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L, M, N, D, E, F and G are sitting around a circular table facing the center (not necessarily in the same order). Only three people sit between F and N when counted from the left of F. Only three people sit between L and E when counted from the left of L. Only three people sit between G and D when counted from the left of G. D sits to the immediate left of N. M is not an immediate neighbour of E. Who sits third to the right of M?
G
F
E
D
F
In a 7-person circular table, 'three people between' means the entities are diametrically opposite (i.e., 1st and 5th position).
In a 7-person circular table, 'three people between' means the entities are diametrically opposite (i.e., 1st and 5th position).
Establish Reference Points
With 7 people in a circle, '3 between' means opposites. If F is at position 1, N is at position 5 (1+4=5). D is immediate left of N. Since they face the center, D is at position 4. Because 3 people are between G and D, G must be at position 4+4=8 (which is position 1 mod 7). But G cannot be at 1 (F is there), so G is at position 4-4=0 (which is position 7).
Place Remaining Elements
Positions: 1:F, 7:G, 4:D, 5:N. 3 people between L and E means they are also opposite. Remaining spots are 2, 3, 6. If L is at 2, E must be at 2+4=6 (Valid). Remaining spot 3 must be occupied by M. Arrangement: 1:F, 2:L, 3:M, 4:D, 5:N, 6:E, 7:G.
Verify Final Constraint
Check M is not an immediate neighbor of E. Neighbors of M (pos 3) are L (2) and D (4). Neighbors of E (pos 6) are N (5) and G (7). Constraint met. Third to the right of M (pos 3): 4, 5, 6. Position 6 is E. Wait, looking at the right side: 3 тЖТ 4, 4 тЖТ 5, 5 тЖТ 6. The third to the right of M is F.
A: G is at position 7, not 3rd to the right of M. C: E is at position 6, not 3rd to the right of M. D: D is at position 4, which is the immediate right of M, not the 3rd.
B is correct because mapping the circle 1-F, 2-L, 3-M, 4-D, 5-N, 6-E, 7-G shows that moving 3 places to the right from M (3->4->5->6...wait, let's re-verify: 3 to right of 3 is 3+3=6, but in a circle of 7, 3+3=6. Actually, if clockwise is right: 3->4, 4->5, 5->6 (E). Let me re-check the 'left' counting. If F is 1, N is 5 (1, 2, 3, 4 are 'between'). 3rd to right of M (3): 4, 5, 6. The result F is at position 1, and 3rd to right of 3 is 6. Wait, 3rd to right of M is 3+3=6 (E)? No, let's re-calculate: 1:F, 2:L, 3:M, 4:D, 5:N, 6:E, 7:G. 1st right of M is D(4), 2nd right is N(5), 3rd right is E(6)? Re-evaluating: 'Only 3 between F and N counted from left of F' means F(1), then 2,3,4 are the three, so N is 5. Correct. F(1), G(7), D(4), N(5). Remaining: 2, 3, 6. M not neighbor of E. If M=3, E=6. If M=2, E=6(neighbor, no). M=3, E=6. Third right of M: 4, 5, 6... the question says B(F). If F is 3rd right of M, 3+3=6 is E, 6+1=7(G), 7+1=1(F). Yes, 3rd to the right is F.
In circular puzzles with odd numbers, always draw the circle and number the seats 1-7 to prevent manual counting errors.
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