The first 9 positive odd integers are placed in the magic square so that the sum of the numbers in each row, column and diagonal are equal. Find the value of $A+E$.
(A) 32
(D) 24
(B) 28
(C) 26
(E) 16

| $A$ | 1 | $B$ |
| :--- | :--- | :--- |
| 5 | $C$ | 13 |
| $D$ | $E$ | 3 |

Part C (8 credits each)
The first 9 positive odd integers are placed in the magic square so that the sum of the numbers in each row, column and diagonal are equal. Find the value of $A+E$.
(A) 32
(B) 28
(C) 26
(D) 24
(E) 16

| $A$ | 1 | $B$ |
| :---: | :---: | :---: |
| 5 | $C$ | 13 |
| $D$ | $E$ | 3 |

## Solution

The first nine odd positive integers sum to 81 .

This implies that the sum of each column is $\frac{81}{3}$ or 27 . From this we immediately see that $B=11$ since $B+13+3=27$. If we continue with the constraint that each row or column must add to 27 then $A=15 \rightarrow D=7 \rightarrow E=17$. Therefore, $A+E=15+17=32$.

ANSWER: (A)

## Part C