Whats the smallest number ("the magic number") that can satisfy these conditions?
 its positive
 it is not divisible by any number below 20 (excluding 1)
 the average of the digits is an even number between 3 and 9
The average of 3 and 7, which I think everyone will agree are the only two digits in the number 37, is 5, which I also think everyone will agree is an odd number (hence, it is not even).
Also, any number is divisible by itself (if you have 17 apples, can you split them into 17 equal groups?). Thus, any number below 20 is by definition also divisible by a number below 20.
The lowest number that meets all the criteria, and the solution to this problem, is 53, as Charlie has already stated in his apparently muchoverlooked solution.

Posted by DJ
on 20040317 12:52:26 