Ok, real brain teaser time!
 

My calculus teacher introduced this as a bonus problem, don't worry, it doesn't involve calculus, just some hard core algebra!

At some random highschool there are 1000 students, and 1000 lockers. At the beginning of the day, all of the lockers are closed. The first kid comes in, and opens every locker. The second kid comes in and reverses the order of every 2nd locker, 3rd kid reverses the order of every 3rd locker, (reverses the order meaning if its open the kid will close it, if it is closed, the kid will open it) 4th kid reverses the order of every 4th locker - all the way to the 1000th kid that reverses the order of locker #1000, the question is, how many lockers are open, and how many are closed at the end of the day? (Hint look at the multiples) This is a fun one!

Re: Ok, real brain teaser time!
 

im guessing its all closed? but kaos already won this one

Re: Ok, real brain teaser time!
 

nope, 31 open and 969 closed, reason being is that the only way a locker can be open, is if it changed an odd amount of times, and the only time it changes is when the number is a multiple. The only numbers with even multiples are perfect squares, so the lockers that are open are 1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,25 6,289,324,361,400,441,484,529,576,625,676,729,784, 841,900,961

add em up, you get 31 open!

basically these numbers are 1^2, 2^2, 3^2,4^2...39^2 perfect squares

Re: Ok, real brain teaser time!
 

is you guess 50/50? or all closed? :)

Re: Ok, real brain teaser time!
 

nice, i shoulda thought of that, i need to eat some food...gotta get on my A game.

Re: Ok, real brain teaser time!
 

damn that took too long to type, or I would have recieved my 10 dollars...

Re: Ok, real brain teaser time!
 

haha yea when i offer incentive i follow through too :P you woulda lucked out

Re: Ok, real brain teaser time!
 

yup 10 bucks for me...bwahhhhhhhhhhhhh:yahoo: