Have you noticed how often magic
squares pop up in mathematics? They can be different sizes (a three
by three square or even a five by five square), use different
numbers (single or more digits) and have different totals (15, 34
or something completely different). There are many variations on
how magic squares work.
Here is one type of magic square that you can make to baffle and
bewilder friends? Is there a trick to making them? Not a trick but
certainly a method.
This example uses a four by four square, but you can draw whatever
size square you choose.
You will need
Paper and a pencil.
- On the outside of the square, write a series of numbers.
- Add the numbers together to find their total. Write the total
on a card.
- The total of the numbers below is 40.
- You might want to adjust your numbers to get a particular
- Add the number at the beginning of a row with the number above
the column and write the total in the corresponding cell on the
- E.g. Above, 7 has been added to 4 and the sum, 11, placed in
the corresponding cell. 2 has been added to 5 and the sum, 7,
placed in the corresponding cell.
- Continue until the matrix is completed and then cut it
- Find a friend to baffle
- Put the card with the total on in an envelope and hand it to
- Ask your friend to choose any number from the top row and to
- Then, cross out all of the other numbers in that row, and the
numbers in the column the number is in.
- In the second row, circle a number that is not crossed
- Cross out the remaining numbers in its row and column.
- Do the same in the other two rows.
- Have your friend add the circled numbers together. Now add the
numbers on each diagonal. Compare the three answers.
- Ask your friend to open the envelope and let them be surprised
that the answers are all the same.
- You can always have your friend repeat the steps and choose
different numbers from the rows.
- What do you think will happen? Can you explain why?