Evens and Odds in the Multiplication Table

Date: 09/11/2005 at 09:24:44
From: Lala
Subject: multiplication tables

Dear Dr. Math - in the multiplication table, is there the same number
of even numbers as odd numbers, or is there more of one kind than the 
other?  Can you explain why?

Date: 09/11/2005 at 10:44:25
From: Doctor Ian
Subject: Re: multiplication tables

Hi Lala,

Let's make a small multiplication table, but instead of using actual
numbers, we'll just use "e" for even numbers and "o" for odd:

   x   o   e   o   e 
 
   o  oo  oe  oo  oe   
 
   e  eo  ee  eo  ee
  
   o  oo  oe  oo  oe

   e  eo  ee  eo  ee

In this table, "ee" means "an even times an even", and so on. 

By looking at the table, can you see how to answer your question? 
Note that the product of an even number and any other number will 
always be even. 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/