Problem

Source: Moldova TST 2019

Tags: combinatorics



Let $n\ge 2,$ be a positive integer. Numbers $\{1,2,3, ...,n\}$ are written in a row in an arbitrary order. Determine the smalles positive integer $k$ with the property: everytime it is possible to delete $k$ numbers from those written on the table, such that the remained numbers are either in an increasing or decreasing order.