 1,8 # 21 pairs * PAIR A5: 6,9 BLK 4 C6: 6,9,1 # reduction candidate for 6,9 C6: 1 => CTR * 5471928632196387.586375.12.4..5.6937675...2..3918275461324756..7..2...5195.3.1472 C6: 6,9 # 22 pairs * PAIR E4: 1,2 BLK 5 E6: 1,2,4,9 # reduction candidate for 1,2 E6: 1,2 => CTR * 5.71.28632..6387.586375.12.4..5.6937675...2.83..8.75.61324756897..2.935195.3.1472 E6: 4,9 # 22 pairs * PAIR E4: 1,2 ROW 4 B4: 1,2,8 # reduction candidate for 1,2 B4: 8 # 22 pairs B4: 1,2 # 20 pairs * PAIR D5: 3,9 BLK 5 F5: 3,9,4 # reduction candidate for 3,9 F5: 3,9 => SOLVED * 547192863291638745863754129418526937675913284329847516132475698784269351956381472 F5: 4 => CTR * 5.71428632416387958637591244.85.693797531428.3..8.75..1324756..7..2.3451.54981372 * PAIR H6: 1,4 BLK 6 H5: 1,4,8 # reduction candidate for 1,4 H5: 1,4 => CTR * 5.71.28632..6387958637591244..5.6937675..42183..8.75461324756897..2.345195...1.72 H5: 8 => SOLVED * 547192863291638745863754129418526937675913284329847516132475698784269351956381472 * PAIR H6: 1,4 ROW 6 E6: 1,4,2,9 # reduction candidate for 1,4 E6: 1,4 => SOLVED * 547192863291638745863754129418526937675913284329847516132475698784269351956381472 E6: 2,9 # 23 pairs * PAIR I6: 4,6 BLK 6 I5: 4,6,8 # reduction candidate for 4,6 I5: 4,6 => SOLVED * 547192863291638745863754129418526937675913284329847516132475698784269351956381472 I5: 8 => CTR * 5.71.28632..63879586375912.4..5.6937675...2.83..8.75.61324756897..2...5195.3.1472 * PAIR A9: 6,9 BLK 7 C8: 6,9,4,8 # reduction candidate for 6,9 C8: 6,9 # 23 pairs C9: 6,9,4,8 # reduction candidate for 6,9 C9: 6,9 => SOLVED * 547192863291638745863754129418526937675913284329847516132475698784269351956381472 C9: 4,8 # 21 pairs * PAIR E8: 6,8 ROW 8 C8: 6,8,4,9 # reduction candidate for 6,8 C8: 6,8 # 22 pairs C8: 4,9 # 20 pairs * PAIR F8: 3,9 COL F F5: 3,9,4 # reduction candidate for 3,9 F5: 3,9 => SOLVED * 547192863291638745863754129418526937675913284329847516132475698784269351956381472 F5: 4 => CTR * 5.71428632416387958637591244.85.693797531428.3..8.75..1324756..7..2.3451.54981372 * PAIR E9: 6,8 ROW 9 C9: 6,8,4,9 # reduction candidate for 6,8 C9: 6,8 => SOLVED * 547192863291638745863754129418526937675913284329847516132475698784269351956381472 C9: 4,9 => CTR * 5.71.28632..6387.586375.12.4..5.69379753.42.63.68975.41324756.87..263451654981372 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-077-base-pr-000.dot * REASONING * DIS # E5: 4,9 => CTR => E5: 1 * DIS # F5: 4,9 => CTR => F5: 3 * PRF # F5: 3 => SOL * DIS # B4: 2 => CTR => B4: 1,8 * DIS # C6: 1 => CTR => C6: 6,9 * DIS # E6: 1,2 => CTR => E6: 4,9 * PRF # F5: 3,9 => SOL * DIS # F5: 4 => CTR => F5: 3,9 * DIS # H5: 1,4 => CTR => H5: 8 * PRF # H5: 8 => SOL * PRF # E6: 1,4 => SOL * PRF # I5: 4,6 => SOL * DIS # I5: 8 => CTR => I5: 4,6 * PRF # C9: 6,9 => SOL * PRF # F5: 3,9 => SOL * DIS # F5: 4 => CTR => F5: 