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Seven people, A, B, E, F, P, Q and R, are sitting in a row, facing north. No one sits to the right of F. Only three people sit between F and E. Only two people sit between E and P. A sits third to the left of R. Q sits to the immediate right of R. How many people sit between B and P?
Four
Two
Three
One
Three
Fix the anchor point (F at the right end since nothing is to its right) and place remaining entities relative to it using the constraints.
Fix the anchor point (F at the right end since nothing is to its right) and place remaining entities relative to it using the constraints.
Fixing the positions
There are 7 people: A, B, E, F, P, Q, R. Since no one sits to the right of F, F is at the 7th position (right end). 'Three people sit between F and E' means E is at position 3 (7-4 = 3). 'Two people sit between E and P' means P could be at 6 or 0; since only 7 seats exist, P is at position 6 (3+3 = 6).
Placing A, Q, and R
We have positions 1, 2, 4, 5 open for A, B, Q, R. 'Q sits to the immediate right of R' means R and Q form a block (R, Q). 'A sits third to the left of R'. If R is at 5, A is at 2. If R is at 4, A is at 1. Testing R=5, Q=6 (occupied), R=4, Q=5. If R=4 and Q=5, then A=1. The remaining position 2 is for B. Sequence: A(1), B(2), E(3), R(4), Q(5), P(6), F(7).
Calculating the distance
The positions are: 1:A, 2:B, 3:E, 4:R, 5:Q, 6:P, 7:F. Between B (pos 2) and P (pos 6), the people are E(3), R(4), and Q(5). There are 3 people between them.
A: Represents 4, which is incorrect as only 3 people sit between B and P. B: Represents 2, which is incorrect. D: Represents 1, which is incorrect.
C is correct because according to the derived sequence A, B, E, R, Q, P, F, there are exactly three people (E, R, Q) sitting between B and P.
In linear seating puzzles, always identify the fixed end-point first to narrow down the search space for relative positions.
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