MathDB
Football team

Source: Tuymaada 2015, Day 1, Problem 1, Senior League

July 10, 2017
combinatoricsalgebra

Problem Statement

On the football training there was nn footballers - forwards and goalkeepers. They made kk goals. Prove that main trainer can give for every footballer squad number from 11 to nn such, that for every goal the difference between squad number of forward and squad number of goalkeeper is more than nāˆ’kn-k.
(S. Berlov)