A Prime Summandification of n: 11045
Manoj Prakash Singh, Richard Stong · American Mathematical Monthly · 2005
11178. Proposed by Jon Bentley and Colin Mallows, Avaya Labs, Basking Ridge, NJ. Balls are to be thrown independently into unequally likely boxes 1, 2, ... , K, with P (ball lands in box j) = qj, until n balls have been thrown. The player bets that when the next ball is thrown it will go into whichever box has received the most balls out of the first n throws. (If there are ties, she breaks the tie at random.) Prove that, whatever the values of q, ... , qk, her probability of winning is a strictly increasing function of