Magic Square

By an exhaustive process of elimination I can work this out as 39, but there must be a quicker strategy for solving these kind of questions. Advice please.


1 Answer 1


Hint: The sum of all $9$ numbers is $43+51+59+39+47+55+63+67+71 = 495$, so each row must sum to $495/3 = 165$.

EDIT: Alternatively, you can apply the linear transformation $x \to \dfrac{x-35}{4}$ to all of the numbers. Then, the numbers already filled in are $2$, $4$, and $6$ and the missing numbers are $1$, $3$, $5$, $7$, $8$, and $9$. So, if you know what a $3 \times 3$ magic square looks like, you can easily fill in the missing numbers. Finally, undo the transformation using $x \to 4x+35$.


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