Not sure if that is counter to the spirit of the post, because while the answer is either −1 or 0, it involves an intermediate calculation which vastly exceeds 10100.
Feynman once challenged people to come up with a problem that could be stated quickly but he couldn’t solve to within 10% in a minute, and a colleague stumped him with finding tan(10100).
If you mean something like cos(3^^^3 * pi), then I think that one should be solveable. Maybe try induction.
EDIT: Whoops, I didn’t see the floor symbols. Nevermind me. With not-quite-so-large numbers it’s an interesting problem that might be solveable by finding digits of pi in linear time, but linear time is of limited help here.
n=⌊sin(3↑↑↑↑3)⌋
Not sure if that is counter to the spirit of the post, because while the answer is either −1 or 0, it involves an intermediate calculation which vastly exceeds 10100.
Feynman once challenged people to come up with a problem that could be stated quickly but he couldn’t solve to within 10% in a minute, and a colleague stumped him with finding tan(10100).
If you mean something like cos(3^^^3 * pi), then I think that one should be solveable. Maybe try induction.EDIT: Whoops, I didn’t see the floor symbols. Nevermind me. With not-quite-so-large numbers it’s an interesting problem that might be solveable by finding digits of pi in linear time, but linear time is of limited help here.
↑ is not ^
https://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation
I was too lazy to find the right character. Whoops, looks like I misread the comment though.