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National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2018 India PRMO
12
12
Part of
2018 India PRMO
Problems
(1)
2018 preRMO p12, 8tuples wanted, multiple of 3, in {-1,1 }
Source:
8/8/2019
Determine the number of
8
8
8
-tuples
(
ϵ
1
,
ϵ
2
,
.
.
.
,
ϵ
8
)
(\epsilon_1, \epsilon_2,...,\epsilon_8)
(
ϵ
1
,
ϵ
2
,
...
,
ϵ
8
)
such that
ϵ
1
,
ϵ
2
,
.
.
.
,
8
∈
{
1
,
−
1
}
\epsilon_1, \epsilon_2, ..., 8 \in \{1,-1\}
ϵ
1
,
ϵ
2
,
...
,
8
∈
{
1
,
−
1
}
and
ϵ
1
+
2
ϵ
2
+
3
ϵ
3
+
.
.
.
+
8
ϵ
8
\epsilon_1 + 2\epsilon_2 + 3\epsilon_3 +...+ 8\epsilon_8
ϵ
1
+
2
ϵ
2
+
3
ϵ
3
+
...
+
8
ϵ
8
is a multiple of
3
3
3
.
algebra
number theory