UPDATE (1 February):
As there have not been any correct solutions so far, this riddle will run
another month, in parallel to a new February riddle. However, to make the
riddle easier next month, solvers can also answer about a largest set of
mutually orthogonal Latin squares of order p for a prime p.
Separate solver lists will be kept for each of the two cases.
This month's problem is a well-known one, so no Internet searching, please. I thank Ian Wanless for pointing it out to me. Let us begin with some definitions:
A
Here is an example of a Latin square of order 3 (which is to say:
Two Latin squares, R) is a bijection.
_{ij}An example of an order 3 Latin square that is orthogonal to the first one given is:
A set of Latin squares is called Now, to the question.
Let |
## List of solvers:## Prime order:Jim Boyce (1 February 07:42)Harald Bögeholz (8 February 09:13) ## Power of two order:Jim Boyce (1 February 07:42)Harald Bögeholz (10 February 07:27) |

Elegant and original solutions can be submitted to the puzzlemaster at __riddlesbrand.scso.com__.
Names of solvers will be posted on this page. Notify if you don't want
your name to be mentioned.

The solution will be published at the end of the month.

Enjoy!