A group of mathematicians who happen to be teenage girls decide to form a fashion gang. The rules of the gang are that every day each girl must wear a tank top that is either blue or black; sunglasses whose rims are either black or brown; capri pants that are black, red, white or pink; and lipstick that is pink, red or brown. Each pair of girls must differ in at least two of these items. For example, if they wear the same color tank top and lipstick, then they must differ in their choice of sunglass rims and capris. Differing in more than two items is also acceptable.

There are two challenges: What is the largest number of girls who could be in this gang, and what might each girl wear in that case? What is the minimum number of girls that could be in this gang so that they satisfy the difference constraint but adding one girl would violate the constraint? Again, show a possible outfit.

This article was originally published with the title Fashion Gang.

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