Analysis of xx-top500-205-base.sdk
Contents
Original Sudoku
level: medium
position: .8....2......43......17....7......3....6..8....1.......6.2..5..3......74......... initial
Autosolve
position: .8....2.....843......172...7..4...3....6..8....1.......6.2..5..3......74......... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # F9: 5,9 => SOL * CNT 1 HDP CHAINS / 13 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # F9: 5,9 => SOL * STA F9: 5,9 * CNT 1 HDP CHAINS / 10 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .8....2......43......17....7......3....6..8....1.......6.2..5..3......74......... | initial |
| .8....2.....843......172...7..4...3....6..8....1.......6.2..5..3......74......... | autosolve |
| 483956217172843965956172483798425136235617849641398752867234591329581674514769328 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) A1: 1,4 C1: 3,7 D1: 5,9 H1: 1,4 I1: 3,7 C4: 6,8 A6: 6,8 D6: 3,7 D8: 5,9 D9: 3,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,H1: 1.. / A1 = 1 => 0 pairs (X) / H1 = 1 => 11 pairs (_) B8,C8: 2.. / B8 = 2 => 13 pairs (_) / C8 = 2 => 10 pairs (_) H9,I9: 2.. / H9 = 2 => 10 pairs (_) / I9 = 2 => 10 pairs (_) A2,A5: 2.. / A2 = 2 => 10 pairs (_) / A5 = 2 => 13 pairs (_) C1,I1: 3.. / C1 = 3 => 0 pairs (*) / I1 = 3 => 0 pairs (X) E7,I7: 3.. / E7 = 3 => 0 pairs (*) / I7 = 3 => 0 pairs (X) D6,D9: 3.. / D6 = 3 => 0 pairs (*) / D9 = 3 => 0 pairs (X) G3,G9: 3.. / G3 = 3 => 0 pairs (X) / G9 = 3 => 0 pairs (_) F7,F9: 4.. / F7 = 4 => 0 pairs (*) / F9 = 4 => 0 pairs (X) A1,H1: 4.. / A1 = 4 => 11 pairs (_) / H1 = 4 => 0 pairs (X) G3,G6: 4.. / G3 = 4 => 0 pairs (*) / G6 = 4 => 0 pairs (X) D1,D8: 5.. / D1 = 5 => 11 pairs (_) / D8 = 5 => 10 pairs (_) E1,F1: 6.. / E1 = 6 => 11 pairs (_) / F1 = 6 => 11 pairs (_) C4,A6: 6.. / C4 = 6 => 9 pairs (_) / A6 = 6 => 8 pairs (_) C1,I1: 7.. / C1 = 7 => 0 pairs (X) / I1 = 7 => 0 pairs (_) F5,I5: 7.. / F5 = 7 => 0 pairs (*) / I5 = 7 => 0 pairs (X) C7,F7: 7.. / C7 = 7 => 0 pairs (*) / F7 = 7 => 0 pairs (X) B2,B9: 7.. / B2 = 7 => 0 pairs (*) / B9 = 7 => 0 pairs (X) D6,D9: 7.. / D6 = 7 => 0 pairs (X) / D9 = 7 => 0 pairs (_) G2,G6: 7.. / G2 = 7 => 0 pairs (X) / G6 = 7 => 0 pairs (_) H3,I3: 8.. / H3 = 8 => 11 pairs (_) / I3 = 8 => 10 pairs (_) C4,A6: 8.. / C4 = 8 => 8 pairs (_) / A6 = 8 => 9 pairs (_) D1,D8: 9.. / D1 = 9 => 10 pairs (_) / D8 = 9 => 11 pairs (_) * DURATION: 0:00:34.244141 START: 09:48:44.945202 END: 09:49:19.189343 2017-05-04 * CP COUNT: (23) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,C1,C4,D1,D6,D8,D9,H1,I1) * .8....2.....843......172...7..4...3....6..8....1.......6.2..5..3......74......... * PAIR A1: 1,4 COL A A7: 1,4,8,9 # reduction candidate for 1,4 A7: 1,4 # 11 pairs A9: 1,4,5,8,9 # reduction candidate for 1,4 A9: 1,4 # 14 pairs * PAIR D1: 5,9 BLK 2 E1: 5,9,6 # reduction candidate for 5,9 E1: 5,9 # 11 pairs F1: 5,9,6 # reduction candidate for 5,9 F1: 5,9 # 11 