# Competition #5: Magic Squares

In Competition #1 the last question has a magic square.

Please read the rules in Competition #1 or in the New Competition  (#2) before you answer the questions below.

Q1. Below is a 3 x 3 magic square. Please put the numbers 1, 2, …, 9 (once only) in the cells below so that each row, column, and diagonal adds up to the same number. See the clue below if you need to! Q2. What must each row, column, and diagonal add up to in a 4 x 4 magic square?

Q3. The solution to a 4 x 4 magic square similar to the one in Competition #1 was known at least as early as 16th century. Find an artwork that contains this magic square.

Please make sure you try the last question in Competition #1  before you answer Q3.

Read a clue to solving the 3 x 3 magic square below (scroll down): Every row, column, and diagonal needs to add up to the same number.

Since all the columns contain the numbers 1, 2, …, 9, the sum of all the columns needs to add up to 1+2+3+4+5+6+7+8+9 = 45.

Since there are 3 columns, each column must add up to 45/3 = 15.

What number do you think will go in the middle square in the 3 x 3 magic square?

What must each row, column, and diagonal add up to in a 4 x 4 magic square?

Try to complete the 4 x 4 magic square in Competition #1.