Unveiling The Magic Trick

Discrete Mathematics Level pending

A magician has cards numbered from 1 to 100 distributed in 3 boxes of different colors so that no box is empty. His trick consists in letting one person of the crowd choose 2 cards from different boxes--one card from each of the two boxes chosen--without the magician watching. Then the person tells the magician the sum of the numbers on the two cards, and the magician has to guess from which box no card was taken.

In how many ways can the magician distribute the cards so that his trick always works?

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