This is a Multiple Choice Question :(

Discrete Mathematics Level 2

Suppose that you have a multiset \(A\) of \(1000\) rational numbers. All of these rational numbers have \(1000\) as their denominators. Brilli the Ant claims that it is always possible to find a non-empty sub-multiset of \(A\) such that the sum of the elements of that multiset is an integer. Is she right?

Details and assumptions:

I tried to frame this problem so that it would have a numerical answer but I failed. That's why this is a multiple choice question \( :(\)

A multiset is like a set but it can have elements that can appear more than once. \(\{1,3, 3\}\) is an example of a multiset. \(\{3, 3\}\) is a sub-multiset of \(\{1,3,3\}\).

The sum of one number is the number itself.


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