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Problems
Contests
National and Regional Contests
Korea Contests
Korea National Olympiad
2020 Korea National Olympiad
5
5
Part of
2020 Korea National Olympiad
Problems
(1)
Tricky Sequence
Source: Korean National Olympiad P5
11/24/2020
For some positive integer
n
n
n
, there exists
n
n
n
different positive integers
a
1
,
a
2
,
.
.
.
,
a
n
a_1, a_2, ..., a_n
a
1
,
a
2
,
...
,
a
n
such that
(
1
)
(1)
(
1
)
a
1
=
1
,
a
n
=
2000
a_1=1, a_n=2000
a
1
=
1
,
a
n
=
2000
(
2
)
(2)
(
2
)
∀
i
∈
Z
\forall i\in \mathbb{Z}
∀
i
∈
Z
s
.
t
.
s.t.
s
.
t
.
2
≤
i
≤
n
,
a
i
−
a
i
−
1
∈
{
−
3
,
5
}
2\le i\le n, a_i -a_{i-1}\in \{-3,5\}
2
≤
i
≤
n
,
a
i
−
a
i
−
1
∈
{
−
3
,
5
}
Determine the maximum value of n.
combinatorics
Integer sequence