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There are 1000 light bulbs and 1000 tutors. All light bulbs are off. Tutor 1 goes flipping light bulb 1,2,3,4... tutor 2 then flips 2,4,6,8... tutor 3 then 3,6,9...etc until all 1000 tutors have done this. What is the status of light bulb 25? 93? 576? Is there a general solution to find out the status of any light bulb? How many light bulbs are on after all 1000 tutors have gone by?

Not homework but a UK university interview question. Please help.

  • 0
    How might you go about figuring out how many times a particular switch gets flipped?2010-11-21
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    Stan Wagon wrote up (in the solution to one of the POWs) a very general solution to the inverse of this sort of problem-if you know what set of lockers you want locked, what instruction do you give to the tutors to produce it? Unfortunately, I don't have it.2010-11-21
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    Hint: if a number $n$ is divisible by $k$, it is divisible by $n/k$.2010-11-21
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    I think, it is given by the euler's totient function $\phi(n)$, depending on whether it is odd or even.2017-02-15

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