# magic circles?

• Nov 17th 2008, 12:12 PM
gager23
magic circles?
Can anyone help me understand how to arrange the digits (odd only) 9-25 in a magic circle so that the sum of the numbers in each straight line is the same? There is one circle inthe middle and 8 around it. There must be a formula to this. Thank you.
• Nov 17th 2008, 03:05 PM
Soroban
Hello, gager23!

Quote:

Arrange the odd numbers from 9 to 25 in a magic circle
so that the sum of the numbers in each straight line is the same.
There is one circle inthe middle and 8 around it.

There really isn't any formula for this, but there is a very logical procedure.

$\text{We have the numbers: }\;9, 11,13,15,\underbrace{17}_{\uparrow},19,21,23,25$
Isn't it reasonable to put the middle number in the center of the circle?

Next, take pairs of numbers "from each end": . $(9,25),\:(11,23),\:(13,21),\:(15,19)$
. .
Note that the pairs have the same sum: 34.

Place the pairs on opposite ends of a diameter.

Then one possible solution looks like this:
Code:

              * 9 *           *    |    *       19      |      11       *  \    |    /  *             \  |  /       *      \ | /      *     21 - - - -17 - - - - 13       *      / | \      *             /  |  \       *  /    |    \  *       23      |      15           *    |    *               *25 *
• Nov 17th 2008, 03:28 PM
gager23
magic circle
Thanks for the reply--it makes sense and is appreciated.