IMO 2017 Shortlist C4
Let N ě 2 be an integer. NpN 1q so er players, no two of the same height, stand in a row in some order. Coa h Ralph want...
Category: Combinatorics
Problem
Let N ě 2 be an integer. NpN ` 1q so er players, no two of the same height, stand in a row in some order. Coa h Ralph wants to remove NpN ´ 1q people from this row so that in the remaining row of 2N players, no one stands between the two tallest ones, no one stands between the third and the fourth tallest ones, . . . , and nally no one stands between the two shortest ones. Show that this is always possible. (Russia)