The Lockers
Lockers numbered to stand in a row in the gym. When the first student, he opens all lockers. The second student change the state of every locker that is a multiple of and in general, the -th student changes the state of a locker that is numbered a multiple of .
After passes through, how many lockers are closed?
The answer is 9900.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Whether the doors are closed or open depends on the number of factors the door number has. If the no. of factors is odd, the door will be open. Only squares have an odd number of factors, and square-numbered doors will be open. There are 100 squares under 10000 (100^2=10000), and thus 100 doors will be open.
So, 10000-100=9900 doors will be closed