There was a [question][1] which could be interpreted as a question about Latin squares.  I presented at a problem session at our research group meeting at Monash, where it was completely resolved (at least, the part I'm directly interested in).

PS: Although, this is hardly a breakthrough.


  [1]: https://mathoverflow.net/questions/17255/counting-colored-rook-configurations-in-the-cube-when-is-it-even/17274#17274