Consider the following chess variant: before each of White's moves, Black chooses one move which White is not allowed to make.
(The rules for which positions constitute checkmate are unchanged - Black can't nullify a checkmate by "vetoing" the move where White takes Black's king.)
Suppose Black has a lone king. What is the minimum amount of material White needs to guarantee a win? Assume that the white pieces start on the first rank, and the black king starts on e5.
Let's say that quantity of material is defined by adding up the classic point values of White's pieces: Q=9, R=5, B=3, N=3. White isn't allowed any pawns. And of course White always has a king.
Full disclosure: I don't know the answer to this puzzle.