The nation of Griddonesia consists of eighty-one equally-spaced islands represented by intersections of the lines in the following grid, where north is up and east is right as on a standard map. Each island is connected to all its adjacent islands by horizontal and vertical bridges exactly one-mile long. There are no diagonal bridges. A Griddonesian oceanic engineer labels each island with a different integer from 1, 2, ..., 81 to identify them. In how many ways can he number the islands, where the number 1 is always assigned to the central island?

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First, let's look at a simpler problem

How many ways do we have assigning 3 letters (A,B,C) to three boxes?

we have three ways to assign the letter "A":

A _ _ , _ A _ , _ _ A

Once this letter is assigned, we have two empty boxes. Thus we have for each original configuration two ways to assign the ...

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The solution explains the way to find teh number of possible permutations out of a sample.

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