Seven people, D, A, N, U, B, E and S are sitting in a row, facing north. No…

Concept: In a single-row arrangement every clue is first turned into seat numbers rather than names. Number the seats 1 to 7 from left to right for a north-facing row; then "no one sits to the right of X" pins X to the last seat, "exactly k people sit between P and Q" means the two seat numbers differ by k + 1, "P sits nth to the left of Q" means seat(P) = seat(Q) - n, and "immediate right" means one seat higher. Beginning with the clue that fixes an extreme seat turns the whole puzzle into arithmetic on positions.

Application: the clues resolve in this order.

1. S has nobody to its right, so S occupies seat 7.

2. Exactly three people sit between S and B, so the seat numbers of S and B differ by 4: B occupies seat 7 - 4 = 3.

3. Exactly two people sit between B and A, so the seat numbers of B and A differ by 3, giving A at seat 3 + 3 = 6, because seat 3 - 3 = 0 does not exist.

4. E is third to the left of D, so seat(E) = seat(D) - 3; U is immediately to the right of D, so seat(U) = seat(D) + 1.

5. Only seats 1, 2, 4 and 5 are still free. seat(D) = 5 would force seat(U) = 6, which A already holds, so seat(D) = 4, giving seat(E) = 1 and seat(U) = 5.

6. N is left with the only vacant seat, seat 2.

Cross-check: the completed row satisfies every clue - S sits at the extreme right; D, U and A are the three people between S and B; D and U are the two people between B and A; E at seat 1 is third to the left of D at seat 4; and U at seat 5 is immediately to the right of D.

Reading the same row from the opposite side merely mirrors it, so the number of people sitting between N and A does not depend on that convention.

N sits at seat 2 and A at seat 6, so seats 3, 4 and 5 lie strictly between them: three people - B, D and U - sit between N and A.