Number of members
Algebra
Level
2
From the members of a club, four committees are formed such that:
- Each member belongs to only two committees.
- Each pair of committees has only one common member.
Find the number of members of the club.
The answer is 6.
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1 solution
Hint: The problem may be interpreted as a finite geometry of 4 lines and 6 points, so that each pair of lines has only one 1 point in common and each pair of lines has only one 1 line in common.