On the empty matrix, cover a random number with a penny. Cover all of the numbers in the same row with a paperclip (or whatever you have). Cover all of the numbers in the same column with a paperclip. Pick another number and do it again. Then do it twice more. You’ll be left with one uncovered number. Cover it with a penny.

Add up all of the numbers under the pennies. No matter what numbers are covered, you will always get 57 as the answer.

Here’s how it works.

The numbers outside of the matrix sum to 57. The value in each cell is the sum of that cell’s column + row. E.g., 12 + 7 = 19; 1 + 7 = 8; 4 + 7 = 11; … . In this square the 10 numbers outside the square add up to 57. When we put five pennies on cells, we’ve reduced that number of values we add together, but those five values must also sum to 57.

If you want to make your own magic square to amuse your family and friends, just take any old string of numbers, add them up, lay them out as in Fig. 9 (outside the matrix), do the calculation for each cell.

Alternatively, let’s say a family member’s birthday is coming up. You can work backwards to make a card which will reveal her age.

Wasn’t that an interesting diversion?