I like your idea mathsy!
Seems like one piece Hits another piece and Pushes it!
The puzzle involves a chessboard that contains:
-One white piece
-One black king
-Some other black pieces
The white piece moves around the board capturing things, and acquiring the properties of whatever it has just captured. It wants to capture the black king.
One puzzle might look like this:
Here the solution would be to capture the bishop, then the rook and finally the king.
Here's a (hopefully) harder one: