The Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

Sum of Integers in a Set

Date: 06/19/2001 at 01:32:00
From: C. Martin
Subject: The sum of integers in this set

Consider the set of all four-digit integers, each of which is formed 
using the digits 1,2,3,5, or 7 at most once. Find the sum of the 
integers in this set.

I realize there are 120 possible combinations of four-digit numbers.  
I can write out all 120 and then add them together, but that just 
seems too long. Is there an easier (more efficient) way to solve this 

Thanks for your help.

Date: 06/19/2001 at 11:59:31
From: Doctor Ian
Subject: Re: The sum of integers in this set

Hi C, 

Sometimes the way to attack a large problem is to look at a smaller 
problem first. Suppose I want to find the sum of all the three-digit 
numbers that I can make from digits a, b, and c.  I can write down the 


I can expand them this way:

  a*10^2 + b*10^1 + c*10^0
  a*10^2 + c*10^1 + b*10^0
  b*10^2 + a*10^1 + c*10^0
  b*10^2 + c*10^1 + a*10^0
  c*10^2 + a*10^1 + b*10^0
  c*10^2 + b*10^1 + a*10^0

Now if I add these up, I get

  2(a+b+c)*10^2 + 2(a+b+c)*10^1 + 2(a+b+c)*10^0 

which simplifies to 

  2(a+b+c)(10^2 + 10^1 + 10^0)

Does this shed some light on your problem? 

- Doctor Ian, The Math Forum   
Associated Topics:
High School Permutations and Combinations
High School Sets

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.