Solution #21

Think of each club member as a point, and each committee as a line (the committee members will then be the points of intersection between lines). Then we want a four-line diagram in which each pair of lines intersect, and in which we never have more than two lines intersecting at the same point.

So each pair of lines must determine a unique intersection point. Since there are 4C2 = 6 pairs of lines, there must be 6 intersection points, and hence 6 members of the club.