3 problems

Let $(a,b,c)$ be the side lengths of the triangular tile, and say that a positive real number $X$ is equiconstructible by $(a,b,c)$ when an equilateral triangle with side length…

Let $T_6(n)$ denote the maximum number of equilateral triangles determined by a set of $n$ points in $\mathbb{R}^6$. Erdős's conjecture. Any set of $n$ points in $\mathbb{R}^6$ can…

Triangular-row conjecture. For most $n$, there is an optimal configuration with $N$ rows. The $j$th row has $j$ points for $j\leq J$. If $n>N(N+1)/2$, the rows with $j>J$ each have…