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Seven people, P, Q, R, S, T, U and V, are sitting in a row, facing north. Only three people sit between R and T. V sits to the immediate left of T. No one sits to the right of U. Only two people sit between U and V. P sits to the immediate right of S. How many people sit between Q and P?
1
2
3
0
2
Start by placing the person with no one to their right at position 7, then work backward using constraints to fix the absolute positions.
Start by placing the person with no one to their right at position 7, then work backward using constraints to fix the absolute positions.
Establish the row framework
There are 7 positions (1, 2, 3, 4, 5, 6, 7). U is at the extreme right (7) because no one sits to their right.
Place V, T, and R
Two people sit between U(7) and V, so V is at position 4. V is to the immediate left of T, so T is at 5. Three people sit between R and T(5), so R must be at 1 (since 5-4=1, 5-3=2, 5-2=3, 5-1=4, 5+1=6, 5+2=7; 5-4=1 is the only valid slot for R).
Place S, P, and Q
Current positions: R(1), _, _, V(4), T(5), _, U(7). P is to the immediate right of S. The only remaining adjacent pair is (2, 3). Thus, S is at 2 and P is at 3. The remaining person Q takes position 6.
Verify final arrangement
The final row is: R(1), S(2), P(3), V(4), T(5), Q(6), U(7). Counting between P(3) and Q(6): V(4) and T(5) are between them, but the question asks for the number of people between Q and P. Specifically, the people are 4 and 5, totaling 2 people.
A: 1 is incorrect as the gap is 2. C: 3 is incorrect as there are only 2 people between them. D: 0 is incorrect as Q and P are not adjacent.
B is correct because the final arrangement is R, S, P, V, T, Q, U, and between P(position 3) and Q(position 6) sit V and T, meaning 2 people.
In seating puzzles, always look for the anchor point (e.g., 'no one to the right') to lock down the row boundary before filling other variables.