IL-GILLIS 2011 Problem 6

There are $N$ red cards and $N$ blue cards. Each card has a positive integer between $1$ and $N$ (inclusive) written on it. Prove that we can choose a (non-empty) subset of the red cards and a (non-empty) subset of the blue cards, so that the sum of the numbers on the chosen red cards equals the sum of the numbers on the chosen blue cards.