P, Q, R, S, T, U and V are sitting in a row, facing north. No one sits to the left of U. Only four people sit between U and R. Only three people sit to the right of V. P sits to the immediate left of S. Q is not an immediate neighbour of V. How many people sit between P and T?
Understanding the Seating Arrangement Puzzle
This problem involves arranging seven people – P, Q, R, S, T, U, and V – in a single row, all facing the same direction (north). We need to use the given clues to determine their exact positions and then find the number of people sitting between P and T.
Analyzing the Clues Step-by-Step
Let's represent the row with 7 positions, numbered 1 to 7 from left (West) to right (East), since they are facing north.
Positions: $1$ $2$ $3$ $4$ $5$ $6$ $7$
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"No one sits to the left of U."
Since everyone faces north, the leftmost position is position 1. This clue tells us that U must be in the first position.
Arrangement: U _ _ _ _ _ _
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"Only four people sit between U and R."
U is at position 1. If there are 4 people between U and R, R must be 5 positions to the right of U (U, person1, person2, person3, person4, R). So, R is at position 1 + 5 = 6.
Arrangement: U _ _ _ _ R _
(Positions: 1 2 3 4 5 6 7)
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"Only three people sit to the right of V."
This means V cannot be in the last three positions (5, 6, 7). If 3 people are to the right of V, V must be in the 4th position from the right, which is position 7 - 3 = 4.
Arrangement: U _ _ V _ R _
(Positions: 1 2 3 4 5 6 7)
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"P sits to the immediate left of S."
This means P and S sit together as a block "PS". We need to find two adjacent empty slots for them.
The empty slots are 2, 3, 5, 7.
- Can PS be at 2, 3? Yes. Arrangement: U P S V _ R _
- Can PS be at 3, 4? No (V is at 4).
- Can PS be at 5, 6? No (R is at 6).
- Can PS be at 6, 7? No (R is at 6).
Therefore, P must be at position 2 and S at position 3.
Arrangement: U P S V _ R _
(Positions: 1 2 3 4 5 6 7)
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Determining positions for Q and T
The remaining people are Q and T. The remaining positions are 5 and 7.
Two possibilities exist:
- Possibility A: Q is at 5, T is at 7. Arrangement: U P S V Q R T
- Possibility B: T is at 5, Q is at 7. Arrangement: U P S V T R Q
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"Q is not an immediate neighbour of V."
Let's check our possibilities against this clue:
- Possibility A: U P S V Q R T. Here, V is at 4 and Q is at 5. They are immediate neighbours. This violates the clue, so Possibility A is incorrect.
- Possibility B: U P S V T R Q. Here, V is at 4 and Q is at 7. They are not immediate neighbours. This fits the clue, so Possibility B is the correct arrangement.
Final Arrangement and Answer
The final arrangement of the people in the row is:
| Position 1 | Position 2 | Position 3 | Position 4 | Position 5 | Position 6 | Position 7 |
| U | P | S | V | T | R | Q |
Now, we need to find how many people sit between P and T.
- P is at position 2.
- T is at position 5.
- The people between position 2 and position 5 are those at positions 3 and 4.
- These people are S and V.
- Therefore, there are 2 people sitting between P and T.
Important Questions from Seating Arrangement (Notes)
- Five friends are sitting on a bench in the following order :
(i) P is sitting next to Q and R is next to S.
(ii) S is not sitting with T; T is on the extreme left hand side of the bench and R is on second position from the right hand side.
(iii) P is on the right hand side of Q and to the right side of T. (iv) P and R sitting together
Who is sitting exactly in the middle ? Seven people, C, D, E, F, L, M and N, are sitting in a row, facing north.
Only two people sit to the right of C. Only two people sit between C and L. Only two people sit between E and N. N sits to the immediate left of C. M sits to the immediate right of F. