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Problem #53

Harry and his Magical Boxes

There are 7 magical boxes each containing a label depicting a number. The labels of the boxes are given as 5, 2, 7, 8, 7, 4, 6. Harry Potter goes to each jar once and shouts a spell. When Harry shouts a spell near a box with label x he gets a random integer n from the box such that, 1<=n<=x. Thus he gets a collection of seven numbers by shouting once near each box. One such collection is 4, 2, 1, 2, 6, 4, 6. Two collections are same if one is a permutation of other. So 1, 2, 1, 1, 1, 1, 6 is same as 2, 1, 1, 1, 1, 1, 6. Now Harry expects you to tell the total number of different collections he can get by repeatedly performing this act.

Contributed by Rajat Jain

Solved by 83 users

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