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UKMT Junior Mathematical Olympiad, 2023

Number theory Difficulty 1.0 Junior Prove it United Kingdom

The sum of four fractions is less than 1. Three of these fractions are $\dfrac{1}{2}$ , $\dfrac{1}{3}$ and $\dfrac{1}{10}$ . The fourth fraction is $\dfrac{1}{n}$ , where $n$ is a positive integer. What values could $n$ take?

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