I am sure you have already heard about this problem. Given a list of natural numbers, is it possible to divide them into two piles of equal sums? If yes, write two lines with objects in each pile.
Is this some well-known problem? Does it have a name? Is it NP-Complete? If not, what is the fastest solution?
This is the Partition problem, which is NP-Complete. It is a variant of Subset SUM.
Which is the fastest, really depends on the data you have. For instance, if they were bounded, you could use dynamic programming etc.