Alpha Magic Squares

One of the newest development in the area of study related to magic squares is Alphamagic Squares.  

What are Alphamagic squares?   

Well if you have a magic square, and you copy that magic square, but instead of copying the numerals, but instead write the name of the number (5 becomes “five”, 18 becomes “eighteen”, etc.).  Now create a third square, but instead of writing the names of the numbers count the number of letters in the name of each number and write that number in the new square.  If the 3^rd square is a magic square then the first square is a alpha magic square.

Example:

5	22	18
28	15	2
12	8	25

Now consider the array of corresponding number words.

five	twenty-two	eighteen
twenty-eight	fifteen	two
twelve	eight	twenty-five

Counting the letters in each number word generates the following square which turns out to also be magic.

4	9	8
11	7	3
6	5	10

This square as a magic constant of 21.  All of the columns, all of the rows, and both diagonals sum to 21.  So the first square is an Alphamagic Square in English.  I may not work in French, or other languages.

REFERENCES:

http://en.wikipedia.org/wiki/Alphamagic_square

http://en.wikipedia.org/wiki/Lee_Sallows

http://www.leesallows.com/index.php?page_menu=Magic%20Squares&pagename=Alphamagic%20Squares

David