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
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
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)