the similar but easier game "spot it!" works better for playing with kids, i find. (i prefer it as an adult too - i thought i'd love set, but playing it feels more like work than fun to me.)
That post mentions the Fano Plane, which, incidentally, I first read about in the book How Not to Be Wrong by Jordan Ellenberg, a mathematician quoted in the article about Set that started this thread. In the book, he uses the Fano Plane to explain how to pick numbers for a specific kind of lottery.
[1] http://stackoverflow.com/questions/6240113/what-are-the-math...