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National and Regional Contests
Switzerland Contests
Switzerland Team Selection Test
2000 Switzerland Team Selection Test
2
2
Part of
2000 Switzerland Team Selection Test
Problems
(1)
\sum a_i = 100 and \sum a_i^2 = 1000 , max a_i =?
Source: Switzerland - Swiss TST 2000 p2
2/19/2020
Real numbers
a
1
,
a
2
,
.
.
.
,
a
16
a_1,a_2,...,a_{16}
a
1
,
a
2
,
...
,
a
16
satisfy the conditions
∑
i
=
1
16
a
i
=
100
\sum_{i=1}^{16}a_i = 100
∑
i
=
1
16
a
i
=
100
and
∑
i
=
1
16
a
i
2
=
1000
\sum_{i=1}^{16}a_i^2 = 1000
∑
i
=
1
16
a
i
2
=
1000
. What is the greatest possible value of
a
1
6
a_16
a
1
6
?
inequalities
Sum
max
algebra