kayakers with high-fives
Source: 12th Dürer Math Competition ,First Round, Category E , P2
August 18, 2020
combinatorics
Problem Statement
a) 11 kayakers row on the Danube from Szentendre to Kopaszi-gát. They do not necessarily start at the same time, but we know that they all take the same route and that each kayaker rows with a constant speed. Whenever a kayaker passes another one, they do a high five. After they all arrive, everybody claims to have done precisely high fives in total. Show that it is possible for the kayakers to have rowed in such a way that this is true.b) At a different occasion kayakers rowed in the same manner; now after arrival everybody claims to have done precisely high fives. Prove that at least one kayaker has miscounted.