2014 IMO Problems/Problem 5

Problem

For each positive integer $n$ , the Bank of Cape Town issues coins of denomination $\frac{1}{n}$ . Given a finite collection of such coins (of not necessarily different denominations) with total value at most $99+$ \frac{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
Preceded by Problem 4	1 • 2 • 3 • 4 • 5 • 6	Followed by Problem 6
All IMO Problems and Solutions

Page

Toolbox

Search

2014 IMO Problems/Problem 5

Problem

Solution

See Also