This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 1

2010 Romania Team Selection Test, 4
Tags: cauchy-davenport theorem , floor function , combinatorics
Let $X$ and $Y$ be two finite subsets of the half-open interval $[0, 1)$ such that $0 \in X \cap Y$ and $x + y = 1$ for no $x \in X$ and no $y \in Y$. Prove that the set $\{x + y - \lfloor x + y \rfloor : x \in X \textrm{ and } y \in Y\}$ has at least $|X| + |Y| - 1$ elements. [i]***[/i]