My Math Forum Maximize the thinking power of dragon heads

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 September 18th, 2011, 10:59 PM #1 Newbie   Joined: Sep 2011 Posts: 8 Thanks: 0 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? THANKS
 September 19th, 2011, 12:17 AM #2 Senior Member   Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3 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) < x² and consider replacing the last few dragons.
 September 22nd, 2011, 12:51 PM #3 Newbie   Joined: Sep 2011 Posts: 8 Thanks: 0 Re: Maximize the thinking power of dragon heads sorry but I don't understand
 September 22nd, 2011, 10:35 PM #4 Senior Member   Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3 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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