Skip to content # Lockers: An Open-and-Shut Case

## Activity Guide

# This guide looks at the activity in detail and goes into the underlying math.

Johnston, Elgin. (2022). Lockers: An Open-and-Shut Case. In S. Bowen (Ed.), Math Circle Activity Database. American Institute of Mathematics. https://mathcircles.org/activity/lockers

Contributor(s): Elgin Johnston

Math Circles: MTC Network

- Activity Description
- Topics Covered
- Session Styles
- Mathematical Practices

A classic Math Circle problem! At a large high school, there are 10000 lockers. The lockers are numbered, in order, 1, 2, 3, . . . , 10000, and to start, each locker is closed. There are also 10000 students, also numbered 1, 2, 3, . . . , 10000. The students walk the length of the corridor, opening and closing lockers according to a set of rules. How many lockers remain open? Which lockers? What if the rules were slightly different? Can you manipulate the rules to obtain specific outcomes?
This collection of nine locker problems is suitable for student circles, teacher circles, or the classroom.