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 The least by Mattias)

"...no symbol is to be used more than once."

Those restrictions should apply to even alphabetic characters, more than one set of parenthesis, brackets, braces, etc.  Thus iteration of exclamation points for multiple factorials would not be permitted. (An exception might be made to the use of the double factorial, as the symbol of the double exclamation point has a unique character code value in Unicode.)

Also, I am iffy on the stacking of some trigonometric functions, such as TAN(SIN(x)) to be allowable, as both functions contain an N.  Of course, perhaps if one were to use lower case for one.  And, if repeated letters were allowable because they are part of a "word" unit or because they are represented in different case, then is not ArcTan(x) where x is a very, very small value, smaller than Sin(x)?

Though not listed in the special rules, symbols and characters representing specific values (numbers) other than those listed (pi and Euler's number) would not be allowed for the same reason as those that are listed. 

Symbolic letters such as the E used in exponential notation would be permitted as it does not represent the value 10. With the notation before and following it, it is quantity of 10 being raised to the given power following it to be multiplied by the number preceding it: nE+x is n*10^x and nE-x is n*10^-x.  Yet, it is important that the expression is properly formatted -- ie. .1E3 would not be proper notation, but .1E+3 would. (E can be either upper or lower case.)

Edited on July 22, 2006, 2:58 pm

Posted by Dej Mar on 2006-07-22 06:53:14