1 2 3 4 5 6 7 8 9 0 = 100
Date: 01/24/2002 at 05:52:15 From: Connie Subject: Numbers Adding Together Dear Dr. Math, 1 2 3 4 5 6 7 8 9 0 = 100 Leave the numerals in this order. Place only addition and subtraction signs to make it a true statement. I have figured out that you can leave some of the numbers, for example you don't have to put signs in every one of them. You can say: 123 - 4 + 5 + 6 + 7890 = 100 or something like that. Please write back. Connie Chen
Date: 01/27/2002 at 10:59:17 From: Doctor Steve Subject: Re: Numbers Adding Together Dear Connie Chen, I like what you have figured out. My first thought is that there must be lots of ways to do this and I think the key is to pick some combination as a starting point and then see if I can make the other numbers work out. In this case I tried starting with a simple combination that I know would make 100, and see if I can make the rest of the numbers cancel each other out. If I use 90, then I just need 10 more to make 100. I could add 8 and 2 to make 10. So far I have: + 2 + 8 + 90 = 100 Then all I need to do is figure out how 1,3,4,5,6,and 7 can be combined to cancel each other out. So I'll use my method again and pick a combination and see if I can make it work. 6 + 7 is 13. Can I make the other numbers equal to 13? Hey, 1 + 3 + 4 + 5 is 13. So, I just need to subtract those. - 1 - 3 - 4 - 5 + 6 + 7 Perfect. Now I could just combine those numbers with my original choices and I'll have 100. Do you see how? Try another combination and see if you can make it work. - Doctor Steve, The Math Forum http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.