Four Twos Puzzle

Date: 05/31/99 at 23:56:25
From: Jonathan Ma
Subject: Using 4 twos to get special numbers

How can I get 15, 17, 19 and 21 using 4 twos? I've tried to use 
exponents, radicals, and the order of operations. 

Thank you for your time and help.

Date: 06/02/99 at 02:31:05
From: Doctor Floor
Subject: Re: Using 4 twos to get special numbers

Hi, Jonathan,

Thanks for your question!

I found three of your numbers, using the trick of writing .2 for 0.2:

     15 = ( 2 + 2/2)/.2
     19 = (2*2 - .2)/.2
     21 = (2*2 + .2)/.2

Here's a weird possibility for 17:
                 
     17 = 22 - sqrt(.2^(-2))

Here, .2^(-2) is .2 to the power -2, which equals 25.

Good luck!

Best regards,
- Doctor Floor, The Math Forum
  http://mathforum.org/dr.math/