The oriented Oberwolfach problem (with only one table) and its solution are the following.
In a meeting of $n$ people during $n-1$ days (combinatorists at Oberwolfach for concreteness), they all have diner around one table. As they only speak to their right neighbour, everybody wants to be seated each day with a different right neighbour. For which $n$ is this possible?
The answer is : this is always possible unless $n=4$ or $n=6$, as stated in this other question Round-robin party presents (or: Graeco-Latin square with additional cycle property) .
This can be rephrased abstractly in terms of graph theory, see the answer to the question above.
My question is : if $n=p$ is a prime, then one can use multiplication by the $p-1$ units in $\mathbf F_p$ to build a solution.
However, for other values of $n$, I don't know (and I didn't find it in the papers solving the problem, although it must be in there somewhere) how to build solutions.
For example, can anyone explain to me how to build a solution for $n=8$ (if possible with a strategy no too ad hoc)?
