IMO Shortlist 2000 problem C1

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Dodao/la: arhiva
2. travnja 2012.
A magician has one hundred cards numbered 1 to 100. He puts them into three boxes, a red one, a white one and a blue one, so that each box contains at least one card. A member of the audience draws two cards from two different boxes and announces the sum of numbers on those cards. Given this information, the magician locates the box from which no card has been drawn.

How many ways are there to put the cards in the three boxes so that the trick works?
Izvor: Međunarodna matematička olimpijada, shortlist 2000