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 9 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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