# Investigating Remainders in the British Mathematics Olympiad

## BMO 2017 Round 1 — Problem 1

Helen divides 365 by each of 1, 2, 3, . . . , 365 in turn, writing down a list of the 365 remainders. Then Phil divides 366 by each of 1, 2, 3, . . . , 366 in turn, writing down a list of the 366 remainders. Whose list of remainders has the greater sum and by how much?