MathDB
Problems
Contests
National and Regional Contests
Spain Contests
pOMA and PErA mathematical olympiads
2024 PErA
P1
P1
Part of
2024 PErA
Problems
(1)
Standard and easy combo
Source: PErA 2024/1
3/4/2024
Let
n
n
n
be a positive integer, and let
[
n
]
=
{
1
,
2
,
…
,
n
}
[n]=\{1,2,\dots,n\}
[
n
]
=
{
1
,
2
,
…
,
n
}
. Find the maximum posible cardinality of a subset
S
S
S
of
[
n
]
[n]
[
n
]
with the property that there aren't any distinct
a
,
b
,
c
∈
S
a,b,c\in S
a
,
b
,
c
∈
S
such that
a
+
b
=
c
a+b=c
a
+
b
=
c
.
combinatorics