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Junior Balkan MO
2021 Junior Balkаn Mathematical Olympiad
4
4
Part of
2021 Junior Balkаn Mathematical Olympiad
Problems
(1)
Junior Balkan Mathematical Olympiad 2021- P4
Source: JBMO 2021
7/1/2021
Let
M
M
M
be a subset of the set of
2021
2021
2021
integers
{
1
,
2
,
3
,
.
.
.
,
2021
}
\{1, 2, 3, ..., 2021\}
{
1
,
2
,
3
,
...
,
2021
}
such that for any three elements (not necessarily distinct)
a
,
b
,
c
a, b, c
a
,
b
,
c
of
M
M
M
we have
∣
a
+
b
−
c
∣
>
10
|a + b - c | > 10
∣
a
+
b
−
c
∣
>
10
. Determine the largest possible number of elements of
M
M
M
.
Junior
Balkan
Sets
maximum
combinatorics