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National and Regional Contests
Hungary Contests
Kürschák Math Competition
1953 Kurschak Competition
1
1
Part of
1953 Kurschak Competition
Problems
(1)
A,B subsets of 1-n |A|+|b|> n-
Source: 1953 Hungary - Kürschák Competition p1
10/10/2022
A
A
A
and
B
B
B
are any two subsets of
{
1
,
2
,
.
.
.
,
n
−
1
}
\{1, 2,...,n - 1\}
{
1
,
2
,
...
,
n
−
1
}
such that
∣
A
∣
+
∣
B
∣
>
n
−
1
|A| +|B|> n - 1
∣
A
∣
+
∣
B
∣
>
n
−
1
. Prove that one can find
a
a
a
in
A
A
A
and
b
b
b
in
B
B
B
such that
a
+
b
=
n
a + b = n
a
+
b
=
n
.
combinatorics
Subsets