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A, B, C, D, E, F and G are sitting around a circular table facing the centre. Only two people are seated between E and F when counted from the right of E. Only two people are seated between F and D when counted from the left of D. Only three people are seated between E and B when counted from the left of B. C is seated to the immediate left of G. How many people are seated between A and F when counted from the right of F?
3
1
2
4
1
Fix the first element (E) at position 1 and map relative positions clockwise, then verify the constraints against the remaining slots.
Fix the first element (E) at position 1 and map relative positions clockwise, then verify the constraints against the remaining slots.
Initial Setup
Fix E at position 1. Since only 2 people are between E and F counted from the right of E (clockwise), counting 1, 2, 3 positions clockwise places F at position 4.
Placement of D and B
Only 2 people between F and D from left of D (counter-clockwise) means if D is at pos 1, F is at pos 4; testing slots, D is at position 7. Only 3 people between E (pos 1) and B from left of B means B is at position 5.
Placement of G, C, and A
C is immediate left of G. Slots available are 2, 3, 6. Positioning G at 3 and C at 2 satisfies this. A must occupy the last remaining slot, position 6.
Final Verification
Seating arrangement (clockwise): E(1), C(2), G(3), F(4), B(5), A(6), D(7). Counting from the right of F (counter-clockwise/towards center): F is at 4, A is at 6. Only one person (B) is between A and F.
A: 3 is incorrect as the gap is only 1 person. C: 2 is incorrect as it implies two people are in between, which contradicts the derived order. D: 4 is incorrect as it is mathematically impossible within a 7-person circle given these constraints.
B is correct because the final circular arrangement places A at position 6 and F at position 4, resulting in exactly one person (B) sitting between them.
In circular arrangements, always define a fixed reference point (like E) to avoid ambiguity when counting clockwise versus counter-clockwise.
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