Numbers that are greater than all its right\left neighbours
Source: VI Caucasus Mathematical Olympiad
March 14, 2021
combinatorics
Problem Statement
Integers from 1 to 100 are placed in a row in some order. Let us call a number large-right, if it is greater than each number to the right of it; let us call a number large-left, is it is greater than each number to the left of it. It appears that in the row there are exactly large-right numbers and exactly large-left numbers. Find the maximal possible value of .