MathDB
Problems
Contests
National and Regional Contests
Mongolia Contests
Mongolian Mathematical Olympiad
2002 Mongolian Mathematical Olympiad
Problem 1
Problem 1
Part of
2002 Mongolian Mathematical Olympiad
Problems
(1)
minimal cardinality of a set such that there exist subsets
Source: Mongolian MO 2002 Grade 10 P1
4/9/2021
Let
n
,
k
n,k
n
,
k
be given natural numbers. Find the smallest possible cardinality of a set
A
A
A
with the following property: There exist subsets
A
1
,
A
2
,
…
,
A
n
A_1,A_2,\ldots,A_n
A
1
,
A
2
,
…
,
A
n
of
A
A
A
such that the union of any
k
k
k
of them is
A
A
A
, but the union of any
k
−
1
k-1
k
−
1
of them is never
A
A
A
.
combinatorics