Henry Ernest Dudeney/Puzzles and Curious Problems/107 - A Square of Digits

Puzzles and Curious Problems by Henry Ernest Dudeney: $107$

A Square of Digits

$\qquad \begin{array}{|c|c|c|} \hline 2 & 1 & 8 \\ \hline 4 & 3 & 9 \\ \hline 6 & 5 & 7 \\ \hline \end{array} \qquad \begin{array}{|c|c|c|} \hline 2 & 7 & 3 \\ \hline 5 & 4 & 6 \\ \hline 8 & 1 & 9 \\ \hline \end{array} \qquad \begin{array}{|c|c|c|} \hline 3 & 2 & 7 \\ \hline 6 & 5 & 4 \\ \hline 9 & 8 & 1 \\ \hline \end{array}$

The $9$ digits may be arranged in a square in many ways,

so that the numbers formed in the first row and second row will sum to the third row.

We give $3$ examples, and it will be found that the difference between the first total, $657$, and the second total, $819$,

is the same as the difference between the second, $819$, and the third, $981$ --

that is, $162$.

Now, can you form $8$ such squares, every one containing the $9$ digits,

so that the common difference between the $8$ totals is throughout the same?

Of course it will not be $162$.

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $107$. -- A Square of Digits
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $135$. A Square of Digits