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 3rd 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:
David
Some interesting background history on Magic Squares in art, science and culture on this blog: www.glennwestmore.com.au
ReplyDeleteExploring alpha magic squares blends the elegance of recreational mathematics with the quirky linguistic challenges of wordplay. Unlike traditional magic squares—where rows, columns, and diagonals sum to the same constant—an alphamagic square takes the concept a step further: when you replace each number with the word for that number (like "five" or "twelve"), the count of letters in those words forms yet another valid magic square. Pioneered by mathematician Lee Sallows, these fascinating dual structures challenge codebreakers, mathematicians, and puzzle lovers to test the limits of language-dependent symmetry. For anyone taking a quick breather from solving combinatorial math puzzles, exploring linguistic curiosities, and looking for engaging digital entertainment to check out, feel free to visit https://spinmamas.com.
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