Ten students A, B, C, D, E, F, G, H, I and J are sitting in a row facing west.…

2014

Ten students A, B, C, D, E, F, G, H, I and J are sitting in a row facing west. B and F are not sitting on either of the edges; G is sitting to the left of D and H is sitting to the right of I; There are four persons between E and A; I is to the north of B and F is to the South of D; J is between A and D and G is between E and F. There are two persons between H and C.
Who are the immediate neighbours of I?

  1. A.

    B and C

  2. B.

    B and H

  3. C.

    A and H

  4. D.

    D and J

Attempted by 30 students.

Show answer & explanation

Correct answer: B

CONCEPT: In a linear seating puzzle, every relational clue ("left/right of", "between", "north/south", a count of people between two others) is translated onto ONE consistent position axis, then the resulting order/adjacency constraints are solved step by step. When everyone in the row faces the same direction (here, west), the compass clues and the left/right clues describe the SAME axis: facing west, a person's right hand points north and left hand points south, so "right of"/"north of" both mean a higher position on the axis, and "left of"/"south of" both mean a lower position.

APPLICATION:

  1. Four persons between E and A means E and A are exactly 5 seats apart on the axis.

  2. G is (immediately) between E and F, and F is south of D while G is left of D, so E, G, F form three consecutive seats sitting south of D.

  3. J is (immediately) between A and D, so A, J, D also form three consecutive seats.

  4. Combining these with the 5-seat E-A gap fixes one block of six consecutive seats, in order: E, G, F, D, J, A.

  5. Two persons between H and C, with H north of (right of) I, places the remaining four people in order: C, B, I, H.

  6. Together, the six-seat block E, G, F, D, J, A and the four-seat block C, B, I, H exactly fill all ten seats, so the two blocks must sit end to end in one of two orders (either block first); in both cases, I sits inside the C, B, I, H block, flanked by B on one side and H on the other, because that adjacency is fixed within the block regardless of which end of the row the block occupies.

CROSS-CHECK: Verify every clue against one such tiling, say E, G, F, D, J, A, C, B, I, H: B(8) and F(3) are not on either edge; G(2) is left of D(4); H(10) is right of I(9); E(1) and A(6) have exactly G, F, D, J (4 people) between them; I(9) is north of B(8); F(3) is south of D(4); J(5) sits immediately between A(6) and D(4); G(2) sits immediately between E(1) and F(3); H(10) and C(7) have exactly B, I (2 people) between them - every clue holds. The other tiling (the same two blocks in the opposite order) satisfies every clue in the same way and keeps I's neighbours unchanged.

So, in every arrangement consistent with the clues, I's immediate neighbours are B and H.

Explore the full course: Niacl Ao It Specialist