Norman Do The Joy of SET 1

Certainly many a mathematician, from amateurs to professionals of some repute, have dabbled in the analysis of games. A particular one which has captured my own mathematical curiosity of recent times is the delightful, though little known, card game called SET. Some of the Gazette’s readership may already be well-acquainted with the game, but for the unenlightened, let us begin to answer the question, “What exactly is SET?” SET is a game played with a special deck of cards, each of which depicts either one, two or three objects. These objects can be any of three different shapes — oval, squiggle or diamond — and they are portrayed in one of three different colours — red, green or purple. Furthermore, the objects come in three different shadings — empty, striped or solid. One will never find two different shapes, colours or shadings on the same card. Therefore, each card can be described by the four attributes number, shape, colour and shading; and each of these attributes can take on one of three values as listed in the table below. Of course, you have probably already guessed that there are 3 = 81 cards in the standard SET deck, exactly one for every possible combination of number, shape, colour and shading.