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2018 Baltic Way
1
1
Part of
2018 Baltic Way
Problems
(1)
About balanced sets of real numbers
Source: Baltic Way 2018, Problem 1
11/6/2018
A finite collection of positive real numbers (not necessarily distinct) is balanced if each number is less than the sum of the others. Find all
m
≥
3
m \ge 3
m
≥
3
such that every balanced finite collection of
m
m
m
numbers can be split into three parts with the property that the sum of the numbers in each part is less than the sum of the numbers in the two other parts.