pairs * PAIR H1: 1,4 COL H H5: 1,4,2,5,9 # reduction candidate for 1,4 H5: 1,4 # 12 pairs H5: 2,5,9 # 10 pairs * PAIR D8: 5,9 BLK 8 E8: 5,9,1,6,8 # reduction candidate for 5,9 E8: 5,9 # 14 pairs F8: 5,9,1,6,8 # reduction candidate for 5,9 F8: 5,9 # 14 pairs E9: 5,9,1,3,6,8 # reduction candidate for 5,9 E9: 5,9 # 11 pairs F9: 5,9,1,4,6,7,8 # reduction candidate for 5,9 F9: 5,9 => SOLVED * 483956217172843965956172483798425136235617849641398752867234591329581674514769328 F9: 1,4,6,7,8 # 10 pairs * PAIR D8: 5,9 ROW 8 B8: 5,9,1,2 # reduction candidate for 5,9 B8: 5,9 # 14 pairs C8: 5,9,2,8 # reduction candidate for 5,9 C8: 5,9 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-205-base-pr-000.dot * REASONING * PRF # F9: 5,9 => SOL * CNT 1 HDP CHAINS / 13 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,C1,C4,D1,D6,D8,D9,H1,I1) * .8....2.....843......172...7..4...3....6..8....1.......6.2..5..3......74......... * PAIR A1: 1,4 COL A A7: 1,4,8,9 # reduction candidate for 1,4 A7: 1,4 # 11 pairs A9: 1,4,5,8,9 # reduction candidate for 1,4 A9: 1,4 # 14 pairs * PAIR D1: 5,9 BLK 2 E1: 5,9,6 # reduction candidate for 5,9 E1: 5,9 # 11 pairs F1: 5,9,6 # reduction candidate for 5,9 F1: 5,9 # 11 pairs * PAIR H1: 1,4 COL H H5: 1,4,2,5,9 # reduction candidate for 1,4 H5: 1,4 # 12 pairs H5: 2,5,9 # 10 pairs * PAIR D8: 5,9 BLK 8 E8: 5,9,1,6,8 # reduction candidate for 5,9 E8: 5,9 # 14 pairs F8: 5,9,1,6,8 # reduction candidate for 5,9 F8: 5,9 # 14 pairs E9: 5,9,1,3,6,8 # reduction candidate for 5,9 E9: 5,9 # 11 pairs F9: 5,9,1,4,6,7,8 # reduction candidate for 5,9 F9: 5,9 => SOLVED * 483956217172843965956172483798425136235617849641398752867234591329581674514769328 * DURATION: 0:00:09.209552 START: 09:49:30.009846 END: 09:49:39.219398 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-205-base-pr-001.dot * REASONING * PRF # F9: 5,9 => SOL * STA F9: 5,9 * CNT 1 HDP CHAINS / 10 HYP OPENED
Header Info
Top 500 Minimum 17 205 solution: 483956217172843965956172483798425136235617849641398752867234591329581674514769328 info: 1894 FNBTHWY S8.f 23368 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 483956217172843965956172483798425136235617849641398752867234591329581674514769328 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 # A7: 1,4 => UNS * INC # A9: 1,4 => UNS * INC # E1: 5,9 => UNS * INC # F1: 5,9 => UNS * INC # H5: 1,4 => UNS * INC # H5: 2,5,9 => UNS * INC # E8: 5,9 => UNS * INC # F8: 5,9 => UNS * INC # E9: 5,9 => UNS * PRF # F9: 5,9 => SOL * INC # F9: 1,4,6,7,8 => UNS * INC # B8: 5,9 => UNS * INC # C8: 5,9 => UNS * CNT 13 HDP CHAINS / 13 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A7: 1,4 => UNS * INC # A9: 1,4 => UNS * INC # E1: 5,9 => UNS * INC # F1: 5,9 => UNS * INC # H5: 1,4 => UNS * INC # H5: 2,5,9 => UNS * INC # E8: 5,9 => UNS * INC # F8: 5,9 => UNS * INC # E9: 5,9 => UNS * PRF # F9: 5,9 => SOL * STA F9: 5,9 * CNT 10 HDP CHAINS / 10 HYP OPENED