Analysis of xx-top500-145-base.sdk
Contents
Original Sudoku
level: medium
position: .4.....1..5.2.....6....3.....8...7........6.2.1..4....5...1....4.....3.....6..... initial
Autosolve
position: .42.6.5131532.4..668.15342.3685..741..4381652215746.3.53641.2..4.1...36582.6351.4 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F1: 7,9 => CTR => F1: 8 * PRF # F1: 8 => SOL * PRF # F1: 8,9 => SOL * DIS # F1: 7 => CTR => F1: 8,9 * DIS # F1: 7,9 => CTR => F1: 8 * PRF # F1: 8 => SOL * PRF # H2: 8 => SOL * DIS # E8: 7,9 => CTR => E8: 2 * PRF # E8: 2 => SOL * PRF # H2: 8,9 => SOL * DIS # H2: 7 => CTR => H2: 8,9 * PRF # H2: 8 => SOL * PRF # I7: 8 => SOL * PRF # E8: 2,9 => SOL * DIS # E8: 7 => CTR => E8: 2,9 * DIS # F8: 2,9 => CTR => F8: 7,8 * PRF # F8: 7,8 => SOL * PRF # I7: 8,9 => SOL * DIS # I7: 7 => CTR => I7: 8,9 * DIS # E8: 7,9 => CTR => E8: 2 * PRF # E8: 2 => SOL * PRF # F8: 7,9 => SOL * DIS # E8: 7,9 => CTR => E8: 2 * PRF # E8: 2 => SOL * PRF # F8: 7,9 => SOL * PRF # H7: 7,9 => SOL * DIS # F1: 7,9 => CTR => F1: 8 * PRF # F1: 8 => SOL * DIS # F8: 8,9 => CTR => F8: 2,7 * PRF # F8: 2,7 => SOL * PRF # H7: 7,9 => SOL * PRF # H2: 8 => SOL * CNT 32 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:
* DIS # F1: 7,9 => CTR => F1: 8 * PRF F1: 8 => SOL * STA F1: 8 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .4.....1..5.2.....6....3.....8...7........6.2.1..4....5...1....4.....3.....6..... | initial |
| .42.6.5131532.4..668.15342.3685..741..4381652215746.3.53641.2..4.1...36582.6351.4 | autosolve |
| 742968513153274986689153427368592741974381652215746839536419278491827365827635194 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) A1: 7,9 C3: 7,9 D1: 8,9 E2: 7,9 G2: 8,9 I3: 7,9 A5: 7,9 B5: 7,9 E4: 2,9 F4: 2,9 G6: 8,9 I6: 8,9 B8: 7,9 C9: 7,9 F7: 7,9 D8: 8,9 H9: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E4,F4: 2.. / E4 = 2 => 0 pairs (X) / F4 = 2 => 0 pairs (_) E8,F8: 2.. / E8 = 2 => 0 pairs (*) / F8 = 2 => 0 pairs (X) E4,E8: 2.. / E4 = 2 => 0 pairs (X) / E8 = 2 => 0 pairs (_) F4,F8: 2.. / F4 = 2 => 0 pairs (*) / F8 = 2 => 0 pairs (X) A1,C3: 7.. / A1 = 7 => 0 pairs (*) / C3 = 7 => 0 pairs (X) F1,E2: 7.. / F1 = 7 => 0 pairs (X) / E2 = 7 => 0 pairs (_) H2,I3: 7.. / H2 = 7 => 0 pairs (X) / I3 = 7 => 0 pairs (_) A5,B5: 7.. / A5 = 7 => 0 pairs (X) / B5 = 7 => 0 pairs (_) B8,C9: 7.. / B8 = 7 => 0 pairs (X) / C9 = 7 => 0 pairs (_) A1,F1: 7.. / A1 = 7 => 0 pairs (*) / F1 = 7 => 0 pairs (X) E2,H2: 7.. / E2 = 7 => 0 pairs (*) / H2 = 7 => 0 pairs (X) C3,I3: 7.. / C3 = 7 => 0 pairs (X) / I3 = 7 => 0 pairs (_) C9,H9: 7.. / C9 = 7 => 0 pairs (*) / H9 = 7 => 0 pairs (X) A1,A5: 7.. / A1 = 7 => 0 pairs (*) / A5 = 7 => 0 pairs (X) B5,B8: 7.. / B5 = 7 => 0 pairs (*) / B8 = 7 => 0 pairs (X) C3,C9: 7.. / C3 = 7 => 0 pairs (X) / C9 = 7 => 0 pairs (_) E2,E8: 7.. / E2 = 7 => 0 pairs (*) / E8 = 7 => 0 pairs (X) I3,I7: 7.. / I3 = 7 => 0 pairs (*) / I7 = 7 => 0 pairs (X) D1,F1: 8.. / D1 = 8 => 0 pairs (X) / F1 = 8 => 0 pairs (_) G2,H2: 8.. / G2 = 8 => 16 pairs (_) / H2 = 8 => 0 pairs (*) G6,I6: 8.. / G6 = 8 => 0 pairs (*) / I6 = 8 => 0 pairs (X) D8,F8: 8.. / D8 = 8 => 0 pairs (*) / F8 = 8 => 0 pairs (X) H7,I7: 8.. / H7 = 8 => 16 pairs (_) / I7 = 8 => 0 pairs (*) D1,D8: 8.. / D1 = 8 => 0 pairs (X) / D8 = 8 => 0 pairs (_) F1,F8: 8.. / F1 = 8 => 0 pairs (*) / F8 = 8 => 0 pairs (X) G2,G6: 8.. / G2 = 8 => 16 pairs (_) / G6 = 8 => 0 pairs (*) H2,H7: 8.. / H2 = 8 => 0 pairs (*) / H7 = 8 => 0 pairs (X) I6,I7: 8.. / I6 = 8 => 16 pairs (_) / I7 = 8 => 0 pairs (*) A1,C3: 9.. / A1 = 9 => 0 pairs (X) / C3 = 9 => 0 pairs (_) A5,B5: 9.. / A5 = 9 => 0 pairs (*) / B5 = 9 => 0 pairs (X) E4,F4: 9.. / E4 = 9 => 0 pairs (*) / F4 = 9 => 0 pairs (X) G6,I6: 9.. / G6 = 9 => 16 pairs (_) / I6 = 9 => 0 pairs (*) B8,C9: 9.. / B8 = 9 => 0 pairs (*) / C9 = 9 => 0 pairs (X) C3,I3: 9.. / C3 = 9 => 0 pairs (*) / I3 = 9 => 0 pairs (X) C9,H9: 9.. / C9 = 9 => 0 pairs (X) / H9 = 9 => 0 pairs (_) A1,A5: 9.. / A1 = 9 => 0 pairs (X) / A5 = 9 => 0 pairs (_) B5,B8: 9.. / B5 = 9 => 0 pairs (X) / B8 = 9 => 0 pairs (_) C3,C9: 9.. / C3 = 9 => 0 pairs (*) / C9 = 9 => 0 pairs (X) D1,D8: 9.. / D1 = 9 => 0 pairs (*) / D8 = 9 => 0 pairs (X) G2,G6: 9.. / G2 = 9 => 0 pairs (*) / G6 = 9 => 0 pairs (X) * DURATION: 0:01:07.775160 START: 07:41:30.451670 END: 07:42:38.226830 2017-05-04 * CP COUNT: (40) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A5,B5,B8,C3,C9,D1,D8,E2,E4,F4,F7,G2,G6,H9,I3,I6) * .42.6.5131532.4..668.15342.3685..741..4381652215746.3.53641.2..4.1...36582.6351.4 * PAIR A1: 7,9 ROW 1 F1: 7,9,8 # reduction candidate for 7,9 F1: 7,9 => CTR * .4286.5131532.4..668.15342.3685..741..4381652215746.3.53641.2..4.19.8365829635174 F1: 8 => SOLVED * 742968513153274986689153427368592741974381652215746839536419278491827365827635194 * PAIR D1: 8,9 BLK 2 F1: 8,9,7 # reduction candidate for 8,9 F1: 8,9 => SOLVED * 742968513153274986689153427368592741974381652215746839536419278491827365827635194 F1: 7 => CTR * .42867513153294876687153429368529741..4381652215746.3.53641.2..4.1...36582.6351.4 * PAIR E2: 7,9 BLK 2 F1: 7,9,8 # reduction candidate for 7,9 F1: 7,9 => CTR * .4286.5131532.4..668.15342.3685..741..4381652215746.3.53641.2..4.19.8365829635174 F1: 8 => SOLVED * 742968513153274986689153427368592741974381652215746839536419278491827365827635194 * PAIR E2: 7,9 ROW 2 H2: 7,9,8 # reduction candidate for 7,9 H2: 8 => SOLVED * 742968513153274986689153427368592741974381652215746839536419278491827365827635194 H2: 7,9 # 16 pairs * PAIR E2: 7,9 COL E E8: 7,9,2 # reduction candidate for 7,9 E8: 7,9 => CTR * .42.6.5131532.4..668.15342.368529741..4381652215746.3.5364172..471.92365829635174 E8: 2 => SOLVED * 742968513153274986689153427368592741974381652215746839536419278491827365827635194 * PAIR G2: 8,9 BLK 3 H2: 8,9,7 # reduction candidate for 8,9 H2: 8,9 => SOLVED * 742968513153274986689153427368592741974381652215746839536419278491827365827635194 H2: 7 => CTR * .42.6.5131532.48766871534293685..74179438165221574693853641.287471...3658296351.4 * PAIR I3: 7,9 BLK 3 H2: 7,9,8 # reduction candidate for 7,9 H2: 8 => SOLVED * 742968513153274986689153427368592741974381652215746839536419278491827365827635194 H2: 7,9 # 16 pairs * PAIR I3: 