Seven people F, G, H, L, M, O and Q are sitting in a row facing north. No one sits to the right of M. Only three people sit between O and M. Only one person sits between M and L. H sits to the immediate left of G. Q is not an immediate neighbor of M. How many people sit between F and H?
Four
Number the seats 1 to 7 from left to right, facing north. No one sits to the right of M, so M is at seat 7.
Only three people sit between O and M, so O is at seat 3 (seats 4, 5, 6 lie between O and M). Only one person sits between M and L, so L is at seat 5.
Q is not an immediate neighbour of M, so Q is not at seat 6. H sits immediately left of G, so H and G form a consecutive pair. The free seats are 1, 2, 4, 6; the only consecutive free pair is 1 and 2, giving H at seat 1 and G at seat 2.
Seats 4 and 6 remain for F and Q. Since Q cannot be at seat 6 (next to M), Q takes seat 4 and F takes seat 6. Final row: H(1), G(2), O(3), Q(4), L(5), F(6), M(7).
Between F (seat 6) and H (seat 1) sit seats 2, 3, 4, 5, that is four people.
Hence, four people sit between F and H.
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Important Questions from Linear Arrangement
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