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Possible Duplicate:
Question about the “Cat in the Hat” problem

I'm looking at the Cat in the Hat problem. Can anyone explain to me how a simple math logic is used to derive this equation?

(N/(N+1))^(M-1) = B/A 
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    @pcraft: it is protocol o$n$ this site to make your questions self-contained, rather than relying on outside links. If you want people to give you answers, you will have to define your problem.2011-09-16

1 Answers 1

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It can be broken down into two parts:

a. Number of working cats: We know that inside each cat's hat (that isn't a working cat) there are N smaller cats (all of the same size) and that there is M different sizes of cats. Therefore, there must be N^(M-1) working cats.

But we know that there are B working cats, hence B = N^(M-1).

b. Size of the largest cat: We know that the size of the working cats is 1 and that if the cat is of size H, then the cat who has it in its hat is of size H*(N+1). Given that there are M different sizes of cats this means the largest cat must be 1 * (N+1)^(M-1).

But we know that the largest cat is of size A, hence A = (N+1)^(M-1).

Now we put these two equations together.

B/A = N^(M-1)/((N+1)^(M-1)) = (N/N+1)^(M-1)

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    Thanks at-last for not suggesting edits and stuff and simply answering .2011-09-17