Question 36
A bicycle race on a circular circuit in Cordisburgo has three cyclists: Guimarães, Rosa and João. During the first hour Guimarães completes exactly 230 laps and João exactly 111 laps. Rosa's number of laps is unknown, but it is an integer greater than João's and less than Guimarães's. Each rides at constant speed, and they all start together at the same point. Including overtakes at the initial instant, how many overtakes occur in total during the first hour?