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A club with $x$ members is organized into four committees such that

(1) each member is in exactly two committees,

(2) any two committees have exactly one member in common.

Then $x$ has

(A) exactly two values both between $4$ and $8$

(B) exactly one value and this lies between $4$ and $8$

(C) exactly two values both between $8$ and $16$

(D) exactly one value and this lies between 8 and 16.

Any hints on how to approach this problem ?

Shaun
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square_one
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  • Please share your thoughts so far :) – Shaun May 06 '14 at 12:13
  • I just started arranging from scratch. Like there are 4 bins. I put member1 in bins 1 and 2. Then member2 in bins 2 and 3 .. and so on. I arrived at 6 members. I dont know how to check if there is a solution between 8 and 16 or any other option .. :( – square_one May 06 '14 at 12:21

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