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Math Prize For Girls Problems
2016 Math Prize for Girls Problems
14
14
Part of
2016 Math Prize for Girls Problems
Problems
(1)
Math Prize 2016 Problem 14
Source:
9/12/2016
We call a set
X
X
X
of real numbers three-averaging if for every two distinct elements
a
a
a
and
b
b
b
of
X
X
X
, there exists an element
c
c
c
in
X
X
X
(different from both
a
a
a
and
b
b
b
) such that the number
(
a
+
b
+
c
)
/
3
(a + b + c)/3
(
a
+
b
+
c
)
/3
also belongs to
X
X
X
. For instance, the set
{
0
,
1008
,
2016
}
\{ 0, 1008, 2016 \}
{
0
,
1008
,
2016
}
is three-averaging. What is the least possible number of elements in a three-averaging set with more than 3 elements?
Math Prize for Girls