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

Modern Puzzles by Henry Ernest Dudeney: $171$

An Irregular Magic Square

Here we have a perfect magic square composed of the numbers $1$ to $16$ inclusive.

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

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 $15$.

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Magic Square Problems: $171$. -- An Irregular Magic Square
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Combinatorial & Topological Problems: Magic Square Puzzles: $384$. An Irregular Magic Square