6

Part of 2016 Korea Summer Program Practice Test

Problems(1)

Partitioning into groups of equal sum

Source: Korean Summer Program Practice Test 2016 6

S

of positive integers is given. Show that there is a positive integer

N

dependent only on

S

, such that any

x_1, \dots, x_m \in S

whose sum is a multiple of

N

, can be partitioned into groups each of whose sum is exactly

N

x_1, \dots, x_m

need not be distinct.)