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

by : $107$

 * A Square of Digits
 * $\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 $162$.