Equal number of left and right jumps
Source: Tournament of Towns 2016 Fall Tour, A Senior, Problem #7
April 22, 2017
combinatorics
Problem Statement
Several frogs are sitting on the real line at distinct integer points. In each move, one of them can take a -jump towards the right as long as they are still in on distinct points. We calculate the number of ways they can make moves in this way for a positive integer . Prove that if the jumps were all towards the left, we will still get the same number of ways.(F. Petrov)(Translated from [url=http://sasja.shap.homedns.org/Turniry/TG/index.html]here.)