Sum of Integers Not an Integer

Date: 02/20/2003 at 20:36:16
From: Juliet
Subject: Picking a set of integers with a certain mean

I need to pick a set of 9 integers with a mean of 3.5.

I can't make it work with an odd number of integers.

Date: 02/20/2003 at 22:54:51
From: Doctor Ian
Subject: Re: Picking a set of integers with a certain mean

Hi Juliet, 

Before we try lots of combinations, let's think about this. We're 
trying to pick 9 integers such that

  1st + 2nd + ... + 9th 
  --------------------- = 3.5
            9 

Now, what this means is that

  1st + 2nd + ... + 9th = 9 * 3.5

                        = 31.5

Does that make sense? 

If so, is there _any_ way to pick 9 integers that add up to something
that isn't an integer? 

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