MathDB
Very good lists

Source: Mexico National Olympiad 2019 P4

November 12, 2019
combinatorics

Problem Statement

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 10,34,34,22,30,2210,34,34,22,30,22 the sublist 22,30,2222,30,22 is good and 10,34,34,2210,34,34,22 is not. A list is very good if all its sublists are good. Find the minimum value of kk such that there exists a very good list of length 20192019 with kk different values on it.