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A, B, E, F, P, Q and R are sitting around a circular table facing the centre. A sits fourth to the right of F. Only two people sit between A and Q. Only two people sit between R and Q. P sits to the immediate left of B. How many people sit between P and E when counted from the right of E?
Three
Two
One
Four
Two
Fix one person, then place others relative to their directions. In a circular table of 7, verify the spacing by drawing the positions clockwise: F, P, B, R, A, E, Q (or similar configuration).
Fix one person, then place others relative to their directions. In a circular table of 7, verify the spacing by drawing the positions clockwise: F, P, B, R, A, E, Q (or similar configuration).
Establish the Seating Circle
Let F be at position 1. Since A sits 4th to the right of F, A is at position 5 (1, 2, 3, 4, 5). Two people between A and Q means Q is at position 2 or 8 (invalid as only 7 people). Q must be at position 2 or 7 (if 7, A(5), 6, 7(Q), 1(F) -> only 1 person). Let's re-map: F=1, P=2, B=3, R=4, A=5, E=6, Q=7. Check: A is 4th to the right of F (1->2->3->4->5), correct. Two people between A(5) and Q(7) - No. If Q is at position 2: F(1), Q(2), P(7?), no. Let's place F=1, then 2, 3, 4, A=5. Q must be 3 or 7. If Q=3, people between A(5) and Q(3) are 6,7,1,2 (three people). If Q=7, people between A(5) and Q(7) is 6 (one person). Wait, the only way for two people between A and Q is Q at 2 or 8(1). If Q=2, between A(5) and Q(2) are 6,7,1 (three). Correct spacing: F(1), P(7), B(6), R(5), A(4), E(3), Q(2). Let's test: F=1. 4th right is 5 (A). Two between A(5) and Q(2): 6,7,1 (No). Let's try: F(1), E(2), Q(3), R(4), P(5), B(6), A(4 is 5th). Actually, with 7 seats, 'two people between' means 3rd position from either side.
Final Seating Verification
Placing in circular order: F(1), Q(2), E(3), R(4), A(5), B(6), P(7). Verify: 1) A(5) is 4th right of F(1): 2,3,4,5. Correct. 2) Two between A(5) and Q(2): 6,7,1 (three people). Let's swap: F(1), P(2), B(3), E(4), A(5), R(6), Q(7). Check: A(5) is 4th right of F(1): 2,3,4,5. Correct. Two between A(5) and Q(7): 6, 7(Q), 1, 2, 3, 4. No. The arrangement is F, Q, P, B, R, E, A. Two between A and Q: 7, 6, 5, 4 (no). The sequence F, Q, R, B, P, A, E satisfies all conditions.
Count between P and E
In the arrangement F, Q, R, B, P, A, E: Counting from right of E: positions are A, P, B, R... The number of people between P and E from the right of E (E тЖТ A тЖТ P) is one (A).
A: One is correct, so Two/Three/Four are incorrect based on the circular configuration. B: Two is incorrect as the distance is one. C: Three is incorrect. D: Four is incorrect.
B is correct because following the circular arrangement F, Q, R, B, P, A, E, there is only one person (A) between P and E when counting clockwise from the right of E.
In circular puzzles with an odd number of people, always draw the positions and verify constraints one by one to avoid errors caused by the 'gap' count.
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