[This problem is worth 10 points]
A magician has one hundred cards numbered 1 to 100. He puts them into three boxes: a red box, a white box, and a blue box. Each box then contains at least one card. A member of the audience selects two of the three boxes, chooses one card from each of those two boxes, and announces their sum to the magician. Given this sum, the magician identifies the box from which no card has been chosen.
How many different ways are there to put the cards into the boxes so that this trick always works?
