I've got a problem I'd like to solve and I haven't done any probability in years. Here's the problem. There are two M*M grids of squares. An N*N mask is placed randomly on the second grid, such that it covers at least one square, but up to N*N squares. (i.e, the majority of the mask may lie outside the grid) If the covered squares are then copied into the corresponding squares in the first grid, then n is the average number of times I will have to perform this step to have covered at least 50% of the first grid with squares from the second grid. What is n in terms of N and M? M > N > 0 I don't even know where to begin. Taking repeating squares into account seems especially difficult. Anyone have any tips for this?