Problem: A club with members is organized into four committees in accordance with these two rules: (1) Each member belongs to two and only two committees. (2) Each pair of committees has one and only one member in common. Then :
Answer Choices:
A. cannot be determined
B. has a single value between and
C. has two values between and
D. has a single value between and
E. has two values between and
Solution:
This problem may be interpreted as a miniature finite geometry of lines and points, so that each pair of lines has only point in common, and each pair of points has only line in common.
or
, displayed as follows