MathDB

24

Part of 2014 Harvard-MIT Mathematics Tournament

Problems(1)

2014 Guts #24: Mean of Elements in Subset is an Integer

Source:

4/21/2014
Let A={a1,a2,…,a7}A=\{a_1,a_2,\ldots,a_7\} be a set of distinct positive integers such that the mean of the elements of any nonempty subset of AA is an integer. Find the smallest possible value of the sum of the elements in AA.