16 Nov
2017
16 Nov
'17
9:44 a.m.
"What's the largest number expressible with three digits?" I think this was meant to be without additional arithmetic signs, since 999!!!!... is unbounded with an arbitrary number of !s. It was probably intended as a trick puzzle, with the wrong answer being 999. The answer given is 9^(9^9), which has around 300M digits, and can be written sign-free with superscripts. At the time, this was too big to compute as a decimal digit string. [Using 1s, 2s, or 3s, and four or more digits makes a more interesting puzzle.]
How about the 9th tetration of (the 9th tetration of 9)? That would be written with three 9s, with left superscripts. About how many digits would that have? Kerry