The smallest possible symmetric latin square is the order of 4 which is $$\matrix{1&2&3&4\cr 2&1&4&3\cr 3&4&1&2\cr 4&3&2&1}$$ but i'm also wondering if any order of odd/even latin square can be symmetrical like for example the order of 9 & 10?
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What about the latin square of order 2? $\begin{array}{rr} 1&2\2&1 \end{array}$ – xxxxxxxxx Jun 14 '17 at 04:09
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For any $n$, $$\matrix{1&2&3&\cdots&n\cr 2&3&4&\cdots&1\cr 3&4&5&\cdots&2\cr \vdots&\vdots&\vdots&\ddots&\vdots\cr n&1&2&\cdots&n-1\cr}$$ is a symmetric Latin square.
David
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