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

**Classifications**

Author(s): Elgin Johnston

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.

Topics covered: Number Theory

Mathematical practices: MP1 – Make sense of problems and persevere in solving them., MP2 – Reason abstractly and quantitatively., MP3 – Construct viable arguments and critique others’ reasoning., MP4 – Model with mathematics., MP7 – Look for and make use of structure., MP8 – Look for and express regularity in repeated reasoning.

Supporting materials: Handouts

Associated Math Circles: MTC Network