If $n>2$ is a positive integer, compute \[\max_{1\leqslant k\leqslant n}\max_{n_1+...+n_k=n} \binom{n_1}{2}\binom{n_2}{2}\ldots\binom{n_k}{2}.\] Ioan Tomescu
Source: Romanian TST 1979 Day 1 P6
Tags: algebra, binomial coefficients
If $n>2$ is a positive integer, compute \[\max_{1\leqslant k\leqslant n}\max_{n_1+...+n_k=n} \binom{n_1}{2}\binom{n_2}{2}\ldots\binom{n_k}{2}.\] Ioan Tomescu