(50 POINTS)
The first 9 positive odd integers are placed in the following 3 by 3 grid in such a way that the sum of the numbers in each row, column, and main diagonal is the same. Four of the numbers are shown and the other five numbers are represented by the letters A, B, C, D, and E.
Determine the values of A, B, C, D, and E.

First clue: Looking at the first row and the right column, they both have the letter B in it, but the first row also has A. Since they both have B, A+1=13+3. Simplified, A = 15. So, I have figured out the first value.

Second Clue: I can see that B,C, and D all have a relationship. Because for B, the rows and columns add up to 16 only, but for C, the middle row adds up to 18. Therefore, the value of B must be 2 more than C. For the leftmost column, I can see that the other two numbers would add to 20, and middle row would only add up to 18. This shows that C is 2 more than D.

Using this information, I can find all their values since I know the 9 numbers that are supposed to be in each box. To figure out their values, I have to find three consecutive odd numbers.

The only numbers I have left are 7,9,11, and 17.

Now I know that D=7, C=9, and B=11.

All that is left is the number 17, and the letter E.

E=17.

According to the question, I have to find the value of A+E.

Since A=15, and E=17, 15+17=32.

The value of A+E=32.