MathDB
Problems
Contests
National and Regional Contests
Mexico Contests
Mexico National Olympiad
2019 Mexico National Olympiad
4
4
Part of
2019 Mexico National Olympiad
Problems
(1)
Very good lists
Source: Mexico National Olympiad 2019 P4
11/12/2019
A list of positive integers is called good if the maximum element of the list appears exactly once. A sublist is a list formed by one or more consecutive elements of a list. For example, the list
10
,
34
,
34
,
22
,
30
,
22
10,34,34,22,30,22
10
,
34
,
34
,
22
,
30
,
22
the sublist
22
,
30
,
22
22,30,22
22
,
30
,
22
is good and
10
,
34
,
34
,
22
10,34,34,22
10
,
34
,
34
,
22
is not. A list is very good if all its sublists are good. Find the minimum value of
k
k
k
such that there exists a very good list of length
2019
2019
2019
with
k
k
k
different values on it.
combinatorics