MathDB
Problems
Contests
National and Regional Contests
Netherlands Contests
Dutch IMO TST
2022 Dutch IMO TST
4
4
Part of
2022 Dutch IMO TST
Problems
(1)
every sequence of 1000 numbers has >= k non-overlapping ascending pairs
Source: 2022 Dutch IMO TST 1.4
12/3/2022
In a sequence
a
1
,
a
2
,
.
.
.
,
a
1000
a_1, a_2, . . . , a_{1000}
a
1
,
a
2
,
...
,
a
1000
consisting of
1000
1000
1000
distinct numbers a pair
(
a
i
,
a
j
)
(a_i, a_j )
(
a
i
,
a
j
)
with
i
<
j
i < j
i
<
j
is called ascending if
a
i
<
a
j
a_i < a_j
a
i
<
a
j
and descending if
a
i
>
a
j
a_i > a_j
a
i
>
a
j
. Determine the largest positive integer
k
k
k
with the property that every sequence of
1000
1000
1000
distinct numbers has at least
k
k
k
non-overlapping ascending pairs or at least
k
k
k
non-overlapping descending pairs.
combinatorics