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September 18th, 2011, 10:59 PM   #1
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Maximize the thinking power of dragon heads

The thinking power of a multi-headed dragon depends on how many heads it has. The thinking power of a group of dragons is the product of the number of heads on the individual dragons. A particular group has 100 heads available, how many dragons with what number of heads will maximise the thinking power of the group?
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September 19th, 2011, 12:17 AM   #2
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Re: HELP!!!!!!!!!!! QUESTION

First, suppose that all the dragons have the same number of heads (except maybe the last one). Looking at the maximum of x^(100/x) (or, more manageably, the maximum of (100/x)*log(x)) will give you a hint as to the ideal number of heads on each dragon.

Second, recall that (x-a)(x+a) < x and consider replacing the last few dragons.
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September 22nd, 2011, 12:51 PM   #3
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Re: Maximize the thinking power of dragon heads

sorry but I don't understand
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September 22nd, 2011, 10:35 PM   #4
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Re: Maximize the thinking power of dragon heads

What part? If all the dragons have x heads, what is the thinking power?
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