Something that's bugged me for a long time is this:
How many paths, starting at the origin, taking N steps either up, down, left or right, end up at a particular place (x, y)? Ignoring the fact that x+y has to have the same parity as N, something that goes like e- k(x2 + y2), right? Just central-limit-type reasoning ought to suffice to see that.
(
Read more... )