Minimum Clue Counts (for these cases)?

Programs which generate, solve, and analyze Sudoku puzzles

Minimum Clue Counts (for these cases)?

Postby Mathimagics » Mon Mar 20, 2017 5:47 am

I would appreciate it if someone could help me identify the minimum clue counts for these two cases (standard Sudoku):
Code: Select all

A:
516783924
834295617
927164538
763851492
285349761
491672385
358426179
642917853
179538246

B:
586192347
741863925
923475618
819526473
634781259
257349861
372618594
495237186
168954732


I make it 21 in each case, but my method is rather crude, I'm hoping that somebody has better software for doing reduction testing.
User avatar
Mathimagics
2017 Supporter
 
Posts: 335
Joined: 27 May 2015

Re: Minimum Clue Counts (for these cases)?

Postby Afmob » Mon Mar 20, 2017 7:31 am

So far, I've found a valid 19 clue puzzle for each grid.
Code: Select all
586...........39...2.....1....52...3.....1.....7...8.....6.8......2.....1.....73.
5...8...4.........92..6..3......1.9..85.4.7.............8.2.......9...53.7.......

I've used the subset method described in this thread to get a rough overview on the distribution of the minimal puzzles (with regards to clue count) where I found 19 clue puzzles for grid B and 20 clue puzzles for grid A. Afterwards, I tried to hit the UA (unavoidable sets) of grid A with 19 clues and found a valid puzzle. I don't know whether they also have a valid 18 clue puzzles because I haven't found one so far. I would guess that grid B is more likely to have one.

Edit: Both grids have no valid 18 clue puzzle. Therefore 19 is indeed the minimum clue count.
Last edited by Afmob on Mon Mar 20, 2017 9:31 am, edited 1 time in total.
Afmob
 
Posts: 130
Joined: 28 June 2011

Re: Minimum Clue Counts (for these cases)?

Postby Mathimagics » Mon Mar 20, 2017 9:02 am

Thank you!

These are the orthogonal pair of grids that are the solution to the puzzle here, where the minimum clue count is now down to 23.
User avatar
Mathimagics
2017 Supporter
 
Posts: 335
Joined: 27 May 2015


Return to Software