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

by : $107$

 * A Square of Digits

Solution

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

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


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

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

The common difference is $9$.