Chapter 1.2, Problem 34E

Applying What You’ve Learned.

A magic square is a square arrangement of numbers such that if you add the numbers in any row, column, or diagonal, you always get the same sum. In the magic square shown here, called a 3-by-3 square, the sum of any row, column, or diagonal is always 15.

8	1	6
3	5	7
4	9	2

In Exercise 33 and 34, the magic squares use each of the integers from 1 to 16 exactly once. Use deductive reasoning to

a. Determine the total of all the numbers in the square.

b. Determine the total for each row, column, and diagonal.

c. Complete the magic squares.

Explain your reasoning.

16	3		13
5			8
	6		12
4		14