A question that I posed to a colleague, and passed onto the list, was the task of splitting a set of 200 numbers into two sets that had the same sum.
I claimed that it is unsolvable, in practice, since there is no efficient algorithm, other than testing a huge number of cases (I suggested on the order of 200 C 100).
Two of the respondents have indicated that this problem is NP-Complete, and hence the number of operations rises exponentially compared to the number of values given. Given this, for a large enough set, the problem is effectively unsolvable. So the question becomes, is 200 values sufficiently large?
Here is the test.
The number below have a total of 10 000 000. Can you split it into two sets that each have a sum of 5 000 000? I generated this list using Excel, so there _is_ an answer, that currently only I know. Shane, me old mate, good luck!
BTW, this whole thing arose out of a grade 8 problem on putting 9 songs onto the two sides of a cassette tape.
200 Random Numbers That Can Be Split Into Two Groups Whose Sum Is The Same