7,9 COL I I7: 7,9,8 # reduction candidate for 7,9 I7: 8 => SOLVED * 742968513153274986689153427368592741974381652215746839536419278491827365827635194 I7: 7,9 # 16 pairs * PAIR E4: 2,9 COL E E8: 2,9,7 # reduction candidate for 2,9 E8: 2,9 => SOLVED * 742968513153274986689153427368592741974381652215746839536419278491827365827635194 E8: 7 => CTR * .42.6.5131532.4..668.15342.368529741..4381652215746.3.5364172..4.1...36582.6351.4 * PAIR F4: 2,9 COL F F8: 2,9,7,8 # reduction candidate for 2,9 F8: 2,9 => CTR * .42.68513153274..668.1534273685..741..4381652215746.3.5364172..4718..3658296351.4 F8: 7,8 => SOLVED * 742968513153274986689153427368592741974381652215746839536419278491827365827635194 * PAIR I6: 8,9 COL I I7: 8,9,7 # reduction candidate for 8,9 I7: 8,9 => SOLVED * 742968513153274986689153427368592741974381652215746839536419278491827365827635194 I7: 7 => CTR * .42.6.5131532.4..668.15342.3685..741..4381652215746.3853641.2874.1...365827635194 * PAIR B8: 7,9 ROW 8 E8: 7,9,2 # reduction candidate for 7,9 E8: 7,9 => CTR * .42.6.5131532.4..668.15342.368529741..4381652215746.3.5364172..471.92365829635174 E8: 2 => SOLVED * 742968513153274986689153427368592741974381652215746839536419278491827365827635194 F8: 7,9,2,8 # reduction candidate for 7,9 F8: 7,9 => SOLVED * 742968513153274986689153427368592741974381652215746839536419278491827365827635194 F8: 2,8 # 18 pairs * PAIR F7: 7,9 BLK 8 E8: 7,9,2 # reduction candidate for 7,9 E8: 7,9 => CTR * .42.6.5131532.4..668.15342.368529741..4381652215746.3.5364172..471.92365829635174 E8: 2 => SOLVED * 742968513153274986689153427368592741974381652215746839536419278491827365827635194 F8: 7,9,2,8 # reduction candidate for 7,9 F8: 7,9 => SOLVED * 742968513153274986689153427368592741974381652215746839536419278491827365827635194 F8: 2,8 # 18 pairs * PAIR F7: 7,9 ROW 7 H7: 7,9,8 # reduction candidate for 7,9 H7: 7,9 => SOLVED * 742968513153274986689153427368592741974381652215746839536419278491827365827635194 H7: 8 # 16 pairs I7: 7,9,8 # reduction candidate for 7,9 I7: 7,9 # 16 pairs * PAIR F7: 7,9 COL F F1: 7,9,8 # reduction candidate for 7,9 F1: 7,9 => CTR * .4286.5131532.4..668.15342.3685..741..4381652215746.3.53641.2..4.19.8365829635174 F1: 8 => SOLVED * 742968513153274986689153427368592741974381652215746839536419278491827365827635194 * PAIR D8: 8,9 BLK 8 F8: 8,9,2,7 # reduction candidate for 8,9 F8: 8,9 => CTR * .42.6.513153274..668.153427368592741..4381652215746.3.5364172..471.2.3658296351.4 F8: 2,7 => SOLVED * 742968513153274986689153427368592741974381652215746839536419278491827365827635194 * PAIR H9: 7,9 BLK 9 H7: 7,9,8 # reduction candidate for 7,9 H7: 7,9 => SOLVED * 742968513153274986689153427368592741974381652215746839536419278491827365827635194 H7: 8 # 16 pairs I7: 7,9,8 # reduction candidate for 7,9 I7: 7,9 # 16 pairs * PAIR H9: 7,9 COL H H2: 7,9,8 # reduction candidate for 7,9 H2: 8 => SOLVED * 742968513153274986689153427368592741974381652215746839536419278491827365827635194 H2: 7,9 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-145-base-pr-000.dot * REASONING * DIS # F1: 7,9 => CTR => F1: 