The Joy of Set: Hint 1

Problem: http://gottablogsomewhere.blogspot.com/2012/09/better-living-through-mathematics-set.html

Hint 1: Choosing any two Set cards, there is exactly one card which will complete a Set.

We know this because in a Set, all four attributes of the three cards must be the same, or they must all be different. Each attribute has three values, so the third card has exactly one way to be either the same or different in each attribute from the other two. Each card is unique, giving us 3⁴ = 81 Set cards.