View source for 1994 OIM Problems/Problem 5

== 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,... ,n-1}</math> each of them with exactly <math>k</math> elements and such that, for each integer <math>x</math>, <math>0 \le x \le n-1</math>, there exist <math>x_1</math> in <math>A_1</math>, <math>x_2</math> in <math>A_2</math>, <math>\cdots</math>, <math>x_r</math> in <math>A_r</math> (one element in each set) with

<cmath>x = x+1+x+2+ \cdots +x_r</cmath>

Find the smallest possible value of <math>k</math> as a function of <math>n</math> and <math>r</math>.

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

== Solution ==
{{solution}}

== See also ==
https://www.oma.org.ar/enunciados/ibe9.htm