Re: Distinct distances on a chessboard

On 1 Apr 2007 07:06:09 -0700, "Andrew Usher" <k_over_hbarc@xxxxxxxxx>
wrote:

On Apr 1, 2:21 am, jankri...@xxxxxxxxxxx wrote:

I think the most interesting question would be: is there any n such
that it is possible with n points on an n by n board?

Andrew Usher

You mean, for n >= 8. It is possible for every n up to 7.

OK. I had never considered it.

I don't think it would be too hard to prove that there are no
solutions for n >= 8. For sufficiently _large_ n, we just need a
sufficient number of "distance-pair-generators" - like ((5, 0), (4,
3)) which also gives ((10, 0), (8, 6)), ((15, 0), (12, 9)) and so on.
Then we can use enumeration up to n = 13 (assuming quasi is right),

n = 15 is correct. I just checked it; for n>15 there are not enough
unique distances.

Right -- n=15 is the crossover point.

quasi
.