In a magic square, the sum of the numbers in each row, column, and diagonal is the same. In the magic square below, what is the value of $a+b+c$?

| 16 | 2 | $a$ |
| :---: | :---: | :---: |
| $c$ | 10 | $d$ |
| $b$ | $e$ | 4 |
Solution

The common sum for the rows, columns, and diagonals is $16+10+4=30$. Analyzing the sums of the rows and columns, we have:

I) From $2+10+e=30$, it follows that $e=18$.

II) From $b+e+4=30$, it follows that $b=8$.

III) From $16+c+b=30$, it follows that $c=6$.

IV) From $16+2+a=30$, it follows that $a=12$.

Therefore, $a+b+c=26$.