Find the max and min of sum of all permutations of [1..9] satisfying the following condition:
sum
== a[1] + a[2] + a[3]
== a[3] + a[4] + a[5]
== a[5] + a[6] + a[7]
== a[7] + a[8]
where sum = a[0] + a[1]
A permutation satisfying that condition is a = [9,4,1,8,3,2,5,6,7], and sum is 13.