Ping Pong Simulation

You're going to program a simulation of the following game. Like many probability games, this one involves an infinite supply of ping-pong balls. No, this game is "not quite beer pong."

The balls are numbered 1 through N. There is also a group of N cups, labeled 1 through N, each of which can hold an unlimited number of ping-pong balls (a;ll numbered 1 through N). The game is played in rounds. A round is composed of two phases: throwing and pruning.

• During the throwing phase, the player takes balls randomly, one at a time, from the infinite supply and tosses them at the cups creating a stack of balls in each cup. The throwing phase is over when each cup contains at least one ping-pong ball.
• Next comes the pruning phase. During this phase the player goes through all the balls in each cup and removes any ball whose number does not match the containing cup.

Every ball drawn has a uniformly random number, every ball lands in a uniformly random cup, and every throw lands in some cup. The game is over when, after a round is completed, there are no empty cups.

At the end of the simulation you will print the following:

• How many rounds would you expect to need to play to finish this game?
• How many balls did you draw and throw to finish this game?
• Sort the cups in descending order by the number of balls they hold.