A, B, C, D and E are sitting on a bench. A is sitting next to B, C is sitting…

In a linear (single-row) seating-arrangement puzzle, first fix the people pinned by absolute clues -- an end position, or an "Nth from left/right" position. Then use each adjacency clue ("sits next to", "sits together") to attach a person to one of the two open seats beside an already-fixed person. Finally use any comparative clue ("to the right of") to break a remaining tie. A seat is confirmed only once every clue holds at the same time.

1. There are 5 seats, numbered 1 (left end) to 5 (right end). E sits on the left end, so E = seat 1.

2. C is second from the right, so C = seat 4.

3. C sits next to D, so D occupies one of the two seats beside seat 4 -- seat 3 or seat 5.

4. A and C sit together, so A also occupies one of the two seats beside seat 4 -- the same pair D is choosing from.

5. If A took seat 5, B (who must sit immediately to A's left, since A sits next to B and to the right of B) would need seat 4 -- but seat 4 already belongs to C, so this is impossible.

6. So A must take seat 3, leaving seat 5 for D. B then takes the seat immediately to A's left, seat 2.

7. This gives the complete order, left to right: E, B, A, C, D -- so A's immediate neighbours are B (seat 2) and C (seat 4).

Checking every original condition against E-B-A-C-D confirms it: A sits next to B (seats 3 and 2); C sits next to D (seats 4 and 5); D does not sit with E (seats 5 and 1 are not adjacent); E is on the left end (seat 1); C is second from the right (seat 4 of 5); A sits to the right of both B and E (seat 3 is right of seats 2 and 1); and A sits next to C (seats 3 and 4). Every clue holds, so A's position -- between B and C -- is the only one that fits.