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The Famous Five have been given 20 sweets as a reward for solving a tricky crime. They have agreed that the oldest of them must receive more than the next oldest, who must receive more than the next oldest, and so on. Assuming that each of the five gets at least one sweet, in how many different ways can they share the sweets?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.