You can use the digits 1,2,and 3 once only and any mathematical symbols you are aware of, but no symbol is to be used more than once. The challenge is to see if you can make the smallest positive number.

Special rules: You cannot use Euler's number or pi or infinity.

Special thanks to: Rhonda Wendel for Make the most of these digits and for the problem text which was slightly altered.

C'mon, everybody! The answers proposed so far aren't even within orders of orders of magnitude of our best efforts. It seems to me that the place to start is with Nick's solution to "Make the Most of These Digits". In this problem, it was shown that the largest number we could think to make using the digits 1, 2, and 3 and the same limitation of not repeating any symbols was

(.1^-2e3)!

where 2e3 = 2000, e being the symbol for exponent in scientific notation. So a STARTING point for our search of the smallest positive number we can get might be

.1^2e3! (which = .1^2000!)

Some improvements on this include

Tan(.1)^2e3!
In degrees, not radians, Tan(.1) = 0.001745331024189

Sin[Tan(.1)]^2e3!
Sin[Tan(.1)] = 3.046177290459e-5

We could keep on in this vein using hyperbolic trig functions, but we might run out of types of brackets to use.

Now, does anyone have any ideas for improving on this? And can someone with a really big calculator tells us what the last expression is equal to?

I better tell Nick there's a bigger number than his solution, while I'm at it.

Posted by Bryan on 2003-04-13 18:04:09