text: math geniuses - please help a 7th grader out!!!? please..please - please!!! math geniuses - help***?  please give me the answer and explain how it is confusing... a school has 1000 students and 1000 lockers. the lockers are numbered from 1 to 1000. the students enter the school 1 at a time. - the 1st student opens all the lockers _ the 2nd student begins w/ locker #2 and closes all of the even number lockers.  - the 3rd student becasue w/ the 3rd locker and changes - either by opening closed doors or closing ipen doors - all lockers w/ numbers that are multiples of 3. - the 4th student begins w/ the 4th locker and changes all lockers with numers that are multiples of 4 ***repeat this pattern until all the students walk past the lockers - after the last student has gone by, which lockers are opended? <>> student #1 represents a factor of 1... in other words, he opens all 1000 lockers (that have 1 as a factor) student #2 represents a factor of 2... in other words, he toggles all lockers that have 2 as a factor (2, 4, 6, 8, etc.) student #3 represents a factor of 3... he toggles all lockers that have 3 as a factor...  now think of a specific locker, say #12.  it has the following factors: 1, 2, 3, 4, 6, 12 that's an even number of factors, opened, closed, opened, closed, opened, closed.  so it will end up closed.  try another locker, say #20.  it has the following factors: 1, 2, 4, 5, 10, 20... again an even number of factors, so it will end up closed.  in fact, most numbers have an even number of factors.  generally factors pair up... so for 20 you have: 1 x 20 = 20 2 x 10 = 20 4 x 5 = 20  the exceptions are the *perfect squares* because they end having one number that doesn't pair up (except with itself).  so locker #1, for example.  the only factor is 1, so it is open. locker #4, has factors of 1, 2, 4 which is odd.  so again it is open. locker #9, has factors of 1, 3, 9 which is odd.  so again it is open. locker #16, has factors of: 1 x 16 2 x 8 4 odd number of factors, so it will be open.  the answer is only the lockers that are *perfect squares* will be open.  specifically the open lockers are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900 and 961.