Is there / Can there be an algorithm with acceptable time complexity that solves the following?
Given $n \leq 20$ non-negative numbers, determine whether the $n$ numbers can be divided into $k \leq 10$ disjoint subsets such that each subset has equal sum and each element of the set is used in only one of the subsets.
If the sum of the input numbers is $S$, determine if we can make $k$ subsets with sum $\frac Sk$ each.
Best Answer
This link might be helpful: https://stackoverflow.com/questions/3866528/equal-k-subsets-algorithm
Unfortunately, k-subset is known to be NP-Hard problem, so no algorithm with polynomial time complexity is known.