The New Sudoku Players' Forum

[jmehat]

I searched all the fully symmetric dispositions of 17 givens on a 9x9 grid, with a program I wrote, and found no valid problem : every disposition of values had more than one solution. The search used the spare cycles of half a dozen of PCs for around three month.

It is not really a proof, as the validity of my search program is unproven. I, at least, am convinced this (negative) result is exact.

My 2 c.

[tarek]

I suppose you searched through 19s & 18s prior to your 3 month search started.......

tarek

[gfroyle]

I searched all the fully symmetric dispositions of 17 givens on a 9x9 grid, with a program I wrote, and found no valid problem : every disposition of values had more than one solution. The search used the spare cycles of half a dozen of PCs for around three month.

It is not really a proof, as the validity of my search program is unproven. I, at least, am convinced this (negative) result is exact.

My 2 c.

Well done.... I am sure that you are correct...

Now for the puzzles with symmetry groups of order 4!

gordon

[claudiarabia]

....all the fully symmetric dispositions of 17 givens on a 9x9 grid,....had more than one solution. .....[/quote]

As far as I know, none of the 17ers are symmetric. The 18ers are at least rotational symmetric and only with the 19ers the full mirror-symmetry begins. So you did everything correct.

Claudia

[ab]

there are 17s with diagonal symmetry:
http://forum.enjoysudoku.com/viewtopic.php?t=3570&highlight=symmetric

[claudiarabia]

there are 17s with diagonal symmetry:
http://forum.enjoysudoku.com/viewtopic.php?t=3570&highlight=symmetric

thank you, ab