  Given groups $A$ and $B$, what is the minimal commutator length of the 2020th
(for instance) power of an element $g\in A*B$ not conjugate to elements of the
free factors? The exhaustive answer to this question is still unknown, but we
can give an almost answer: this minimum is one of two numbers (simply depending
on $A$ and $B$). Other similar problems are also considered.
