Say you have a grid of 16x16 squares. Label them A through P and 1 through 16.
Now say that at H8 there's a mouse that moves at 1 slot every turn. Also, you get to block a tile every turn.
Say the mouse gets to move first; can you, with perfect play by both you and the mouse, completely box the mouse in, before it escapes the board? If so, how, and how many turns will it take? If not, explain why.
BONUS: What is the smallest square board size (1x1, 2x2, 3x3, 4x4, 5x5, 6x6, etc.) for which this is possible? What's the largest that's impossible? You may assume the rules above apply, except the one about the mouse starting at H8; the mouse begins as close to the center as possible.