## Minimum number of Clues for Jigsaw Sudoku

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Minimum number of Clues for Jigsaw Sudoku

Despite the fact that I have a topic about jigsaw sudoku, I am posting this question here, because I know that the best math people are sort of glued to this forum.

We have a hunch, but no proof regarding the minimum number of clues for a classic sudoku. I can't find anything about minimum clues for a jigsaw. This depends on the pattern, of course.

Does anybody know what the best pattern is to generate low-clue jigsaws and what the minimum number of clues are for certain patterns? Has any research been done in this area?

This is what triggered my question. A 15-clue jigsaw, which is solved with singles and a few LoL eliminations.

Code: Select all
`.---------------.---.---------------.| .   .   .   . | . | .   .   9   . ||       .-------'   '---.           || 7   . | .   .   .   3 | .   .   . ||       |---.   .---.   '---.---.   || .   . | . | . | . | 8   . | . | 1 ||   .---'   '---:   |   .---'   |   || . | .   .   . | . | . | 1   . | 3 |:---'   .-------'   '---'---.   '---:| .   . | .   .   6   .   . | .   . |:---.   '---.---.   .-------'   .---:| 3 | .   5 | . | . | .   .   . | . ||   |   .---'   |   |---.   .---'   || 4 | . | .   1 | . | . | . | .   . ||   '---'---.   '---'   '---:       || .   .   . | 4   .   .   . | .   8 ||           '---.   .-------'       || .   9   .   . | . | .   .   .   . |'---------------'---'---------------'`

I was amazed that the same number of constraints could result in less clues required.

Any thoughts on this?

Ruud.
Ruud

Posts: 664
Joined: 28 October 2005

Eight clues is the minimum required given for 9x9 jigsaw.

See: http://www.bumblebeagle.org/dusumoh/9x9/index.html

If some type of symmetry is required -- either for the clues, the jigsaw or both -- it may very well increase this minimum.
tso

Posts: 798
Joined: 22 June 2005