AbstractWe generalize the original tennis ball problem to the case in which the number of balls received and the number of balls discarded can vary from move to move, and derive formulas solving the problem in that case. We then use these formulas to obtain new and simpler proofs of the relation between the solution to the original tennis ball problem and the Catalan numbers, as well as a considerably simpler proof for the generalization in which a fixed number
A solution to the tennis ball problem
