Analysis of xx-top500-253-base.sdk
Contents
Original Sudoku
level: medium
position: 2...1..........4.3......5....53.7.........26..........82.....7....5...1.6..4..... initial
Autosolve
position: 243.157.651.7..4237.62..5.1965327148.3..5.26...2...35.824....753..5.2.1465147..32 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F2: 8,9 => CTR => F2: 6 * DIS # F2: 8,9 => CTR => F2: 6 * PRF # D6: 8,9 => SOL * PRF # E6: 6,8 => SOL * DIS # F2: 8,9 => CTR => F2: 6 * CNT 5 HDP CHAINS / 23 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F2: 8,9 => CTR => F2: 6 * PRF F2: 6 # D6: 8,9 => SOL * STA F2: 6 + D6: 8,9 * CNT 2 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 2...1..........4.3......5....53.7.........26..........82.....7....5...1.6..4..... | initial |
| 243.157.651.7..4237.62..5.1965327148.3..5.26...2...35.824....753..5.2.1465147..32 | autosolve |
| 243815796518796423796243581965327148437158269182964357824631975379582614651479832 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (20) C2: 8,9 B3: 8,9 D1: 8,9 E3: 3,4 F3: 3,4 H1: 8,9 H3: 8,9 A5: 1,4 C5: 7,8 A6: 1,4 B6: 7,8 I5: 7,9 I6: 7,9 B8: 7,9 C8: 7,9 E8: 6,8 F9: 8,9 G7: 6,9 G8: 6,8 G9: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A5,A6: 1.. / A5 = 1 => 20 pairs (_) / A6 = 1 => 18 pairs (_) D7,F7: 1.. / D7 = 1 => 22 pairs (_) / F7 = 1 => 19 pairs (_) E3,F3: 3.. / E3 = 3 => 20 pairs (_) / F3 = 3 => 18 pairs (_) E7,F7: 3.. / E7 = 3 => 18 pairs (_) / F7 = 3 => 20 pairs (_) E3,E7: 3.. / E3 = 3 => 20 pairs (_) / E7 = 3 => 18 pairs (_) F3,F7: 3.. / F3 = 3 => 18 pairs (_) / F7 = 3 => 20 pairs (_) E3,F3: 4.. / E3 = 4 => 18 pairs (_) / F3 = 4 => 20 pairs (_) A5,A6: 4.. / A5 = 4 => 18 pairs (_) / A6 = 4 => 20 pairs (_) A5,F5: 4.. / A5 = 4 => 18 pairs (_) / F5 = 4 => 20 pairs (_) E3,E6: 4.. / E3 = 4 => 18 pairs (_) / E6 = 4 => 20 pairs (_) E2,F2: 6.. / E2 = 6 => 0 pairs (X) / F2 = 6 => 21 pairs (_) G7,G8: 6.. / G7 = 6 => 18 pairs (_) / G8 = 6 => 19 pairs (_) E8,G8: 6.. / E8 = 6 => 18 pairs (_) / G8 = 6 => 19 pairs (_) D6,D7: 6.. / D6 = 6 => 21 pairs (_) / D7 = 6 => 17 pairs (_) C5,B6: 7.. / C5 = 7 => 0 pairs (*) / B6 = 7 => 0 pairs (X) I5,I6: 7.. / I5 = 7 => 0 pairs (X) / I6 = 7 => 0 pairs (_) B8,C8: 7.. / B8 = 7 => 0 pairs (*) / C8 = 7 => 0 pairs (X) C5,I5: 7.. / C5 = 7 => 0 pairs (*) / I5 = 7 => 0 pairs (X) B6,I6: 7.. / B6 = 7 => 0 pairs (X) / I6 = 7 => 0 pairs (_) B6,B8: 7.. / B6 = 7 => 0 pairs (X) / B8 = 7 => 0 pairs (_) C5,C8: 7.. / C5 = 7 => 0 pairs (*) / C8 = 7 => 0 pairs (X) C2,B3: 8.. / C2 = 8 => 0 pairs (*) / B3 = 8 => 0 pairs (X) H1,H3: 8.. / H1 = 8 => 0 pairs (X) / H3 = 8 => 0 pairs (_) C5,B6: 8.. / C5 = 8 => 0 pairs (X) / B6 = 8 => 0 pairs (_) E8,F9: 