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1994 OIM Problems/Problem 5

Revision as of 13:31, 13 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== Problem == Let <math>n</math> and <math>r</math> be two positive integers. We wish to construct <math>r</math> subsets <math>A_1, A_2, \cdots , A_r</math> of <math>{0,1,......")
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Problem

Let $n$ and $r$ be two positive integers. We wish to construct $r$ subsets $A_1, A_2, \cdots , A_r$ of ${0,1,... ,n-1}$ each of them with exactly $k$ elements and such that, for each integer $x$, $0 \le x \le n-1$, there exist $x_1$ in $A_1$, $x_2$ in $A_2$, $\cdots$, $x_r$ in $A_r$ (one element in each set) with

\[x = x+1+x+2+ \cdots +x_r\]

Find the smallest possible value of $k$ as a function of $n$ and $r$.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

https://www.oma.org.ar/enunciados/ibe9.htm

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