Magic Triangle Sums
Date: 02/04/2003 at 10:44:56 From: Keri Subject: Consecutive Numbers There is a triangle with spots for 6 numbers. Each side must add up to the same sum using each number only once. Find 6 consecutive odd numbers such that their magic triangle sum is 25. Find 6 consecutive numbers such their magic triangle sum is 4. I'm certain this is simple but I just had a brain lock.
Date: 02/04/2003 at 12:00:35 From: Doctor Kastner Subject: Re: Consecutive Numbers Hi Keri - The following answer from the Dr. Math archive will tell you some of what you want to know: Magic Triangle Puzzle http://mathforum.org/library/drmath/view/57520.html But some intuition and trial and error will help with these problems. For the first one, I looked at the required sum of 25 and thought that the numbers 7,9,11 would probably be in there, since they are about 1/3 of the sum. Note that you can't use 1, since if that were your first odd number, your set would have to be 1,3,5,7,9,11 and the largest sum you can make with 1 is 1+9+11 = 21, which is too small. On the flip side, you can't use 15, since that set would be 5,7,9,11,13,15 and the smallest sum you can make with 15 is 15+7+5 = 27, which is too big. Therefore, I used 3, 5, and 13, and the set that works is 3,5,7,9,11,13. For the second problem, it was clear that I have to have negative numbers if I only want a sum of 4, so I tried starting with -2. That gives me the set -2,-1,0,1,2,3, but the largest sum I can get from using the number -2 is -2+2+3 = 3, so that can't work. Starting with the number -1 looked better as it would result in the set -1,0,1,2,3,4 and it can cancel out the 5 that results from 4+1 or 3+2. I hope this helps. Let me know if you'd like to talk about this some more, or if you have any other questions. - Doctor Kastner, The Math Forum http://mathforum.org/dr.math/
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