2014 IMO Problems/Problem 5

Problem

For each positive integer $n$ , the Bank of Cape Town issues coins of denomination $\tfrac{1}{n}$ . Given a finite collection of such coins (of not necessarily different denominations) with total value at most $99+\tfrac{1}{2}$ , prove that it is possible to split this collection into $100$ or fewer groups, such that each group has total value at most $1$ .

Solution

Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.

2014 IMO (Problems) • Resources
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2014 IMO Problems/Problem 5

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