TOT 2006 Spring - Senior A-Level p6 12 grasshoppers on circumference
Source:
February 25, 2020
combinatoricsnumber theory
Problem Statement
On a circumference at some points sit grasshoppers. The points divide the circumference into arcs. By a signal each grasshopper jumps from its point to the midpoint of its arc (in clockwise direction). In such way new arcs are created. The process repeats for a number of times. Can it happen that at least one of the grasshoppers returns to its initial point after
a) jumps? (4)
a) jumps? (3)