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National and Regional Contests
Netherlands Contests
Dutch Mathematical Olympiad
2005 Dutch Mathematical Olympiad
3
3
Part of
2005 Dutch Mathematical Olympiad
Problems
(1)
Smallest possible value of m
Source: Dutch Mathematical Olympiad
9/19/2005
Let
a
1
,
a
2
,
a
3
,
a
4
,
a
5
a_1,a_2,a_3,a_4,a_5
a
1
,
a
2
,
a
3
,
a
4
,
a
5
be distinct real numbers. Consider all sums of the form
a
i
+
a
j
a_i + a_j
a
i
+
a
j
where
i
,
j
∈
{
1
,
2
,
3
,
4
,
5
}
i,j \in \{1,2,3,4,5\}
i
,
j
∈
{
1
,
2
,
3
,
4
,
5
}
and
i
≠
j
i \neq j
i
=
j
. Let
m
m
m
be the number of distinct numbers among these sums. What is the smallest possible value of
m
m
m
?