8.. / E8 = 8 => 19 pairs (_) / F9 = 8 => 18 pairs (_) G8,G9: 8.. / G8 = 8 => 18 pairs (_) / G9 = 8 => 19 pairs (_) D1,H1: 8.. / D1 = 8 => 0 pairs (*) / H1 = 8 => 0 pairs (X) B3,H3: 8.. / B3 = 8 => 0 pairs (X) / H3 = 8 => 0 pairs (_) E8,G8: 8.. / E8 = 8 => 19 pairs (_) / G8 = 8 => 18 pairs (_) F9,G9: 8.. / F9 = 8 => 18 pairs (_) / G9 = 8 => 19 pairs (_) B3,B6: 8.. / B3 = 8 => 0 pairs (X) / B6 = 8 => 0 pairs (_) C2,C5: 8.. / C2 = 8 => 0 pairs (*) / C5 = 8 => 0 pairs (X) C2,B3: 9.. / C2 = 9 => 0 pairs (X) / B3 = 9 => 0 pairs (_) H1,H3: 9.. / H1 = 9 => 0 pairs (*) / H3 = 9 => 0 pairs (X) I5,I6: 9.. / I5 = 9 => 0 pairs (*) / I6 = 9 => 0 pairs (X) B8,C8: 9.. / B8 = 9 => 0 pairs (X) / C8 = 9 => 0 pairs (_) G7,G9: 9.. / G7 = 9 => 19 pairs (_) / G9 = 9 => 18 pairs (_) D1,H1: 9.. / D1 = 9 => 0 pairs (X) / H1 = 9 => 0 pairs (_) B3,H3: 9.. / B3 = 9 => 0 pairs (*) / H3 = 9 => 0 pairs (X) F9,G9: 9.. / F9 = 9 => 19 pairs (_) / G9 = 9 => 18 pairs (_) B3,B8: 9.. / B3 = 9 => 0 pairs (*) / B8 = 9 => 0 pairs (X) C2,C8: 9.. / C2 = 9 => 0 pairs (X) / C8 = 9 => 0 pairs (_) * DURATION: 0:01:15.425976 START: 11:25:54.914978 END: 11:27:10.340954 2017-05-04 * CP COUNT: (42) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B3,B6,B8,C2,C5,C8,D1,E3,E8,F3,F9,G7,G8,G9,H1,H3,I5,I6) * 243.157.651.7..4237.62..5.1965327148.3..5.26...2...35.824....753..5.2.1465147..32 * PAIR C2: 8,9 ROW 2 E2: 8,9,6 # reduction candidate for 8,9 E2: 8,9 # 21 pairs F2: 8,9,6 # reduction candidate for 8,9 F2: 8,9 => CTR * 2439157865197684237862..591965327148.3815.26...2...35.824....753..582614651479832 F2: 6 # 21 pairs * PAIR D1: 8,9 BLK 2 E2: 8,9,6 # reduction candidate for 8,9 E2: 8,9 # 21 pairs F2: 8,9,6 # reduction candidate for 8,9 F2: 8,9 => CTR * 2439157865197684237862..591965327148.3815.26...2...35.824....753..582614651479832 F2: 6 # 21 pairs * PAIR D1: 8,9 COL D D5: 8,9,1 # reduction candidate for 8,9 D5: 8,9 # 24 pairs D6: 8,9,1,6 # reduction candidate for 8,9 D6: 8,9 => SOLVED * 243815796518796423796243581965327148437158269182964357824631975379582614651479832 D6: 1,6 # 21 pairs * PAIR A5: 1,4 ROW 5 F5: 1,4,8,9 # reduction candidate for 1,4 F5: 1,4 # 24 pairs F5: 8,9 # 19 pairs * PAIR A6: 1,4 ROW 6 F6: 1,4,6,8,9 # reduction candidate for 1,4 F6: 6,8,9 # 25 pairs F6: 1,4 # 19 pairs * PAIR E8: 6,8 COL E E2: 6,8,9 # reduction candidate for 6,8 E2: 6,8 # 23 pairs E6: 6,8,4,9 # reduction candidate for 6,8 E6: 6,8 => SOLVED * 243815796518796423796243581965327148437158269182964357824631975379582614651479832 E6: 4,9 # 21 pairs * PAIR F9: 8,9 COL F F2: 8,9,6 # reduction candidate for 8,9 F2: 8,9 => CTR * 2439157865197684237862..591965327148.3815.26...2...35.824....753..582614651479832 