Crossword, Sudoku, ____ Latin bitrade (?)

It's the question we all have asked ourselves—what is the next puzzle craze going to be that's based on writing symbols in squares?

I noticed this paper that was just put into the arXiv (Nicholas J. Cavenagh, Ales Drapal, Carlo Hamalainen):

A latin bitrade is a pair of partial latin squares which are disjoint, occupy the same set of non-empty cells, and whose corresponding rows and columns contain the same set of entries. Dr\'apal (\cite{Dr9}) showed that a latin bitrade is equivalent to three derangements whose product is the identity and whose cycles pairwise have at most one point in common. By letting a group act on itself by right translation, we show how some latin bitrades may be derived from groups without specifying an independent group action. Properties of latin trades such as homogeneousness, minimality (via thinness) and orthogonality may also be encoded succinctly within the group structure. We apply the construction to some well-known groups, constructing previously unknown latin bitrades. In particular, we show the existence of minimal, $k$-homogeneous latin trades for each odd $k\geq 3$. In some cases these are the smallest known such examples.

Hmmm...How to make these into puzzles?

For example, see pg 13 of this.

Gathering for Gardner signatures

I've been busy working on G4G8, although you won't be able to see anything much there without the password, and even if you had it, there's not much more there that you can't see by clicking this, and scrolling down to the stained glass.

Instead I'll offer two signatures from today's email:

Esther Dyson:

Always make new mistakes!

Wei-Hwa Huang:

Everybody counts in base 10, but not everybody counts in base ten.