Soldiers color grass
Source: St Petersburg Olympiad 2013, Grade 10, P6
October 13, 2017
combinatorics
Problem Statement
There are soldiers with different heigth and age. Every day commander chooses random soldier and send him and also all soldiers that are taller and older than this soldier, or all soldiers that are lower and younger than this soldier to color grass.
Prove that after days we can find two soldiers, that color grass at same days.