Henry Ernest Dudeney/Puzzles and Curious Problems/290 - A Four-Figure Magic Square/Solution
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Puzzles and Curious Problems by Henry Ernest Dudeney: $290$
- A Four-Figure Magic Square
- In this square, as every cell contains the same number -- $1234$ -- the three columns, three rows and two long diagonals naturally add up alike.
$\qquad \begin{array} {|c|c|c|} \hline 1234 & 1234 & 1234 \\ \hline 1234 & 1234 & 1234 \\ \hline 1234 & 1234 & 1234 \\ \hline \end{array}$
- The puzzle is to form and place nine different $4$-figure numbers (using the same figures) so that they shall form a perfect magic square.
- That is, the numbers all together must contain nine of each of $1$, $2$, $3$ and $4$, and they must be proper numbers without using fractions or any other trick like that.
Solution
$\qquad \begin{array} {|c|c|c|} \hline 2243 & 1341 & 3142 \\ \hline 3141 & 2242 & 1343 \\ \hline 1342 & 3143 & 2241 \\ \hline \end{array}$
The magic constant is $6276$.
Sources
- 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $290$. -- A Four-Figure Magic Square
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $390$. A Four-Figure Magic Square