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### 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.

more, or if you have any other questions.

- Doctor Kastner, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Puzzles
Middle School Algebra
Middle School Puzzles

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