Henry Ernest Dudeney/Puzzles and Curious Problems/289 - Magic Square Trick

by : $289$

 * Magic Square Trick
 * Here is an advertising trick that appeared in America many years ago.


 * Place in the empty squares such figures (different in every case, and no two squares containing the same figure)
 * so that they shall add up to $15$ in as many straight directions as possible.


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

\hline \ \ & \ \ & \ \ \\ \hline \ \ & 5 & \ \ \\ \hline \ \ & \ \ & \ \ \\ \hline \end{array}$
 * ''A large prize was offered, but no correct solutions received.

To explain further:
 * Each cell is expected to contain a different number of instances of the same digit, combined to form an expression;
 * Each cell contains a different digit, of whatever multiplicity;
 * The results of evaluation of these expressions should add to $15$ in as many directions as possible;
 * The individual digits themselves, were they to occur singly (as the $5$ does in the example), themselves form a magic square of order $3$.