Minimal sudoku instances with unique solution

Daniel

Hi,

I am looking for minimal instances with respect to the given numbers which have exactly one solution:
E.g. on the web I found the following instance where only 17 numbers are given
(0 means empty field):

006 900 070
000 010 002
800 000 000

020 000 004
000 000 001
005 006 000

000 000 060
000 002 050
010 043 000

This instance has the following unique solution:
146 928 375
593 617 842
872 435 916

721 359 684
968 274 531
435 186 297

257 891 463
384 762 159
619 543 728

I can prove that there exists only this solution based on my solver in
abount 110 seconds.

Are there instances with less than 17 given numbers which have a unique solution?

Daniel

dukuso · Posted: Tue Jul 26, 2005 3:11 pm Post subject:

see here:

http://www.sudoku.com/forums/viewtopic.php?t=605&start=0

Merri · Posted: Fri Aug 12, 2005 10:57 am Post subject:

What are the minimal numbers for bigger grids? 4 x 4 and 5 x 5? With a guess, I'll throw numbers 31 and 49.

dukuso · Posted: Fri Aug 12, 2005 1:44 pm Post subject:

Moschopulus · Posted: Fri Aug 12, 2005 2:23 pm Post subject:

Here is a grid in which any puzzle requires at least 64 clues.

1234567890etabcd
et90cdab34127856
65872143badc09te
dcbate0987654321
90etabcd12345678
34127856et90cdab
badc09te65872143
87654321dcbate09
56781234abcd90et
cdabet9078563412
2143658709tebadc
te09dcba43218765
abcd90et56781234
78563412cdabet90
09tebadc21436587
43218765te09dcba

This can be partitioned into 16 4x4 sudokus.
Each of these requires 4 clues.
Maybe one of these sets of 64 clues works?

Merri · Posted: Fri Aug 12, 2005 2:37 pm Post subject:

I just tried a dumb math without any real background for it. I'll explain it anyways so a few people can have a good laugh Rolling Eyes

First I just figured out how to get 16 or 17 using simple math. Thus:
9 - 1 = 8
8 * 2 = 16 (so this would mean "not enough to have a solid solution)
8 * 8 = 64 (the number of remaining cells)
64 + 17 = 81 (when put together you get the total number of numbers)

Then basically used the same math for 16 x 16 and 25 x 25...

16 - 1 = 15
15 * 2 = 30
15 * 15 = 225
225 + 31 = 256

25 - 1 = 24
24 * 2 = 48
24 * 24 = 576
576 + 49 = 625

I just didn't think about the lowest possibilities... with 4 x 4 grid:

4 - 1 = 3
3 * 2 = 6
3 * 3 = 9
9 + 7 = 16

So... I guess 4 x 4 requires less than seven to be filled completely with one possible solution when there is a minimal case?

Moschopulus · Posted: Fri Aug 12, 2005 2:45 pm Post subject:

pseudo coup · Posted: Thu Sep 01, 2005 10:43 am Post subject: 84 clues

dukuso · Posted: Fri Sep 02, 2005 1:45 pm Post subject: Re: 84 clues

Pat · Posted: Wed Sep 06, 2006 10:37 am Post subject: re: minimum number of clues

for a box-size of 4x4,
gsf (2006.Feb.10) reports a 77-clue puzzle;

and now,