4 problems

Odd-tiling conjecture. There are no such tilings with $N$ odd.

Let $T(n,k)$ be the largest number of points in an $n$ by $k$ regular grid such that no three selected points form an isosceles triangle of nonzero area. Three-column exact-value c…

Let $T(n,k)$ be the largest number of points in an $n$ by $k$ regular grid such that no three selected points form an isosceles triangle of nonzero area. Even-grid upper-bound conj…

Consider an $n$ by $k$ rectangular regular grid with $n,k2$, and let $a_n(k)$ denote the number of isosceles triangles of nonzero area in the grid. Sloane's recurrence conjecture.…