Discussion
Seven friends P, Q, R, S, T, V and W are sitting in a straight line facing north not necessarily in the same order.
T is sitting fourth to the left of V.
W is sitting to the immediate left of T.
Q is sitting third to the right of W.
R is not an immediate neighbor of Q.
S is not an immediate neighbor of V.
V does not sit at an extreme end of the line.
Who amongst the following are sitting at the extreme ends of the line?
Answer: B
The line, from left to right, is W T S Q P V R.
T is fourth to the left of V, W is just left of T, and Q is third to the right of W. Put T in place p: then W is p − 1, Q is p + 2 and V is p + 4. W needs p of at least 2, and V must not be at the end, so p + 4 is at most 6. Only p = 2 works: W 1, T 2, Q 4, V 6.
Places 3, 5 and 7 remain for P, R and S. R is not next to Q, so R is not in 3 or 5 and must be 7. S is not next to V, so S is not 5 or 7 and must be 3. That leaves P in 5.
The extreme ends are therefore W and R (WR). P and S sit in the middle of the line, at places 5 and 3, so WP, PS and SR all name at least one person who is not at an end.
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