# Problem 314: The Mouse on the Moon
The moon has been opened up, and land can be obtained for free, but
there is a catch. You have to build a wall around the land that you
stake out, and building a wall on the moon is expensive. Every country
has been allotted a 500 m by 500 m square area, but they will possess
only that area which they wall in. 251001 posts have been placed in a
rectangular grid with 1 meter spacing. The wall must be a closed series
of straight lines, each line running from post to post. The bigger
countries of course have built a 2000 m wall enclosing the entire 250
000 m2 area. The Duchy of Grand Fenwick, has a tighter budget, and has
asked you (their Royal Programmer) to compute what shape would get best
maximum enclosed-area/wall-length ratio. You have done some preliminary
calculations on a sheet of paper. For a 2000 meter wall enclosing the
250 000 m2 area the enclosed-area/wall-length ratio is 125. Although not
allowed , but to get an idea if this is anything better: if you place a
circle inside the square area touching the four sides the area will be
equal to π\*2502 m2 and the perimeter will be π\*500 m, so the
enclosed-area/wall-length ratio will also be 125. However, if you cut
off from the square four triangles with sides 75 m, 75 m and 75√2 m the
total area becomes 238750 m2 and the perimeter becomes 1400+300√2 m. So
this gives an enclosed-area/wall-length ratio of 130.87, which is
significantly better. Find the maximum enclosed-area/wall-length ratio.
Give your answer rounded to 8 places behind the decimal point in the
form abc.defghijk.