## Minimum Clue Counts (for these cases)?

Programs which generate, solve, and analyze Sudoku puzzles

### Minimum Clue Counts (for these cases)?

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 834295617927164538763851492285349761491672385358426179642917853179538246B:586192347741863925923475618819526473634781259257349861372618594495237186168954732`

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.

Mathimagics
2017 Supporter

Posts: 1926
Joined: 27 May 2015
Location: Canberra

### Re: Minimum Clue Counts (for these cases)?

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: 132
Joined: 28 June 2011

### Re: Minimum Clue Counts (for these cases)?

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.

Mathimagics
2017 Supporter

Posts: 1926
Joined: 27 May 2015
Location: Canberra