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UKMT Junior Mathematical Challenge, 2017

Number theory Difficulty 2.0 Junior Find the answer United Kingdom

In a magic square, the numbers in each row, each column and the two main diagonals have the same total. This magic square uses the integers 2 to 10, with the grid shown having entries 10,510, 5 in the top row (top-left cell blank), 8,48, 4 in the middle row (middle cell blank), and 7,27, 2 in the bottom row (bottom-right cell blank). Which of the following are the missing cells?

(A) 693\begin{array}{c}6\\9\\3\end{array} (B) 639\begin{array}{c}6\\3\\9\end{array} (C) 396\begin{array}{c}3\\9\\6\end{array} (D) 369\begin{array}{c}3\\6\\9\end{array} (E) 963\begin{array}{c}9\\6\\3\end{array}

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