Orthogonal Latin Squares of Order 5/Mistake
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Source Work
1992: David Wells: Curious and Interesting Puzzles:
- The Puzzles:
- The Thirty-six Officers Problem
- $135$
- The Thirty-six Officers Problem
Mistake
- How can five each of As, Bs, Cs, Ds and Es be placed in these cells so that no letter is repeated in any row or column?
$\begin{array} {|c|c|c|c|c|} \hline \ \ & \ \ & \ \ & \ \ & \ \ \\ \hline & & & & \\ \hline & & & & \\ \hline & & & & \\ \hline & & & & \\ \hline \end{array}$
Correction
There is more to it than just arranging the letters so that no letter is repeated in any row or column.
We need to place $2$ letters in each space so that no letter of either pair is repeated in any row or column.
Otherwise we just get something like this boring arrangement:
$\begin{array} {|c|c|c|c|c|} \hline A & B & C & D & E \\ \hline B & C & D & E & A \\ \hline C & D & E & A & B \\ \hline D & E & A & B & C \\ \hline E & A & B & C & D \\ \hline \end{array}$
which is not what is being asked.
Sources
- 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): The Thirty-six Officers Problem: $135$