Post date: Oct 02, 2017 6:58:24 PM
Magic squares have a long history in both Western and Eastern culture and mathematics. They can be found on tablets and temples in India and China and closer to home on Sagrada Família in Barcelona. For the kids they present good puzzles for mental arithmetic and logical thinking.
Follow the link for more info on the Chinese history of the magic square which is referred to as Lo Shu.
The most magic of all 4x4 magic squares. The "Chautisa Yantra" from the Parshvanatha temple in Khajuraho, India.
What we did:
First we played the following 2 player game. Write down the number 1,2,3,4,5,6,7,8,9. The players take alternating turns in choose number from the list. Once a number is chosen it is crossed out and can not be used again. The aim is to be the first player to be able to make a sum of 15 with exactly 3 of the number you have chosen. For example is player 1 ends up with the numbers 4, 6, 1, 5. Then player 1 wins as 4+6+5 = 15. Although it is easy enough to think one move ahead to block your opponent from getting 15 it is had to think 2 moves ahead. What does this have to do with magic squares...well.
Here is an example of a 3x3 magic square (image from https://en.wikipedia.org/wiki/Magic_square).
It is an grid with the number 1 - 9 such that the rows, columns and diagonals add to 9. There is only once such square not counting rotations and reflections.
Once I wrote the magic square on the board some kid saw immediately that......the game we were playing is just tic-tac-toe !!!!
The kids then realized this is now boring and wanted bigger squares, which is just what I had prepared :)
A 4x4 magic square has the numbers 1 - 16. The rows, columns and diagonals add to 34. Although there are 880 such magic squares they are hard to figure out. So I gave the kids a partially filled one and they had to figure out the remaining numbers. (See links below for online games like this.)
Then I showed them the magic square pictured above from the Indian temple.
This is the most perfect of magic squares as it has lots of other "34"s hiding in there, not just rows, columns and diagonals. How many patterns can you see. Looks at the corners of different sized squares. Even looks the "split" diagonals the wrap around the big square (eg, 12, 8, 5, 9).
Things to try at home:
Make up your own versions of the game above. Pick different numbers and totals.
Try to find some other 4x4 magic squares. Just starting at random is very hard. Instead start with 1 to 16 in order in the square and then start rearranging numbers in a systematic way. Warning: This is not easy..don't give up too soon!
Links:
Click on the 4x4 square puzzles here: http://www.magicsquarepuzzles.com/
Here is one way to build a 4x4. http://www.mrexcel.com/tip069.shtml