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Argentina Team Selection Test
2009 Argentina Team Selection Test
2
Find the maximum value
Find the maximum value
Source: Argentina TST 2009
May 15, 2009
inequalities
Clevermath
Problem Statement
Let
a
1
,
a
2
,
.
.
.
,
a
300
a_1, a_2, ..., a_{300}
a
1
,
a
2
,
...
,
a
300
be nonnegative real numbers, with \sum_{i\equal{}1}^{300} a_i \equal{} 1. Find the maximum possible value of
∑
i
≠
j
,
i
∣
j
a
i
a
j
\sum_{i \neq j, i|j} a_ia_j
∑
i
=
j
,
i
∣
j
a
i
a
j
.
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