Question 39
Let $n$ be a positive integer. An $n$-level honeycomb is a plane region covered with regular hexagons of side-length $1$ connected along edges, such that the centres of the boundary hexagons are lined up along a regular hexagon of side-length $n\sqrt{3}$. The diagram shows a $2$-level honeycomb from which the central hexagon has been removed.
A trex is a sequence of $3$ hexagons with collinear centres such that the middle hexagon shares an edge with each of its neighbours in the trex.
An $n$-level honeycomb from which the central size-$1$ hexagon has been removed is to be completely covered by trexes without any overlaps. Find all values of $n$ for which this is possible.
A trex is a sequence of $3$ hexagons with collinear centres such that the middle hexagon shares an edge with each of its neighbours in the trex.
An $n$-level honeycomb from which the central size-$1$ hexagon has been removed is to be completely covered by trexes without any overlaps. Find all values of $n$ for which this is possible.