@1337c0d3r I think that the problem could be explained with more detail. It is not clear from the first reading, what is meant.

I was thinking on the problem and seems that something was lost in translation.

In my view the problem is the following :

Given a number N ( N > 1), gives a set S = [1,2,..., N].

Divide S in two subsets such that S1 ∪ S2 = S and S1 ∩ S2 = Ø and return the number of ways there are subsets with equal sum.

Example:

Given N = 7, S = [1, 2, 3, 4, 5, 6, 7].

since sum of [1, 6, 7] = sum of [2, 3, 4, 5]. - 1 way

sum [7] = [6,1] = [5 ,2] = [4,3] - 2 way

Answer is 2

It is not the number of subsets with equal sum. Because with N = 7 there are more than 2 subsets with eq number

For example :

[1, 6, 7] = sum of [2, 3, 4, 5]

[1, 6, 3,4]] = sum of [2, 7, 5]

[1, 2,4, 7] = sum of [6,3, 5]

[7,3,4] = sumof[2,1,6,5]

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