There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?
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12 comments:
31 lockers are open............
let sal decide the difficulty....... i would think it is worth 1 mark the way i did but then my method might be longer.
wat do u think ananth??
I think that the answer is 31.
The logic behind this is that the number with odd number of factors(in simplest form) should be open...
For example.
1=1[1]
4=1*2*2[3]
9=1*3*3[3]
64=1*2*2*2*2*2*2[7]
Now accordingly
18=1*2*3*3[4] will not be open as
1)1 will open it
2)2 will close it
3)3 will open it
4)9 will close it
Hence 18 will be closed.
Thus my answer is 31.
1,4,9,16,25,36,49,64,81,....,961
My typing is slow and that may have cost me these 2 marks but i think i should get the points as you all know that i have given the appropraite reason of how i got the answer and not just copied shikhs answer.
so u think i copied "tie".
common sall have same rules for urselves and oders..............
i don't deny that u shld get points for this but i am only saying tht i too deserve points for "TIE".
by the way the lockers would be 2nd,5th 10 th and so on till 962 nd..
Please tell me who will close the 1st locker?
the 1000 th child will close the 1st locker.
The right answer is lockers 1,4,9,16,25,..... till 961 which makes it 31 lockers.
ok i got it i misunderstood the questions.
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