Monday, October 19, 2020

Magic Square




I used the technique to solve the magic square that I learnt in high school. I know how to do 3 x 3 magic square, but now I use the method to solve 5 x 5 magic square. 

Things to remember while solving magic square:

1. Always start from the center of the first row and fills the box with your starting number.

2. From that box, follow the diagonal upward arrow (only for one box) to place the next consecutive number.

3. If there is no box at the diagonal upper right, then imagine as a box and follow the arrow vertically (downward) and horizontally (left) to the last empty box of the magic square.

4. If the box at diagonal arrow is filled, then follow the arrow downward(only one box) without using a diagonal arrow.

5. Repeat from step 2 until all the boxes are filled.

Although I know that using this technique, we need to start from the middle of the first row, but due to curiosity, I tried starting from the left corner, right corner, and centre of the second row as well. But this technique does not work for those places. Here are the pictures: 


The technique doesn't work on even number magic squares such as 4 x 4 or 6 x 6 because the square is divided evenly and there is no center for any row or column.


1 comment:

  1. Very cool algorithm, Amrit!! Your 5X5 magic square worked out beautifully. This reminds me of a lecture on magic squares that the late, great John Conway gave at the Bridges Math and Art conference a couple of years ago. Would you be willing to share this in class if we have time?

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