Determine if an array is divisible in pairs of equal sum
You sort the array in increasing order. 

If you pair an element equal to the largest element with any element that is larger than the smallest element, then pairing the smallest element with any other element will give a smaller sum, and therefore a different sum. 

Therefore, to find pairs that all have the same sum, you must pair an element equal to the largest with an element equal to the smallest, and then repeat for the remaining elements. This will give you pairs with equal sums if it is possible. If not possible, then of course you won't get equal sums.