Set game

At Liz and Nodira’s party last weekend (pictures here), we played one of Nodira’s favorite games, Set, at which I suck. The game involves cards with four attributes (shape, number, texture, and color) of three values each, and the goal is to find a set of three cards whose attributes have the same value or all different values. The actual rules are on Wikipedia. While I was losing the game, I had plenty of time to consider the following puzzle: what is the maximum number of cards you can deal without getting a valid set? One deals 12 cards in the game for convenience, but this does not guarantee a valid set (this situation actually came up that evening). The Set website actually has a solution which I think is wrong, so I post my own solution in the comments, which may also end up being wrong. Bonus question: what is the probability that 12 cards chosen uniformly at random does not contain a set?

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~ by Paul Pham on 12 September 2006.

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