3,9 * PRF # C9: 6,8 => SOL * DIS # C9: 4,9 => CTR => C9: 6,8 * CNT 18 HDP CHAINS / 36 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A9,B1,C4,D5,D9,E1,E4,E8,E9,F3,F8,G8,G9,H2,H6,H7,I3,I6,I7) * 5.71.28632..6387.586375.12.4..5.6937.75...2..3..8.75..1324756..7..2...51.5...1.72 * PAIR B1: 4,9 BLK 1 B2: 4,9,1 # reduction candidate for 4,9 B2: 4,9 # 22 pairs C2: 4,9,1 # reduction candidate for 4,9 C2: 4,9 # 23 pairs * PAIR B1: 4,9 COL B B8: 4,9,8 # reduction candidate for 4,9 B8: 4,9 # 22 pairs B8: 8 # 20 pairs * PAIR E1: 4,9 COL E E5: 4,9,1 # reduction candidate for 4,9 E5: 4,9 => CTR * 5.71.28632..6387958637591244..5.6937675..42183..8.75461324756897..2.345195...1.72 * RESTART * PAIR RESTART * PAIR F3: 4,9 COL F F5: 4,9,3 # reduction candidate for 4,9 F5: 4,9 => CTR * 5.71.28632..6387.586375.12.4..5269379753142863268975141324756987..263451654981372 F5: 3 => SOLVED * 547192863291638745863754129418526937675913284329847516132475698784269351956381472 * DURATION: 0:00:09.898850 START: 05:23:50.182456 END: 05:24:00.081306 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-077-base-pr-001.dot * REASONING * DIS # E5: 4,9 => CTR => E5: 1 * DIS E5: 1 # F5: 4,9 => CTR => F5: 3 * PRF E5: 1 + F5: 3 => SOL * STA E5: 1 + F5: 3 * CNT 3 HDP CHAINS / 6 HYP OPENED
Header Info
Top 500 Minimum 17 077 solution: 547192863291638745863754129418526937675913284329847516132475698784269351956381472 info: 1498 FNBHWXY S8.f 32683 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 547192863291638745863754129418526937675913284329847516132475698784269351956381472 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 # B2: 4,9 => UNS * INC # C2: 4,9 => UNS * INC # B8: 4,9 => UNS * INC # B8: 8 => UNS * DIS # E5: 4,9 => CTR => E5: 1 * INC # E5: 1 => UNS * INC # E6: 4,9 => UNS * DIS # F5: 4,9 => CTR => F5: 3 * PRF # F5: 3 => SOL * INC # B2: 4,9 => UNS * INC # C2: 4,9 => UNS * INC # B4: 1,8 => UNS * DIS # B4: 2 => CTR => B4: 1,8 * INC # C6: 6,9 => UNS * DIS # C6: 1 => CTR => C6: 6,9 * DIS # E6: 1,2 => CTR => E6: 4,9 * INC # E6: 4,9 => UNS * INC # B4: 1,2 => UNS * INC # B4: 8 => UNS * PRF # F5: 3,9 => SOL * DIS # F5: 4 => CTR => F5: 3,9 * DIS # H5: 1,4 => CTR => H5: 8 * PRF # H5: 8 => SOL * PRF # E6: 1,4 => SOL * INC # E6: 2,9 => UNS * PRF # I5: 4,6 => SOL * DIS # I5: 8 => CTR => I5: 4,6 * INC # C8: 6,9 => UNS * PRF # C9: 6,9 => SOL * INC # C9: 4,8 => UNS * INC # C8: 6,8 => UNS * INC # C8: 4,9 => UNS * PRF # F5: 3,9 => SOL * DIS # F5: 4 => CTR => F5: 3,9 * PRF # C9: 6,8 => SOL * DIS # C9: 4,9 => CTR => C9: 6,8 * CNT 36 HDP CHAINS / 36 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 4,9 => UNS * INC # C2: 4,9 => UNS * INC # B8: 4,9 => UNS * INC # B8: 8 => UNS * DIS # E5: 4,9 => CTR => E5: 1 * DIS E5: 1 # F5: 4,9 => CTR => F5: 3 * PRF E5: 1 + F5: 3 => SOL * STA E5: 1 + F5: 3 * CNT 7 HDP CHAINS / 6 HYP OPENED