For which values of $n$ can we tile some rectangle with one copy of each free simply-connected $n$-omino (that is, each polyomino with $n$ squares that has no holes)? It appears that it is possible for $n=1$ (trivial), $n=2$ (trivial), $n=5$ (see here), and $n=7$ (see here); and impossible for $n...

A posted answer to this earlier question of mine caused me to think that I had not asked the particular question that I actually wondered about, so that will appear here. A nonempty proper initial segment of $\mathbb Q,$ is a set $A$ satisfying $A\subseteq\mathbb Q,$ and $A\ne\varnothing,$ and $...