2
$\begingroup$

Given $n (n \leq 20)$ positive integers and each integer is $\leq 10,000$. Can they be partitioned into $4$ subsets such that sum of the subsets are pairwise equal to each other.

I am interested in an algorithmic solution.

  • 2
    Clearly it is not always possible: if the total sum is not a multiple of $4$ you can stop looking. Similarly if the sum of the smallest four and largest one is more than a quarter of the total sum, or if the sum of the largest four and smallest one is less than a quarter of the total sum you can stop.2012-02-24

1 Answers 1