# 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: $135$