In Newtown Middle School, there was a school boy named Chris who was an absolute troublemaker. One of his many schemes against the school was drawing squares in permanent marker on all the walls in the school. Thus, when the school decided to make a punishment for Chris, they decided to do something involving squares.

The school made Chris create all possible unique Greco-Latin squares using A-D and 1-4. (A 4x4 Greco-Latin square using A-D and 1-4 is a special 4x4 square. Each cell of the square has exactly one letter of the four and one number of the four within it. The end result will have every letter and every number used once in each row, column, and main diagonal of the square.)

Chris is a very slow boy, and after several hours, he figured out all the possible Greco-Latin squares. How many squares did he find?

A Greco-Latin square can be changed into a solution to the typical magic square problem.

We can just exchange each letter with a different multiple of N (in an NxN square) and add that to the number, and a magic square is created.  Not every magic square solution can be made this way.

I mention this, because earlier, I found myself helping someone do a 4x4 magic square (those math teachers!) and was surprised how long it took.  Only afterwards did I realize that I could use a solution equivalent to one of the Greco-Latin square solutions, which are much easier to find.

Posted by Tristan on 2005-05-24 23:35:38