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.

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- Nov 17th 2008, 12:12 PMgager23magic 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 PMSoroban
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.

**very**logical procedure.

$\displaystyle \text{We have the numbers: }\;9, 11,13,15,\underbrace{17}_{\uparrow},19,21,23,25$

Isn't it reasonable to put the*middle*number in the center of the circle?

Next, take pairs of numbers "from each end": .$\displaystyle (9,25),\:(11,23),\:(13,21),\:(15,19)$

. . 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 PMgager23magic circle
Thanks for the reply--it makes sense and is appreciated.