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![[Post New]](/templates/default/images/icon_minipost_new.gif) 16 Mar 2008 20:14:30 IST
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A student wrote all the natural no. from 2 to 10000 on a blackboard, one after the other. Another student came and erased all perfect cubes. If student come this way and erase all the higher powers, find the no. of students who erase at least one number.
1. 6
2. 7
3. 12
4. 13
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the largest possible no shd be a poweer of a small no so that a^x is less than 10000
also the power must be a prime no....so that it is not already rerased
so only consider 7 and 13
we have 2^13=1024*8 <10000
so ans is 13
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" Always remember money isn't everything but make sure you have made a lot of it before talking such nonsense!"
- Bill Gates |
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16 Mar 2008 20:19:57 IST
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is it 4)
cos 2^14 is greater than 10000
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Impossible To be Impossible is Impossible |
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16 Mar 2008 20:44:18 IST
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1) 6
only the following powers will be erased : 3,4,5,7,11,13
6th powers will be already erased along with the cubes . 8th with the 4th , and so on. and 2^14 > 10000
EDIT : As per the question, only cubes and higher powers r considered. squares r not considered.
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16 Mar 2008 20:48:04 IST
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yes its 6 only note that when squares are cancelled the 4th powers are also squares n are cancelled
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16 Mar 2008 20:49:23 IST
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yes i too was disillusioned by that nadeem, gr8 work! the basic idea is to find the nos between 2 and 13 which doesnt contain 2 nos where one divides the other
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16 Mar 2008 20:49:25 IST
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hey o still dont get it...see my solution...
prime nos cannot be cancelled earlier i think
for eg2^12 will be cancelled at n=2
but 2^13 can only be cancelled at n=13 na?
i might be wrong..plz cear my doubt!
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" Always remember money isn't everything but make sure you have made a lot of it before talking such nonsense!"
- Bill Gates |
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16 Mar 2008 20:51:06 IST
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see my post before yours :) that's why its 6 :D
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16 Mar 2008 20:53:23 IST
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i am really sorry....read the question wrongly i guess...
13 is the last power erased and not the number of students..
sorry again!
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" Always remember money isn't everything but make sure you have made a lot of it before talking such nonsense!"
- Bill Gates |
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16 Mar 2008 20:55:20 IST
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@akhilo
when powers of the form x^2 are deleted. 2^2,2^4,2^6,.... 2^12 will also get deleted. so u have to count only prime powers
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16 Mar 2008 20:56:59 IST
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yes prime would be the word i was searching for :D
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