Eight persons A, B, C, D, E, F, G, and H sit in a row. Four face north and the…

2022

Eight persons A, B, C, D, E, F, G, and H sit in a row. Four face north and the remaining four face south.

At most two persons sit to the right of A, and A does not face north.

Three persons sit between A and B, and B is the only immediate neighbour of C.

Three persons sit between E and G, and neither E nor G sits adjacent to A.

H sits second to the right of C.

B and H face the same direction.

G faces south.

D sits third to the left of G.

H is not adjacent to D.

F sits second to the right of D.

How many persons sit between A and H?

Answer: B. TwoIn a linear seating puzzle where some people face north and others face south, every 'second/third to the right/left of X' clue is read from X's own facing…

  1. A.

    None

  2. B.

    Two

  3. C.

    Three

  4. D.

    Four

  5. E.

    One

Attempted by 10 students.

Show answer & explanation

Correct answer: B

In a linear seating puzzle where some people face north and others face south, every 'second/third to the right/left of X' clue is read from X's own facing direction, not a single fixed reading-order sense: for a north-facing person, right and left match the ordinary left-to-right reading of the row, but for a south-facing person they are mirrored — their right points toward what reading-order calls left, and vice versa. An 'only neighbour' clue is direction-independent and pins someone to a row-end first; the direction-dependent offset clues are then applied one at a time, each using the referenced person's own facing direction.

  1. 'Three persons sit between A and B' fixes their positions four seats apart. Since A faces south, 'at most two persons sit to the right of A' means at most two seats lie on A's mirrored right side, toward the lower-numbered end — so A can only occupy seat 1, 2 or 3. Checking each candidate together with 'B is the only immediate neighbour of C' (which forces C onto seat 1 or seat 8, since only a row-end seat has just one neighbour): only A = seat 3, B = seat 7 leaves a free row-end seat (8) next to B for C to occupy.

  2. C therefore sits at seat 8, with only seat 7 (B) as its neighbour. For 'H sits second to the right of C': if C faced north this would put H at seat 10, which doesn't exist, so C must face south — and a south-facer's mirrored right points toward the lower-numbered end, placing H at seat 8 minus 2, seat 6.

  3. The four remaining seats — 1, 2, 4, 5 — go to D, E, F and G. For 'D sits third to the left of G', G is already known to face south, so G's mirrored left points toward the higher-numbered end: D = G plus 3. Testing G = seat 2 gives D = seat 5, but then no free seat satisfies 'F sits second to the right of D' (checked next); so G = seat 1 and D = seat 4 is the only surviving option.

  4. For 'F sits second to the right of D' at seat 4: a north-facing D would place F at seat 6, already taken by H, so D must face south, and its mirrored right points toward the lower-numbered end, placing F at seat 4 minus 2, seat 2. The one seat left over, seat 5, goes to E.

  5. Checking the remaining clues against this seating: E(5) and G(1) have exactly three seats (2, 3, 4) between them; neither E nor G is adjacent to A(3), whose neighbours are seats 2 and 4; and H(6) is not adjacent to D(4), whose neighbours are seats 3 and 5 — every clue holds.

  6. For direction: A, C, D and G are now fixed to face south (four people), so the remaining four — B, E, F and H — must all face north to keep the four-four split, which also satisfies 'B and H face the same direction'.

  7. Between A (seat 3) and H (seat 6) lie seats 4 and 5, occupied by D and E — so exactly two persons sit between A and H.

Re-checking every one of the ten clues against the completed seating — G (seat 1, south), F (seat 2, north), A (seat 3, south), D (seat 4, south), E (seat 5, north), H (seat 6, north), B (seat 7, north), C (seat 8, south) — confirms none is violated, so exactly two persons between A and H is the unique answer consistent with every condition.

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