# Magic Squares of Even Order (November 29 to December 2)

The students heard the story of Chinese Emperor Yu who found a turtle in the year 2200BC with a magical puzzle on its shell.  The pattern was a three by three grid with dots numbered from 1 through 9.  Each row, column, and diagonal had the same sum.  This magic number 15 was instrumental in bringing good luck to the people of China living on the Yellow River.

In the last few decades, hundereds of charms have been excavated from 4000-2000 years ago depicting 3x3 and 4x4 magic squares.  People of China and India believed if you wore a magic square around your neck, it would bring you good luck and ward off evil spirits.

I told the Mathletes that if they could create magic squares of the order 4x4, 8x8, 12x12, 16x16, etc. that it would bring them great luck and lots of Mathlete dollars.

The learning goals here are:

1. being able to draw diagonals seperated by every four squares; this is a difficult task for many students as they are focused on their pencils instead of the next vertex.  I have supplied a packet of material with the diagonals already printed in case they get frustrated.
2. once they have their diagonals, students start writing down consecutive whole numbers from one to the square of the grid order. For a 4x4 grid, 16; for a 8x8 grid, 64, and so on.  NOTE: only write down numbers in the squares with a diagonal.
3. Once they reach the last square with the proper square number, then they write the whole numbers from one to the square of the grid order, starting with the last square and working backwards, only placing a number in an empty square.
4. Add any row, column or diagonal to find the magic number.  Check a few for accuracy.
The pdf file explains this in detail and the word documents are the templates to create the magic squares.  This challenge has been studied by countless mathematicians over the centuries including Ben Franklin.

AttachmentSize
Magic_Squares_Even.doc204 KB
Magic_Squares_Even_with_diagonals.doc213.5 KB
Magic_Squares_Even_Ordered_Multiples_of_4.pdf412.21 KB