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

Puzzles and Curious Problems by Henry Ernest Dudeney: $289$

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.

$\qquad \begin{array} {|c|c|c|} \hline \ \ & \ \ & \ \ \\ \hline \ \ & 5 & \ \ \\ \hline \ \ & \ \ & \ \ \\ \hline \end{array}$

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 $3$.

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Magic Square, Measuring, Weighing, and Packing Problems: $289$. -- Magic Square Trick
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Combinatorial & Topological Problems: Magic Square Puzzles: $389$. Magic Square Trick