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National and Regional Contests
Russia Contests
Moscow Mathematical Olympiad
2018 Moscow Mathematical Olympiad
1
Easy algebra
Easy algebra
Source: Moscow Olympiad 2018, Grade 9, P1
July 13, 2018
algebra
inequalities
Problem Statement
a
1
,
a
2
,
.
.
.
,
a
81
a_1,a_2,...,a_{81}
a
1
,
a
2
,
...
,
a
81
are nonzero,
a
i
+
a
i
+
1
>
0
a_i+a_{i+1}>0
a
i
+
a
i
+
1
>
0
for
i
=
1
,
.
.
.
,
80
i=1,...,80
i
=
1
,
...
,
80
and
a
1
+
a
2
+
.
.
.
+
a
81
<
0
a_1+a_2+...+a_{81}<0
a
1
+
a
2
+
...
+
a
81
<
0
. What is sign of
a
1
∗
a
2
∗
.
.
.
∗
a
81
a_1*a_2*...*a_{81}
a
1
∗
a
2
∗
...
∗
a
81
?
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