P, Q, R, S and T are five speakers who have to speak on a particular day, not…

Concept: In a linear arrangement of n people, a clue of the form "k speakers after X" fixes X at position n − k, because exactly k positions must follow X. Symmetrically, "k speakers ahead of Y" fixes Y at position k + 1. A stated exclusion (such as “neither first nor last”) then eliminates candidate slots for whichever person remains undetermined, and a stated relative order (“X after Y”) breaks the tie between the last two open slots.

Application: Applying this to the five speakers (n = 5):

1. There are three speakers after S, so S's position is 5 − 3 = 2.

2. There are three speakers ahead of T, so T's position is 3 + 1 = 4.

3. Positions 2 and 4 are now taken by S and T; the remaining positions 1, 3 and 5 are open for P, Q and R.

4. R is neither the first nor the last speaker, so R cannot take position 1 or position 5 — R must take position 3.

5. Only positions 1 and 5 remain, for Q and P. Since P speaks after Q, Q must take the earlier position (1) and P must take the later position (5).

6. So the full order of speaking is Q, S, R, T, P.

Cross-check: Cross-check every clue against this order (Q, S, R, T, P):

• R is at position 3 — neither first nor last. Correct.

• Speakers after S (position 2) are R, T, P — exactly three. Correct.

• Speakers ahead of T (position 4) are Q, S, R — exactly three. Correct.

• P (position 5) speaks after Q (position 1). Correct.

Result: So P is the last speaker to speak.