## Acalytica

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Let $n$ and $r$ be two given positive integers. We wish to construct $r$ subsets $A_1, A_2, \ldots, A_r$ of $\{0,1, \ldots, n-1\}$, each of cardinality $k$, such that for each integer $x$ with $0 \leq x \leq n-1$ there exist elements $x_i \in A_i(i=1, \ldots, n)$ with $x=x_1+x_2+\cdots+x_r$. Find the minimum value of $k$.
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