Henry Ernest Dudeney/Modern Puzzles/171 - An Irregular Magic Square/Solution

by : $171$

 * An Irregular Magic Square
 * Here we have a perfect magic square composed of the numbers $1$ to $16$ inclusive.


 * $\begin{array}{|c|c|c|c|}

\hline 1 & 14 & 7 & 12 \\ \hline 15 & 4 & 9 & 6 \\ \hline 10 & 5 & 16 & 3 \\ \hline 8 & 11 & 2 & 13 \\ \hline \end{array}$


 * The rows, columns, and two long diagonals all add up to $34$.
 * Now, supposing you were forbidden to use the two numbers $2$ and $15$, but allowed, in their place, to repeat any two numbers already used,
 * how would you construct your square so that rows, columns, and diagonals should still add up to $34$?
 * Your success will depend on which two numbers you select as substitutes for $2$ and $15$.

Solution
Substitute $7$ and $10$ for $2$ and $15$, and we get:


 * $\begin{array}{|c|c|c|c|}

\hline 1 & 10 & 9 & 14 \\ \hline 13 & 10 & 5 & 6 \\ \hline 8 & 3 & 16 & 7 \\ \hline 12 & 11 & 4 & 7 \\ \hline \end{array}$