Powers of Two
[P5 Maths and Up: Sums and Differences]
Kept you waiting, huh?
The openness of the problem lies in large with the distances between the numbers attributed. Some numbers, upon their inclusion, removes the possibility from working (e.g. -1 and -3 together makes -4, however -4 is not a power of 2.)
Think you have an answer that the mathematicians couldn't figure out? Try playing with the terms yourself and figuring out the puzzle. It's an open question, everyone is welcome to try.