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.

(In reply to re: That's it. This is the SMALLEST. I got it. by Justin)

Implementing the primorial [ n# ] with the already recognized factorial [ n! -- (or, with the older notation: |n  ) ] is a nice touch.  But why stop there?  How about using the other exponential function symbols, such as the hyperfactorial [ H(n) ] and superfactorial [ n$ ] and tetration [ ^xn ]; and use of the exponential notation [ nE-x ].

My proposal for the smaller number to be presented, as yet, is

sin{.1E-[^H(|3#)$2]}

This expression could be written as sin{ (1/10)*(1/(10^X))} where X is 2^((2^2)^2).....etc., and where the 2 is iterated with each power to include the base number, 2,  (H(30)^^H(30)) times. 

Posted by Dej Mar on 2006-07-22 03:38:05