Sum of Integers in a SetDate: 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 problem? 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 numbers: abc acb bac bca cab cba 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 http://mathforum.org/dr.math/ |
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