Henry Ernest Dudeney/Modern Puzzles/175 - Is it Very Easy/Solution
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Modern Puzzles by Henry Ernest Dudeney: $175$
- Is it Very Easy?
- Here is a simple magic square, the three columns, three rows, and two diagonals adding up to $72$.
$\qquad \begin{array}{|c|c|c|} \hline 27 & 20 & 25\\ \hline 22 & 24 & 26 \\ \hline 23 & 28 & 21 \\ \hline \end{array}$
- The puzzle is to convert it into a multiplying magic square,
- in which the numbers in all the eight lines if multiplied together give the same product in every case.
- You are not allowed to change, or add to, any of the figures in a cell
- or use any arithmetical sign whatever!
- But you may shift the two figures within a cell.
- Thus, you may write $27$ as $72$, if you like.
Solution
All $8$ rows give the same product $4096$:
$\qquad \begin{array}{|c|c|c|} \hline 2^7 & 2^0 & 2^5\\ \hline 2^2 & 2^4 & 2^6 \\ \hline 2^3 & 2^8 & 2^1 \\ \hline \end{array}$
As Dudeney reminds us:
- Of course, every arithmetician knows that $2^0$ equals $1$.
Sources
- 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Solutions: $175$. -- Is it Very Easy?
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $388$. Is it Very Easy?