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

Lockers: An Open-and-Shut Case

Math Circles:
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.

Activity Guide

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