For any grid, x by x, figure out a formula for the greatest number of points that can be put on the inside of the grid such that no three points are colinear.
(In reply to
re(2): So at least the first 32 are reachable... by Jer)
Thanks. I already have 14 problems pending. Assuming the first one is accepted, I estimate it will be at least two weeks before it appears (and maybe 3 or 4 additional months before the fourteenth appears). This site has many talented and prolific contributors.
An easier version used for a mathematics competition at Ohio State University states:
Let T be the set {au+bv  a, b in [0,n1), u=(1,0), v=(.5,sqr(3)/2)}. Show that, given any subset A of T, with A>n(n+1)/3, some three elements of A are the vertices of an equilateral triangle.
I'll consider posting the variation as you suggest, jer. It bothers me, however, to post problems for which a solution is unknown.

Posted by McWorter
on 20050520 18:29:45 