F2: 6 # 21 pairs F5: 8,9,1,4 # reduction candidate for 8,9 F5: 8,9 # 19 pairs F6: 8,9,1,4,6 # reduction candidate for 8,9 F6: 8,9 # 28 pairs * PAIR G7: 6,9 ROW 7 D7: 6,9,1 # reduction candidate for 6,9 D7: 6,9 # 19 pairs E7: 6,9,3 # reduction candidate for 6,9 E7: 6,9 # 20 pairs F7: 6,9,1,3 # reduction candidate for 6,9 F7: 6,9 # 24 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-253-base-pr-000.dot * REASONING * DIS # F2: 8,9 => CTR => F2: 6 * DIS # F2: 8,9 => CTR => F2: 6 * PRF # D6: 8,9 => SOL * PRF # E6: 6,8 => SOL * DIS # F2: 8,9 => CTR => F2: 6 * CNT 5 HDP CHAINS / 23 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B3,B6,B8,C2,C5,C8,D1,E3,E8,F3,F9,G7,G8,G9,H1,H3,I5,I6) * 243.157.651.7..4237.62..5.1965327148.3..5.26...2...35.824....753..5.2.1465147..32 * PAIR C2: 8,9 ROW 2 E2: 8,9,6 # reduction candidate for 8,9 E2: 8,9 # 21 pairs F2: 8,9,6 # reduction candidate for 8,9 F2: 8,9 => CTR * 2439157865197684237862..591965327148.3815.26...2...35.824....753..582614651479832 * RESTART * PAIR RESTART * PAIR D1: 8,9 COL D D5: 8,9,1 # reduction candidate for 8,9 D5: 8,9 # 25 pairs D6: 8,9,1,6 # reduction candidate for 8,9 D6: 8,9 => SOLVED * 243815796518796423796243581965327148437158269182964357824631975379582614651479832 * DURATION: 0:00:05.069310 START: 11:27:33.707905 END: 11:27:38.777215 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-253-base-pr-001.dot * REASONING * DIS # F2: 8,9 => CTR => F2: 6 * PRF F2: 6 # D6: 8,9 => SOL * STA F2: 6 + D6: 8,9 * CNT 2 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 253 solution: 243815796518796423796243581965327148437158269182964357824631975379582614651479832 info: 2076 FNBTWXY S8.f 27267 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 243815796518796423796243581965327148437158269182964357824631975379582614651479832 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 # E2: 8,9 => UNS * DIS # F2: 8,9 => CTR => F2: 6 * INC # F2: 6 => UNS * INC # E2: 8,9 => UNS * DIS # F2: 8,9 => CTR => F2: 6 * INC # F2: 6 => UNS * INC # D5: 8,9 => UNS * PRF # D6: 8,9 => SOL * INC # D6: 1,6 => UNS * INC # F5: 1,4 => UNS * INC # F5: 8,9 => UNS * INC # F6: 1,4 => UNS * INC # F6: 6,8,9 => UNS * INC # E2: 6,8 => UNS * PRF # E6: 6,8 => SOL * INC # E6: 4,9 => UNS * DIS # F2: 8,9 => CTR => F2: 6 * INC # F2: 6 => UNS * INC # F5: 8,9 => UNS * INC # F6: 8,9 => UNS * INC # D7: 6,9 => UNS * INC # E7: 6,9 => UNS * INC # F7: 6,9 => UNS * CNT 23 HDP CHAINS / 23 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E2: 8,9 => UNS * DIS # F2: 8,9 => CTR => F2: 6 * INC F2: 6 # D5: 8,9 => UNS * PRF F2: 6 # D6: 8,9 => SOL * STA F2: 6 + D6: 8,9 * CNT 4 HDP CHAINS / 4 HYP OPENED