A School locker question? If you started with every single locker shut...?

If a locker is changed an even amount of times then it will go back to being closed. If it is changed an odd amount of times, then it will be open. What kind of number has an even number of factors (how many factors a locker number has determines how many times it is changed)? Most numbers have an even amout of factors, because for every factor there is a matching one that when multiplied will equal the locker number. Except for square numbers because for one of their factor pairs the numbers are the same, and so those two factors, being exact same, are only counted as one. That would make the amount of factors for those numbers be odd.

SO the lockers that are square numbers are open (ie. 1,4,9,16,25, 36, 49, 64, ...)

The odd numbered lockers ouwld end up closed, and thwe evn lockers would end up opened. This is because only the last time matters that you pass by a locker. So the first locker ends up closed, because you closed every locker, then the second locker ends up opened, because you opened every second locker. Then the third locker ends up closed, and on, thgough all lockers.

Even lockers would end up open.

The pattern is for every locker, every 3rd, 5th, 7th, ... lockers, the action is close them, and for every 2nd, 4th, 6th, ... lockers, the action is to open them. The actions are regardless whether the locker was already opened or closed.

Thus, even lockers would end up open and odd ones would end up close.

1 2 3 4 5

c o c o c

going back 4 will open 1

1 2 3 4 5 6

c o c o c o

going back 4 results in no change

the way the problem is stated the result is inconclusive.

the even numbered lockers would end up being open and the odd would end up closed

This would depend on how many lockers are in the school.

all of the even number lockers

go ask the locker

the first one

how many lockers???