What is the maximum number of unordered tupels of 2 points in finite subsets (with n elements for future reference) of $\mathbb{R}^d$ that have distance 1 to eachother; in other words, $m=\max_{A\subset\mathbb{R}^d,|A|=n} |\{\{x,y\}\subset A \mid \|x-y\|=1\}|$
Obviously, $m\le \frac{n^2-n}{2}$, for this is when every point in A has distance 1 to any other point in A. This is only achieved for $n\lt d$; To what value can the upper bound be set for $n\ge d$? There will always be such a set A for which the maximum is achieved, how is such a solution constructed?