Assignment:
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?
Provide complete and step by step solution for the question and show calculations and use formulas.