Nine individuals - Z, Y, X, W, V, U, T, S and R - are the only candidates, who can serve on three committees-K1, K2 and K3, and each candidate should serve on exactly one of the committees. Committee K1 should consist of exactly one member more than committee K2. It is possible that there are no members in committee K3. Among Z, Y and X none can serve on committee K1. Among W, V and U none can serve on committee K2. Among T, S and R none can serve on committee K3. In case committee K2 is served by T and Z only, how many of the nine individuals should serve on committee K3?
To solve this puzzle, we can use the given rules about the sizes of the committees, combined with the specific condition provided in the question.
We are given two fundamental rules regarding the number of members (size) in each committee:
We can substitute the first rule into the second rule to create a single equation relating the sizes of committees K2 and K3:
(Size(K2) + 1) + Size(K2) + Size(K3) = 9
2 × Size(K2) + Size(K3) = 8
The question provides a specific scenario to consider: "In case K2 is served by T and Z only".
This statement means that Committee K2 consists of exactly two members, T and Z.
So, for this scenario, Size(K2) = 2.
Now we can substitute Size(K2) = 2 into our combined equation:
2 × (2) + Size(K3) = 8
4 + Size(K3) = 8
Size(K3) = 8 - 4
Size(K3) = 4
Based on the given conditions, the number of individuals who should serve on committee K3 is 4.
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