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

Concept: A single-row seating arrangement is solved by first placing every person fixed by an absolute-position clue (an end of the bench, or a fixed distance from an end), and only then applying the relative clues (adjacent-to, to-the-right-of, together-with) to the remaining seats, testing each candidate placement against every constraint that has not yet been used.

Application:

1. There are 5 seats on the bench, numbered 1 (left end) to 5 (right end). E is on the left end, so E occupies seat 1.

2. C is on the second position from the right, so C occupies seat 4.

3. C sits next to D, so D must occupy seat 3 or seat 5 - the only two seats adjacent to seat 4.

4. A and C are sitting together, so A must also occupy a seat adjacent to seat 4 - the same two candidate seats, 3 and 5.

5. A sits next to B and A is to the right of B, so A's seat number must be exactly one more than B's seat number. Test A = seat 5: D would then take seat 3, leaving seat 2 for B - but seat 5 and seat 2 are not adjacent, so this fails the 'A next to B' clue.

6. Test A = seat 3: D then takes seat 5, leaving seat 2 for B. Seat 3 and seat 2 are adjacent, and seat 3 is to the right of seat 2, so this placement satisfies every clue.

7. The final order is E (seat 1), B (seat 2), A (seat 3), C (seat 4), D (seat 5) - A sits directly between B and C.

Cross-check: A next to B (seats 3, 2) - holds; C next to D (seats 4, 5) - holds; D not sitting with E (seats 5, 1) - holds; E on the left end - holds; C second from the right - holds; A to the right of both B and E - holds; A and C together (seats 3, 4) - holds. Every original clue is satisfied.