8:39 PM
My idea was like that for the triangle, use them in any order (which will not matter for that result). However, even applying a retstriction that yields bounds on the general result would be welcome, e.g. says you have all but two edges specified for the d simplex, what is the probability etc.
Since someone is "listening", here is todays mathfitti. Define a move M as having two bins, each with some positive number of balls, and transferring balls from the larger quantity to the smaller quantity to double the smaller quantity, e.g. (m,n) goes to (m-n, 2n) for m at least n and n positive.
It is not too hard to show that given three bins with balls, there is a sequence of moves of type M that will empty at least one of the bins. Suppose we use moves of type N of the form (x,y,z) goes to Kx-z,y-z,3z), where we insist that the result is nonnegative. Can we empty at least one of three bins this way? Or at least one of four bins?
