Let's analyze the conditions step by step to determine who is sitting at the extreme ends.
1. P is fourth to the right of T:
- This implies if T is at position [tex]\( x \)[/tex], then P must be at position [tex]\( x + 4 \)[/tex].
2. W is fourth to the left of S:
- This implies if S is at position [tex]\( y \)[/tex], then W must be at position [tex]\( y - 4 \)[/tex].
3. R and U, which are not at the ends, are neighbours of Q and T respectively:
- R is a neighbor of Q, so R must be adjacent (either to the left or right) to Q.
- U is a neighbor of T, so U must be adjacent (either to the left or right) to T.
4. W is next to the left of P and P is the neighbour of Q:
- W is immediately to the left of P.
- P is adjacent to Q.
To position them accurately, let's start by placing T and then positioning the others relative to T.
### Step-by-Step Arrangement:
1. T and P:
- Let T be at position 1 (leftmost position).
- Thus, P must be at position 5: [tex]\( \{ T, \_, \_, \_, P, \_, \_, \_ \} \)[/tex].
2. W and S:
- Since W is next to the left of P, W must be at position 4: [tex]\( \{ T, \_, \_, W, P, \_, \_, \_ \} \)[/tex].
- P is supposed to be a neighbor of Q. Let's keep this in mind.
3. Determine S's position:
- W is fourth to the left of S, hence S must be at position 8 (since W is at position 4): [tex]\( \{ T, \_, \_, W, P, \_, \_, S \} \)[/tex].
4. Q and Neighbors:
- Since P is a neighbor of Q and P is at position 5, the only possible positions for Q are 4 or 6. But position 4 is occupied by W, so Q has to be at position 6: [tex]\( \{ T, \_, \_, W, P, Q, \_, S \} \)[/tex].
5. Position of R and U:
- U is a neighbor of T, and the possible positions for U are 2 or 3 (right next to T which is at position 1). Since R is also not at the ends, position 2 is a viable option for U: [tex]\( \{ T, U, \_, W, P, Q, \_, S \} \)[/tex].
- R is a neighbor of Q, and the only open position adjacent to Q (position 6) is position 7: [tex]\( \{ T, U, \_, W, P, Q, R, S \} \)[/tex].
7. Checking placement of P, Q, and W:
- W is placed correctly relative to P.
- P and Q are neighbors.
- R is neighbors with Q, and U is neighbors with T, both not at the ends.
Thus, the final arrangement is: [tex]\( \{ T, U, \_, W, P, Q, R, S \} \)[/tex].
### Who is sitting at the extreme ends?
The ends are T at the leftmost position and S at the rightmost position.
Hence, the answer is:
(d) T and S
