The difficulty of beating the Taxman

The Taxman game has proven to be hard to solve optimally, so efforts have been made to find heuristic strategies that do well in practice. We present results on the NP-hardness of a variant of the game via an equivalence to a particular kind of graph matching problem. Furthermore this equivalence is used to derive a winning strategy for all $n$ along with efficiently computable lower and upper bounds on the optimal achievable score.