[hermitdev]

I wouldn't feel dumb about it. People often look at very difficult problems for a very long time before they conclude a solution is impossible and later to be disproven. I would expect this one to be any different. Yes, there are currently no known solutions, but that doesn't preclude a brilliant mind coming in down the road with a solution.

[afthonos]

In this case, there is provably no solution. A brilliant mind can’t fight that, any more than it can prove that 2+2=5. :-)

(Yes, using the traditional definitions of all those symbols.)