The groundhog problem

Abstract

The Groundhog Problem is stated as follows: “A groundhog has made an infinite number of holes roughly a metre apart in a straight line in both directions on an infinite plane. Every day it travels a fixed number of holes in one direction. A farmer would like to catch the groundhog by shining a torch, but only once a night, into one of the holes at midnight when it is asleep. What strategy can the farmer use to ensure that he catches the groundhog eventually?” It turns out that the solution of this problem relies on a set-theoretic concept usually taught at the tertiary level. One key purpose of this paper is to explicitly articulate the problem solving trajectory of a professional mathematician who is cognizant of his/her own problem solving disposition and thinking.