I said at the end of the $100 billion question thread i would start a new one and here it is. I also said that i would put down new mathematical puzzles and things like that down. However i am going to change the format. I will put down any question i think people will find hard down as i am too lazy to think of maths puzzles but i mite put maths puzzles down if i hear a good one but anyway w/e here is the first new question. Same thing as last time whoever gives the right answer first wins. here is the first q
A secondary skl has an odd head teacher. On day 1, he has his kids perform a dodgy 1st day ceremony:
There are 1000 lockers and 1000 kids in the school. The head teacher asks the 1st kid to go to every locker and open it. Then he has the 2nd kid go to every 2nd locker and close it. The 3rd goes to every 3rd locker and, if it is shut, he opens it, and if it is open, he shuts it. The 4th kid does this to every 4th locker, and so on. After the process is completed with the 1000th kid, how many lockers are open?
Its tough. mite take u quite a wile.1st correct answer wins.
If you don't wanna no the answer (if it is even right) then I suggest you pass on this post.
Anyway, It's quite easy actually. You find every number than has factors of an odd amount. These will be the ones left open. These numbers also happen to be perfect squares I think. Which means the answer is 31.
Look. If a number has an even amount of factors, say 2. It opens (1), then closes (2). If it has a factor of 3, then it opens (1), closes (2), then opens again(3). The sqaure numbers is just a pattern. you know. 4,9,16,etc.
the lockers that are open are the square numbers so it would be 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. Therefore there are 31 lockers left open.
