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## IMO 2014 Problem 5

For every positive integer ${n}$, Cape Town Bank issues some coins that has ${\frac{1}{n}}$ value. Let a collection of such finite coins (coins does not neccesarily have different values) which sum of their value is less than ${99+\frac{1}{2}}$. Prove that we can divide the collection into at most 100 groups such that sum of all coins’ value does not exceed 1.

IMO 2014 Problem 5 (Day 2)