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# logic Watch

1. There is a school with 1,000 students and 1,000 lockers. On the first day of term the headteacher asks the first student to go along and open every single locker, he asks the second to go to every second locker and close it, the third to go to every third locker and close it if it is open or open it if it is closed, the fourth to go to the fourth locker and so on. The process is completed with the thousandth student. How many lockers are open at the end?
2. (Original post by elena2003)
There is a school with 1,000 students and 1,000 lockers. On the first day of term the headteacher asks the first student to go along and open every single locker, he asks the second to go to every second locker and close it, the third to go to every third locker and close it if it is open or open it if it is closed, the fourth to go to the fourth locker and so on. The process is completed with the thousandth student. How many lockers are open at the end?
Nice question. What have you done so far?

I have no idea what the answer is, but it looks like the answer will be closely related to the factorisation of each number on the locker e.g. locker 5 is prime, so will only be "flipped" once, when the 5th pupil goes through the lockers, but locker 10 = 5x2 will be "flipped" by the 2nd pupil and the 5th pupil, and locker 12 will be "flipped" by the 2nd, 3rd, 4th, and 6th pupils.
3. (Original post by atsruser)
Nice question. What have you done so far?

I have no idea what the answer is, but it looks like the answer will be closely related to the factorisation of each number on the locker e.g. locker 5 is prime, so will only be "flipped" once, when the 5th pupil goes through the lockers, but locker 10 = 5x2 will be "flipped" by the 2nd pupil and the 5th pupil, and locker 12 will be "flipped" by the 2nd, 3rd, 4th, and 6th pupils.

i have got the soloution
4. remaining are all the square numbers beecause these are the only numbers divisible by an odd number
5. (Original post by elena2003)
remaining are all the square numbers beecause these are the only numbers divisible by an odd number
What? - 3 is odd and 27 is not a square number.
6. (Original post by Zacken)
What? - 3 is odd and 27 is not a square number.
look on there i cant be bothered to type
http://indy100.independent.co.uk/image/19289-zdov5y.JPG
7. (Original post by elena2003)
look on there i cant be bothered to type
http://indy100.independent.co.uk/image/19289-zdov5y.JPG
(Original post by elena2003)
remaining are all the square numbers beecause these are the only numbers divisible by an odd number
Yeah, I can see that you're not bothered to type.

For anybody else, the solution is the numbers which have an odd number of divisors - which are the square numbers.
8. Spoiler:
Show
yeah that

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Updated: February 22, 2016
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