# One more puzzle

• Feb 15th 2011, 10:58 PM
whyonlyme
One more puzzle
Fill nine squares with numbers between 1 to 9

Rule: total of numbers from any side will be equal to 15.

If it have any formula, please tell me.
• Feb 16th 2011, 07:31 AM
Wilmer
• Feb 16th 2011, 12:15 PM
Soroban
Here's a method for a 4-by-4 Magic Square.

We have a 4-by-4 grid.
Consider the cells on the two diagonals.

. . $\displaystyle \begin{array}{|c|c|c|c|}\hline * &&& * \\ \hline & * & * & \\ \hline & * & * & \\ \hline * &&& * \\ \hline \end{array}$

Start at the upper-left and write then numbers one to sixteen in order,
moving to the right and down, but only in the diagonal cells.

. . $\displaystyle \begin{array}{|c|c|c|c|}\hline {\bf1} &&& {\bf4} \\ \hline & {\bf6} & {\bf7} & \\ \hline & {\bf10} & {\bf11} & \\ \hline {\bf13} &&& {\bf16} \\ \hline \end{array}$

Start at the lower-right and write the numbers 1 to 16 in order,
. . moving left and upward, but only in the empty cells.

. . $\displaystyle \begin{array}{|c|c|c|c|}\hline 1 & {\bf15} & {\bf14} &4 \\ \hline {\bf12} & 6 & 7 & {\bf9}\\ \hline {\bf8} & 10 & 11 & {\bf5}\\ \hline 13 & {\bf3} & {\bf2} & 16 \\ \hline \end{array}$

. . . ta-DAA!

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

This Magic Square is filled to capacity with the sum of 34.

The four rows, four columns, and two diagonals total 34.

And there are numerous symmetric sets which total 34.

. . . .Central 4 . . . . 4 Corners

. . $\displaystyle \begin{array}{cccc} * & * & * & * \\ * & @ & @ & * \\ * & @ & @ & * \\ * & * & * & * \end{array} \quad \begin{array}{cccc} @ & * & * & @ \\ * & * & * & * \\ * & * & * & * \\ @ & * & * & @ \end{array}$

. . $\displaystyle \begin{array}{cccc} @ & @ & * & * \\ @ & @ & * & * \\ * & * & * & * \\ * & * & * & * \end{array} \quad \begin{array}{cccc} * & * & @ & @ \\ * & * & @ & @ \\ * & * & * & * \\ * & * & * & * \end{array} \quad\begin{array}{cccc} * & * & * & * \\ * & * & * & * \\ @ & @ & * & * \\ @ & @ & * & * \end{array} \quad \begin{array}{cccc} * & * & * & * \\ * & * & * & * \\ * & * & @ & @ \\ * & * & @ & @ \end{array}$

. . $\displaystyle \begin{array}{cccc} @ & @ & * & * \\ * & * & * & * \\ @ & @ & * & * \\ * & * & * & * \end{array} \quad \begin{array}{cccc} * & * & @ & @ \\ * & * & * & * \\ * & * & @ & @ \\ * & * & * & * \end{array} \quad\begin{array}{cccc} * & * & * & * \\ @ & @ & * & * \\ * & * & * & * \\ @ & @ & * & * \end{array} \quad \begin{array}{cccc} * & * & * & * \\ * & * & @ & @ \\ * & * & * & * \\ * & * & @ & @ \end{array}$

. . $\displaystyle \begin{array}{cccc} @ & * & @ & * \\ @ & * & @ & * \\ * & * & * & * \\ * & * & * & * \end{array} \quad \begin{array}{cccc} * & @ & * & @ \\ * & @ & * & @ \\ * & * & * & * \\ * & * & * & * \end{array} \quad\begin{array}{cccc} * & * & * & * \\ * & * & * & * \\ @ & * & @ & * \\ @ & * & @ & * \end{array} \quad \begin{array}{cccc} * & * & * & * \\ * & * & * & * \\ * & @ & * & @ \\ * & @ & * & @ \end{array}$

. . $\displaystyle \begin{array}{cccc} * & @ & * & * \\ * & * & * & @ \\ @ & * & * & * \\ * & * & @ & * \end{array} \quad \begin{array}{cccc} * & * & @ & * \\ @ & * & * & * \\ * & * & * & @ \\ * & @ & * & * \end{array}$

Did I miss any?

• Feb 16th 2011, 11:15 PM
whyonlyme
• Feb 17th 2011, 02:41 PM
topsquark
Quote:

Originally Posted by whyonlyme

There is no "equation." But there are various and sundry methods. The one linked above on the 3x3 squares generates the only 3x3 square there is. (There are three others, but are the same square, just rotated around.)

-Dan
• Feb 17th 2011, 07:59 PM
whyonlyme
Can u explain any methods. ??
• Feb 17th 2011, 08:50 PM
Wilmer
• Feb 17th 2011, 08:56 PM
topsquark
Quote:

Originally Posted by whyonlyme
Can u explain any methods. ??

What exactly is it that you are looking for? The question has been answered. Unless there's more to the problem than you have been stating?

-Dan
• Feb 17th 2011, 08:58 PM
topsquark
And why are you posting this as a "puzzle?" It sounds more like a regular question to me?

-Dan
• Feb 17th 2011, 09:27 PM
whyonlyme
Quote:

Originally Posted by Wilmer

Sorry, I didn't see that you've posted the link. Sorry.

(Thinking)(Thinking)(Thinking)
• Mar 28th 2011, 09:56 AM
Inigo
This is an old mentalism trick to convince someone you have super math powers or can read minds.

What is a Magic Square?

Dr. Scott Xavier performs the Magic Square
• Apr 29th 2011, 11:41 PM
dkmathguy
Yes, I see a formula, lets try a 5x5 though so you could see the pattern
Fill 25 squares with numbers between 1 to 25

Rule: total of numbers from any side will be equal to 65.

Start with 1 in the middle top row. Then 2 should be one column to the right and one row up from 1, since there are no spot there, it goes to the way bottom of the column next right column from 1. Then 3 should be one column to the right and one row up. Then 4 should be one column to the right and one row up, since there are no spot there, it goes to the way left of the next top row where the 3 is at. Then 5 should be one column to the right and one row up from 4. Then 6 should be one column to the right and one row up from 5, but since 1 is there, it go below 5. etc

? / ? / 1 / 8 /15
? / 5 / 7 /14/16
4 / 6 /13/ ? / ?
10/12/ ? / ? / 3
11/ ? / ? / 2 / 9