Square=9
Square Root=3
note:prime numbers are bold.
Columns and Rows add up to 15 vertically,horizontally and diagonally.
Notes for Odd-Numbered Magic Math Squares
(they may or may not be applicable to even numbered magic math squares; I haven't done the research yet):
The number in the bottom left corner ("A"), minus the number in the top left corner ("B"), plus the number in the top right corner ("C") equals the number in the lower right corner ("D"). Or: A-B+C=D
Place the square number of the puzzle just above the central puzzle square, where both diagonals cross. Place the number "1" just below the central puzzle square, and the square root just to the left of the central puzzle square.
To find the total sum that all columns, rows or diagonals add up to, take the one number common to both diagonals (the number in the exact center of the puzzle) or "X", and multipy it with the square root. Or: "X" x "square root"="grand total".
For example, in the case of the Three Square, the number common to both diagonals is the number "5". "3" is the square root for the Three magic math square, so 3x5=15.
If the square has been solved correctly, the numbers in all columns, diagonals and rows should total 15.
To find the number common to both diagonals- that is, the number in the exact center of the puzzle, add "1" to the square number and then divide by 2: 1+9=10,10/2=5
Having determined this, you can then proceed to figure out the numbers in the diagonal columns:
1)Numbers in the diagonal column going from the top right-hand corner to the bottom left-hand one increase in increments of whatever number the magic square puzzle is. That is, in this 3 square puzzle they increase by 3- in a five square magic puzzle the increment would be 5, and so on.
2)Numbers in the diagonal column going from the top left-hand corner to the bottom right-hand corner increase in increments of "1"- regardless of whatever the number of magic math square puzzle is.
Personal Note:
I'm not a mathematician, far from it. In fact, most of my life I've been "afraid" of mathematics. It was not until after I had had a concussion (of all things) that I experienced a sudden desire to solve magic math square puzzles. I suppose this was the one "good" side effect, because all the other symptoms were really unpleasant- insomnia, wild mood swings, dizziness,feeling fuzzy, confused and shaky, and in the midst of all those, sudden moments of lucidity. It was during these times of lucidity that suddenly, for the first time in my life, the beauty of mathematics became clear to me.
I don't know how to explain things the way a mathematician would. I don't even know some of the proper mathematical terms yet.
Some of my notes provide no adequate explanation as to why this works (such as the location of the square, square root, and number 1)- this is frustrating to me also. If I find out why, I will then write it. All I know at this time is that this is how I have successfully solved odd-numbered magic math puzzles:-)