06/04/2020 (2011: National Sprint Round, Problem 9)

Q: A pile of marbles has 15^5 + 3 marbles. It can be divided into 7 piles with the same number of marbles in each pile. If there are x marbles left over (0 ≤ x < 7), what is the value of x?

A: 4

We use modulus (which, when expressed as "a mod b" is basically finding the remainder of a when divided by b) to solve this equation:

We get 4 as the remainder, so there are 4 marbles left over.