MathDB
Problems
Contests
National and Regional Contests
Ukraine Contests
Official Ukraine Selection Cycle
Ukraine Team Selection Test
1999 Ukraine Team Selection Test
3
3
Part of
1999 Ukraine Team Selection Test
Problems
(1)
maxi number of elements in F, a family of m elements of 1,2,...,n
Source: Ukrainian TST 1999 p3
2/13/2020
Let
m
,
n
m,n
m
,
n
be positive integers with
m
≤
n
m \le n
m
≤
n
, and let
F
F
F
be a family of
m
m
m
-element subsets of
{
1
,
2
,
.
.
.
,
n
}
\{1,2,...,n\}
{
1
,
2
,
...
,
n
}
satisfying
A
∩
B
≠
∅
A \cap B \ne \varnothing
A
∩
B
=
∅
for all
A
,
B
∈
F
A,B \in F
A
,
B
∈
F
. Determine the maximum possible number of elements in
F
F
F
.
Subsets
combinatorics
max