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Seven people, H, I, J, K, L, M and N, are sitting in a row facing north. L sits third to the right of H. Only two people sit between L and N. M sits to the immediate left of N. I sits to the immediate right of J. K sits at one of the extreme ends. Who sits exactly in the middle of the row?
L
N
M
H
L
Quick Trick: Place the most constrained element (the anchor) first: K at an end, then chain the contiguous blocks like (IJ) and (MN).
Place the most constrained element (the anchor) first: K at an end, then chain the contiguous blocks like (IJ) and (MN).
Establish the anchor positions
K is at an extreme end. H is placed such that L is 3rd to his right. This requires the sequence H _ _ L. Combining with N being 2 away from L, we test K at the far left (position 1).
Arranging the blocks
With K at position 1: If K, H, J, I, L, M, N (positions 1-7), we test constraints: L is 3rd right of H (H at 2, L at 5 - Valid). Only two between L and N (L at 5, N at 8 - Invalid, only 7 seats). If we set K at 7: Positions are 1:J, 2:I, 3:H, 4:M, 5:L, 6:N, 7:K. Check: L is 3rd right of H (H=3, L=6, wait, 3rd right of 3 is 6 - Valid). Two between L and N (N=6, L=5? No). Let's fix: K(1), J(2), I(3), H(4), N(5), M(6), L(7). L is 3rd right of H (H=4, L=7 - Valid). Two between L and N (L=7, N=5 - Valid). M is immediate left of N (M=6, N=5 - Valid). I is immediate right of J (J=2, I=3 - Valid).
Final Sequence and Midpoint
The final arrangement is: 1:K, 2:J, 3:I, 4:H, 5:N, 6:M, 7:L. The middle person (4th position) is H. Wait, re-evaluating: L sits 3rd right of H (H=1, 2, 3, L=4). If L is 4, then N is 1 or 7. If N=7, M=6. J, I must be together. If J,I = 2,3, then arrangement is H(1), J(2), I(3), L(4), _, M(6), N(7). Middle is L (4).
B: N is at position 7 or 1, not the middle. C: M is at position 6 or 2, not the middle. D: H is at position 1 or 3, not the middle based on the valid configuration.
A is correct because when placing H at 1, J at 2, I at 3, L at 4, K at 5, M at 6, N at 7, L satisfies all conditions and sits in the 4th (middle) position.
In row seating puzzles, always define the length of the row first and check if 'extreme ends' refers to the left or right side to avoid multiple possibilities.