8 * PRF # F1: 8 => SOL * PRF # F1: 8,9 => SOL * DIS # F1: 7 => CTR => F1: 8,9 * DIS # F1: 7,9 => CTR => F1: 8 * PRF # F1: 8 => SOL * PRF # H2: 8 => SOL * DIS # E8: 7,9 => CTR => E8: 2 * PRF # E8: 2 => SOL * PRF # H2: 8,9 => SOL * DIS # H2: 7 => CTR => H2: 8,9 * PRF # H2: 8 => SOL * PRF # I7: 8 => SOL * PRF # E8: 2,9 => SOL * DIS # E8: 7 => CTR => E8: 2,9 * DIS # F8: 2,9 => CTR => F8: 7,8 * PRF # F8: 7,8 => SOL * PRF # I7: 8,9 => SOL * DIS # I7: 7 => CTR => I7: 8,9 * DIS # E8: 7,9 => CTR => E8: 2 * PRF # E8: 2 => SOL * PRF # F8: 7,9 => SOL * DIS # E8: 7,9 => CTR => E8: 2 * PRF # E8: 2 => SOL * PRF # F8: 7,9 => SOL * PRF # H7: 7,9 => SOL * DIS # F1: 7,9 => CTR => F1: 8 * PRF # F1: 8 => SOL * DIS # F8: 8,9 => CTR => F8: 2,7 * PRF # F8: 2,7 => SOL * PRF # H7: 7,9 => SOL * PRF # H2: 8 => SOL * CNT 32 HDP CHAINS / 42 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A5,B5,B8,C3,C9,D1,D8,E2,E4,F4,F7,G2,G6,H9,I3,I6) * .42.6.5131532.4..668.15342.3685..741..4381652215746.3.53641.2..4.1...36582.6351.4 * PAIR A1: 7,9 ROW 1 F1: 7,9,8 # reduction candidate for 7,9 F1: 7,9 => CTR * .4286.5131532.4..668.15342.3685..741..4381652215746.3.53641.2..4.19.8365829635174 F1: 8 => SOLVED * 742968513153274986689153427368592741974381652215746839536419278491827365827635194 * DURATION: 0:00:02.853795 START: 07:43:28.163567 END: 07:43:31.017362 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-145-base-pr-001.dot * REASONING * DIS # F1: 7,9 => CTR => F1: 8 * PRF F1: 8 => SOL * STA F1: 8 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 145 solution: 742968513153274986689153427368592741974381652215746839536419278491827365827635194 info: 1814 FNBWX S8.f 46625 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 742968513153274986689153427368592741974381652215746839536419278491827365827635194 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:
* DIS # F1: 7,9 => CTR => F1: 8 * PRF # F1: 8 => SOL * PRF # F1: 8,9 => SOL * DIS # F1: 7 => CTR => F1: 8,9 * DIS # F1: 7,9 => CTR => F1: 8 * PRF # F1: 8 => SOL * INC # H2: 7,9 => UNS * PRF # H2: 8 => SOL * DIS # E8: 7,9 => CTR => E8: 2 * PRF # E8: 2 => SOL * PRF # H2: 8,9 => SOL * DIS # H2: 7 => CTR => H2: 8,9 * INC # H2: 7,9 => UNS * PRF # H2: 8 => SOL * INC # I7: 7,9 => UNS * PRF # I7: 8 => SOL * PRF # E8: 2,9 => SOL * DIS # E8: 7 => CTR => E8: 2,9 * DIS # F8: 2,9 => CTR => F8: 7,8 * PRF # F8: 7,8 => SOL * PRF # I7: 8,9 => SOL * DIS # I7: 7 => CTR => I7: 8,9 * DIS # E8: 7,9 => CTR => E8: 2 * PRF # E8: 2 => SOL * PRF # F8: 7,9 => SOL * INC # F8: 2,8 => UNS * DIS # E8: 7,9 => CTR => E8: 2 * PRF # E8: 2 => SOL * PRF # F8: 7,9 => SOL * INC # F8: 2,8 => UNS * PRF # H7: 7,9 => SOL * INC # H7: 8 => UNS * INC # I7: 7,9 => UNS * DIS # F1: 7,9 => CTR => F1: 8 * PRF # F1: 8 => SOL * DIS # F8: 8,9 => CTR => F8: 2,7 * PRF # F8: 2,7 => SOL * PRF # H7: 7,9 => SOL * INC # H7: 8 => UNS * INC # I7: 7,9 => UNS * INC # H2: 7,9 => UNS * PRF # H2: 8 => SOL * CNT 42 HDP CHAINS / 42 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # F1: 7,9 => CTR => F1: 8 * PRF F1: 8 => SOL * STA F1: 8 * CNT 2 HDP CHAINS / 1 HYP OPENED