Problem 365

Using the second row, we see that the sum of the numbers in each row, column and diagonal must be $3.6 + 3 + 2.4 = 9$. Since the sum of the numbers in the first column must be 9, then the bottom left number must be $9 - 2.3 - 3.6 = 9 - 5.9 = 3.1$. Since the sum of the numbers in the top left to bottom right diagonal must be 9, then the bottom right number must be $9 - 2.3 - 3 = 9 - 5.3 = 3.7$. Since the sum of the numbers in the bottom row must be 9, then $3.1 + x + 3.7 = 9$ and so $x + 6.8 = 9$ or $x = 9 - 6.8 = 2.2$. We can complete the magic square as shown: $$\begin{array}{|c|c|c|} \hline 2.3 & 3.8 & 2.9 \\ \hline 3.6 & 3 & 2.4 \\ \hline 3.1 & 2.2 & 3.7 \\ \hline \end{array}$$