Basic magic square
Figure 5
In the last activity you made 3 × 3 magic squares with the numbers 1 to 9. The center number was 5. The magic sum was 3 × 5 or 15. The even numbers were in the corners of the square.
Suppose you want to make a magic square using the numbers 2 to 10. All you have to do is add a 1 to each number in the magic square you already made. Before you do that, figure out what the magic sum should be. If you add a 1 to each number in a row, the magic sum should be 15 + 3 or 18. The center number is even and the numbers in the corners are odd.
• Sheet of paper. If you have centimeter or ½-inch graph paper, that would be helpful. Lined paper is also good.
• Pencil
• Eraser
• Ruler
1. Draw several squares, divided into nine small squares.
2. Copy a magic square in the previous activity, or use this basic magic square. Figure 5
3. Make a new magic square using the numbers 2 to 10. What is the magic sum? What is the center number?
4. Make another magic square using the even numbers from 2 to 18. Before you make the square, figure out what number to put in the center. What magic sum do you expect?
1. Suppose you take the basic magic square and multiply each number by three. What is the magic sum? What number goes in the center? What is the sum of all the numbers? Check your work by making the magic square.
2. Suppose you add 5 to each number in the basic magic square. What is the center number? What is the magic sum? What is the sum of all the numbers? Make the magic square and check your answers.
3. Choose any page of a monthly calendar. Draw a square around a 3 × 3 block of nine numbers. Figure 6
Rearrange these nine numbers to form a magic square. Here is a hint: the center number remains the same. If it is even, the corner numbers are odd; if it is odd, the corner numbers are even.
What is the sum of all the numbers? How is it related to the center number?
4. Muslim scholars purposely wrote magic squares with mistakes. Find the mistake in this magic square. The magic sum is 30. Figure 7
Calender square
Figure 6
Find the mistake
Figure 7
