MathDB

9th ibmo - brazil 1994/q5.

Source: Spanish Communities

May 7, 2006

functionceiling functioncombinatorics unsolvedcombinatorics

Problem Statement

Let

n

and

r

two positive integers. It is wanted to make

r

subsets

A_1,\ A_2,\dots,A_r

from the set

\{0,1,\cdots,n-1\}

such that all those subsets contain exactly

k

elements and such that, for all integer

x

with

0\leq{x}\leq{n-1}

there exist

x_1\in{}A_1,\ x_2\in{}A_2 \dots,x_r\in{}A_r

(an element of each set) with

x=x_1+x_2+\cdots+x_r

.
Find the minimum value of

k

in terms of

n

and

r

.

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