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(2): How About This Guess ?-- Does this work?
Wow! indeed, the first of the two is indeed smaller. 2^(-(31!)) is about 1/(10^(2.5*10^33)) while 3^(-(21!)) is about 1/(10^(2.4*10^19)).
So the tiniest so far is 2^(-(31!)), and extended precision arithmetic tells us this is about 1.02192753424799x10^-2,475,321,084,412,797,072,581,101,485,711,599.
In fact I don't think both sets of parentheses are needed in your formulation. If they were, they'd run into Alan's prohibition on any symbol's being used more than once.
Posted by Charlie
on 2003-04-13 14:54:27