Let the corners of the square be at (0,0),(1,0),(1,1), and (0,1).

The solution is to dig the following ditches:

- (0,0) to (x,x)
- (1,0) to (x,x)
- (0,1) to (x,x)
- (1/2,1/2) to (1,1)

Where x = (3-sqr(3))/6 =~ 0.2113248654

The total length of all ditches is aproximately 2.6389584338

I'd like to thank the Macalester College Problems of the Week for this problem.

Michael Shackleford, A.S.A.