Can you find a 76 digits multiple of 2^76, written exclusively with sixes and sevens (as asked in
"Spirit of 76"), starting with the (given) value of 2^76, and doing nothing but a (relatively) few sums?
(To be more precise: you should be able to do this by hand, with just pencil and paper, in a reasonably short time -- minutes, not hours or days.)
So I guess then, that after 3 days, the answer is no...