Journal of the Mathematics Council of the Alberta Teachers’ Association
Volume 36 Issue 2, June 1999
49 – 50
The Locker Problem: An Explanation Using the Properties of Primes
Murray L. Lauber
The Problem
A small-town high school, we’ll call it Hamlet High, has exactly I 00 students and exactly 100 lockers, one for each student. After a lesson on combinations, the Math 30 class at Hamlet High decided to conduct an experiment. With the authority that comes from seniority, they lined up all the students in the hall after school, each student next to his or her locker. Then, at their bidding, student I opened every locker, student 2 closed every second locker, student 3 changed the state of every third locker and so on, for what the Math 30 class hoped would be all 100 students.
