Open in the curiosity app

Can You Solve The 100 Lockers Problem?

You may have tried solving the 100 Locker Problem in high school or college math. If you haven't, here's how it goes: 100 students are assigned lockers #1 through #100. The first student opens every locker. The second student closes every second locker (#2, #4, and on from there). The third student changes every third locker -- that is, the student will close every open locker he encounters and open every closed one. The fourth student changes every fourth locker, and so on, until all 100 students have taken their turn. How many lockers will be left open? Watch the video to figure out out to solve this puzzle, and to get the answer.

Explore Related Subjects