Stef posed the following question to me:
In an exceptionally long corridor of a building, there are one thousand windows along one wall. Coincidentally, there are exactly one thousand window cleaners in the building. They've been ordered such that the first cleaner is to open the blinds on every window. Then, the second cleaner is to close the blinds on every second window. Then the third cleaner is told to go to every third window, and close the blinds if they are open, and open the blinds if they are closed. The fourth cleaner does this for every fourth window, and so on.
After all 1000 cleaners complete the process, how many blinds are open?
Interesting question! Thanks Stef. I believe the answer is 31. How I got it... well... I'm still trying to refine my answer.
I can't seem to find the solution (or even the question on the net for that matter) so I can't really verify. Anyway... those of you who like I challenge... have fun. It's not that difficult to solve... once you have the right approach.
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2 comments:
It's not hard...
Label the windows 1 to 1000.
All those that will be open will be those numbers <=1000 which have and ODD number of factors. Those which are closed will have EVEN number of factors.
So for example, the first will definately be open. Windows Nos 2,3,5,7... will be closed.
Window number 6 which has 1,2,3,6 as divisors will be closed while say window number 9 (1,3,9 are divisors) will be open.
You can just write a computer program to find the numbers less than 1000 having odd #divisors. Not a hard thing to do.
U-Liang
actually... you don't even need a computer program. You will observe that the only numbers that have odd number of factors are the square numbers. And there are 31 square numbers less than 1000.
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