Multiple choice general knowledge math & puzzles

A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony: There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?

  1. 237

  2. 31

  3. 500

  4. 250
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Lockers that remain open are those toggled an odd number of times. A locker is toggled once for each of its divisors. Only perfect squares have an odd number of divisors. The number of perfect squares from 1 to 1000 is floor(sqrt(1000)) = 31.

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