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Make the least of these digits (Posted on 2003-04-13) Difficulty: 3 of 5
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.

No Solution Yet Submitted by Alan    
Rating: 3.0000 (10 votes)

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re(3): HELP !! I think I found out the SMALLEST Number | Comment 31 of 67 |
(In reply to re(2): HELP !! I think I found out the SMALLEST Number by Ravi Raja)

Ravi, Bryan's point is that 2e3!, being 2000!, serves as a much larger power than 31!, and starting with .1 instead of what amounts to 1/2 (because of the negative exponent) is using a better (smaller) base.

I, myself, do have problems with the 2e3, as I don't really consider that standard mathematical notation. But even .1^(32!) is a better replacement for 2^{-(31!)} within the solution you propose. Also, looking at what Bryan suggested, shows that one should not stop at sin(tiny expression), but pile other functions on top of it, like tan(sin(tiny expression)), with the caveat we seek the most efficient sequence of the piling on of functions.

I don't know whether we can use indefinitely many variations on parentheses to get around the 1-use-of-each-symbol restriction.
  Posted by Charlie on 2003-04-18 09:42:40

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