Eight colleagues H, I, J, K, L, M, N, and O are seated around an octagonal…

2023

Eight colleagues H, I, J, K, L, M, N, and O are seated around an octagonal table, facing the centre, with exactly one person at each corner. Consider the following clues:

  • H is the second person to the left of K.

  • I is the neighbour of both M and N.

  • O is the second person to the left of N.

  • L sits between J and H.

  • J is immediately next to M.

Who is sitting between O and N?

  1. A.

    J

  2. B.

    M

  3. C.

    H

  4. D.

    K

Attempted by 1 students.

Show answer & explanation

Correct answer: D

Concept: In a circular/polygonal seating puzzle, first convert every relative clue ("neighbour of", "immediately next to", "between") into a block of consecutively seated people, then use directional clues ("second left of") -- always read in the SAME rotational direction throughout the puzzle -- to place the remaining people and close the loop. An arrangement is confirmed only when every clue, including at least one not needed for the initial placement, holds simultaneously.

Application:

  1. I is the neighbour of both M and N, so M and N sit on either side of I -- this fixes the block M-I-N.

  2. J is immediately next to M, and M's other neighbour is already I, so J must take M's free side -- this extends the block to J-M-I-N.

  3. L sits between J and H, meaning L is adjacent to both J and H. J's free side (its other neighbour, M, is already fixed) is where L attaches; H then attaches to L's outer side -- this extends the block to H-L-J-M-I-N, fixing six of the eight seats in order.

  4. Only two seats remain, between N and H, for K and O. Reading "second left" in the same rotational direction used to build the block, O is the second person to the left of N -- so one person sits immediately after N, and O sits immediately after that person, right before H.

  5. Applying that placement: the person immediately after N is K, then O follows K, then H closes the loop -- giving the full order H-L-J-M-I-N-K-O around the table.

Cross-check: Test this against the one clue not yet used for placement -- "H is the second left of K." Counting two seats in the same rotational direction from K (K → O → H) lands exactly on H, matching the clue independently and confirming the arrangement without contradiction.

Result: The finished order around the table is H, L, J, M, I, N, K, O. The person sitting directly between O and N is K.

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