MathDB

Let

n, b

and

c

be positive integers. A group of

n

pirates wants to fairly split their treasure. The treasure consists of

c \cdot n

identical coins distributed over

b \cdot n

bags, of which at least

n-1

bags are initially empty. Captain Jack inspects the contents of each bag and then performs a sequence of moves. In one move, he can take any number of coins from a single bag and put them into one empty bag. Prove that no matter how the coins are initially distributed, Jack can perform at most

n-1

moves and then split the bags among the pirates such that each pirate gets

b

bags and

c

coins.

Problem Statement