math geniuses - PLEASE HELP a 7th grader out!!!?

Question

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?
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Answer 1

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.

Answer 2

Your statement of the problem is somewhat unclear, but my understanding of it is that your statement "repeat this pattern until all all the students walk past the lockers" means that the fifth student would open all the doors just the same as the first student did. Then the ninth student would also open all the doors and so on until thhe 997th student started the pattern over again for the last time by opening all the doors.

If my understanding is correct, then the status of the locker doors after the 1000th student walked past all the lockers would be the same as it was after the 4th student walked past the lockers.

In this case OCCOOOOOCCOC repeats itself every 12 lockers and that will be the final configuration.

O = open and C =closed in the above repeaing pattern.

Answer 3

Haha, that is a problem I am sure nearly everyone has encountered in their lives. That is a very interesting problem, think about it. What numbers are never hit in the first 1000 number sequence?

Need a hint?
What is a 5 letter word, that means a number that has only a factor of 1 and itself?

So, in your problem, only numbers with factors other than the *5 letter word* is hit.

So the answer is all the *5 letter word*

Substitute my "*5 letter word*"s with the answer to my hint

If you still haven't figured it out, the only numbers not hit would be all the prime numbers from 1 to 1000

Now, you will notice that isn't the answer :p
Those are the only lockers that are garunteed to be opened, there are others, I think.

To be honest, I haven't solved this problem yet either, its very interesting. Someday, I'll get to writing a computer program to do this, but for now, I'm too lazy, good luck on figuring this out, I hope I gave you a little inspiration.

Answer 4

I can help you!!


*pick a small muliple and start there... I figure you should try 100
then get a paper and draw 100 lines. when a student opens it draw an x in front of it and if they close it erase the x. after you do that 100 times.... lol then you check what you have... it should be a pattern and then you will need to "line the paper up in your head" and check what you have...


all the even lockers and ones that are multiples of three should be closed....

Answer 5

OK all you have to do is find all of the prime numbers from 1-10 (1,2,3,5,7,9)(nummbers that cannot be multiplied by any number other than one or itself.) So there are your constant numbers... now go through and there should be 500 lockers oopen, now find how many odd numbers 3 makes and add that to 500 then find all the even numbers from 3 and subtract that. Do this for all he numbers (try using a calculator.) And when you get to 10 just multiply it by 100 and then find all the prime numbers from 10-1000 and add that. OK i think that is it....

Answer 6

wow umm... ok. You have internet. Search the title of your math book... with the word answers.
Example: Prentive Hall Pre-Algebra California Edition 2001 Answer Sheet

Answer 7

The lockers that are perfect squares will be open.

Answer 8

The guy above is right. The perfect squares are left open. SURPRISINGLY, IT IS NOT THE PRIME NUMBERS!

Answer 9

whoa! im in advanced algebra in high school and i still dont get that. Im sorry i couldnt help. I will call up one of my friends and see if they get it aight! ill write back later!

Answer 10

wow up i am not sure! I like that problem though! sorry i could not help!