On a $9\times10$ checkerboard with $90$ squares, a game proceeds as follows:
First, you place $x$ rocks on the board. Each rock occupies a single square. No rock may touch the edge of the checkerboard. No rock may be positioned diagonally adjacent to another rock (while positioning them vertically or horizontally adjacent is allowed).
The snake chooses an empty square on the board as its starting point. It moves around by always moving to a (horizontally or vertically, but not diagonally) adjacent square. It must not visit any square twice, and it can not visit any square that is occupied by a rock.
The snake wins the game, if it manages to visit every empty square on the board exactly once. Assume that the snake is a perfect player.
What is the minimum number of rocks required to prevent the snake from winning, and how will you place them?
A harder question: What if the aim of the snake is to visit every empty square exactly twice?