MathDB
Problems
Contests
National and Regional Contests
Hungary Contests
Kürschák Math Competition
2015 Kurschak Competition
3
3
Part of
2015 Kurschak Competition
Problems
(1)
Binary sequences with n terms
Source: Kürschák 2015, problem 3
10/7/2016
Let
Q
=
{
0
,
1
}
n
Q=\{0,1\}^n
Q
=
{
0
,
1
}
n
, and let
A
A
A
be a subset of
Q
Q
Q
with
2
n
−
1
2^{n-1}
2
n
−
1
elements. Prove that there are at least
2
n
−
1
2^{n-1}
2
n
−
1
pairs
(
a
,
b
)
∈
A
×
(
Q
∖
A
)
(a,b)\in A\times (Q\setminus A)
(
a
,
b
)
∈
A
×
(
Q
∖
A
)
for which sequences
a
a
a
and
b
b
b
differ in only one term.
combinatorics
Binary