Primes and Number Riddles

Date: 4/15/96 at 21:17:0
From: Anonymous
Subject: Pre Algebra: Finding primes as the result of solving number 
riddles

I am having difficulty understanding this riddle.  Please help me to 
find the proper method to solve this and future riddles like it.  
Thanks and here is the problem as it appears in its entirety.

Three different one-digit primes
Produce me, if you're using times;
If my digits you add,
Another prime will be had.
Two answers - and nothing else 
rhymes.

Thank you very much for your assistance!

Date: 4/22/96 at 20:19:12
From: Doctor Joshua
Subject: Re: Pre Algebra:  Finding primes as the result of solving 
number riddles

Hi!

By process of elimination, there are only four one-digit primes:
   2,3,5, and 7.  

Multiplying any three of these together:

2X3X5  =  30  Sum of digits = 3, this works!

2X3X7  =  42  Sum of digits = 6

2X5X7  =  70  Sum of digits = 7, this works as well.

3X5X7  =  105 Sum of digits = 6

So the answers to the riddle are 30 and 70.

-Doctor Joshua,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/