Kayla M.

asked • 07/04/14

Word problem

Word problem
A high school has 4657 students and 4657 lockers, all of which are closed. The students line up and walk one at a time down the hall that contains the lockers. The first student opens all the lockers. The second student closes every other locker starting with the second one. The third student changes (closes if opened, opens of closed) every third locker starting with the third. The fourth student changes every fourth locker starting with the fourth. This pattern continues until all 4657 students have passed through the hallway.

In the end, how many lockers are open?

2 Answers By Expert Tutors


Francisco E. answered • 07/04/14

5 (1)

Francisco; Civil Engineering, Math., Science, Spanish, Computers.

Arthur D.

Francisco, correct me if my reasoning is wrong.
Take the first 4 lockers and the first 4 students.
Call the lockers A,B,C, and D.
A    B    C    D    and o for open and c for closed
o    o    o     o  first student
o    c    o     c  second student
o    c    c     c  third student (changes every third locker)
o    c    c     o  fourth student (changes every fourth locker)
The fifth student now starts with the fifth locker and I'm thinking there will be others that are open as well.
Arthur D.


Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.


Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.