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Question

Eight people E, F, G, H, J, K, L and M are sitting around a circular table facing the centre but not necessarily in the same order. F is sitting second to the left of K. H is an immediate neighbour of K. There are only three people sitting between H and E. Only one person sits between L and E. M is sitting to the immediate right of the L. G is to the immediate left of F. What is the position of L with respect to H?

The correct answer is
Fourth to the left

This problem involves arranging people around a circular table based on the given conditions. Let's break it down step-by-step:

  1. Firstly, place K at a random position at the circular table.
  2. According to the conditions, F is sitting second to the left of K. Thus, we place F accordingly.
  3. H is an immediate neighbor of K, so H can be to the immediate left or right of K.
  4. There are only three people sitting between H and E. We have two possibilities for H's position (left or right of K), so place E accordingly:
    • If H is to the immediate left of K, then moving three positions clockwise from H, we can place E.
    • If H is to the immediate right of K, then moving three positions anti-clockwise from H, we place E.
  5. Only one person sits between L and E. Choose the appropriate position for L based on E's position; this will help determine which initial arrangement is valid.
  6. M is sitting immediately to the right of L, so place M accordingly.
  7. G is immediately to the left of F. Ensure G fits correctly in the remaining vacant spot to the left of F.

After applying the above criteria, the correct arrangement aligns with the following configuration:

  • Starting from K and moving clockwise, the order is: K, H, L, M, E, J, F, and G.

Finally, the position of L with respect to H is "Fourth to the left."

This process involves logical deduction and eliminating impossible arrangements based on the constraints. The correctly filled positions indicate L is indeed fourth to the left of H.

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