The following small result has been sitting untouched in my research folder since December, 2014. As I have not been able to produce other interesting results in the field it has remained unpublished until now.
A hypergraph is properly 2-colorable if its vertex set can be colored blue and red such that there is no monochromatic edge.
Lemma 1 (TRM, 2014). Let $\mathcal{H}$ be an $r$-uniform hypergraph on $n$ vertices.

We partially solve an additive combinatorial problem and then use it to construct optimal pairing strategies for certain generalised Tic-Tac-Toe games.

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