Problem link: http://www.codechef.com/download/ACMAMRITA12/H_Min_Max_expression.pdf

I cannot get any idea to solve this problem? I only proved that the expected value of min(x,y) = 1/3 and max(x,y) = 2/3 when x and y in the range [0,1] using double integrals. However, I cannot get any idea to solve the rest of the problem when many min-max branches are involved. Thanks in advance.