iCount Youth Account

Brain Game QUIZ – Answers Below

Imagine a hallway lined with 100 closed lockers. You open every locker. Then you close every second locker. Then you go to every third locker and “toggle” the locker – this means, you open it if it is closed or close it if it is open. Continue toggling every nth locker on pass number n. (So on pass 4, toggle every 4th, on pass 90, toggle every 90th, etc.)

After 100 passes, where you toggle only locker #100, how many lockers are open?

---

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

QUIZ Answers

Brain Game

10 lockers are left open:
Lockers #1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.

You could work this out with a piece of paper and a lot of time, but using math, each of these numbers are perfect squares. This problem is based on the factors of the locker number. Each locker is toggled by each factor; for example, locker #40 is toggled on pass number 1, 2, 4, 5, 8, 10, 20, and 40. That's eight toggles: open-closed-open-closed-open-closed-open-closed.