As NRO’s math guy, I get all sorts of stuff. Today a reader e-mailed in

with a question about the largest number you can make with three digits and

ordinary arithmetic signs. Well, it depends if you consider the

exponentiation symbol (this one: ^, or this one: **, in most computer

languages) to be an ordinary sign. If you don’t, then 999 is the answer.

(9×9×9 and 9×99 are both smaller.) If you do, then the answer is 9^9^9, a

number of 369,693,100 digits, the first few of which are

4,281,247,731,757,470,480,369,871,159,30…… Of course, if you are

willing to allow more exotic symbols, like Ackermann’s function,

or Donald Knuth’s up-arrow notation from

Ramsey Theory, the sky’s the limit. Next!