MathDB

Let

A

be a set of positive integers.

A

is called "balanced" if [and only if] the number of 3-element subsets of

A

whose elements add up to a multiple of

3

is equal to the number of 3-element subsets of

A

whose elements add up to not a multiple of

3

.
a. Find a 9-element balanced set. b. Prove that no set of

2013

elements can be balanced.

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