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T3
BMT 2021 Discrete Tiebreaker p3
BMT 2021 Discrete Tiebreaker p3
Source:
September 27, 2023
combinatorics
Problem Statement
Let
N
N
N
be the number of tuples
(
a
1
,
a
2
,
.
.
.
,
a
150
)
(a_1, a_2,..., a_{150})
(
a
1
,
a
2
,
...
,
a
150
)
satisfying:
∙
\bullet
∙
a
i
∈
{
2
,
3
,
5
,
7
,
11
}
a_i \in \{2, 3, 5, 7, 11\}
a
i
∈
{
2
,
3
,
5
,
7
,
11
}
for all
1
≤
i
≤
99
1 \le i \le 99
1
≤
i
≤
99
.
∙
\bullet
∙
a
i
∈
{
2
,
4
,
6
,
8
}
a_i \in \{2, 4, 6, 8\}
a
i
∈
{
2
,
4
,
6
,
8
}
for all
100
≤
i
≤
150
100 \le i \le 150
100
≤
i
≤
150
.
∙
\bullet
∙
∑
i
=
1
150
a
i
\sum^{150}_{i=1}a_i
∑
i
=
1
150
a
i
is divisible by
8
8
8
. Compute the last three digits of
N
N
N
.
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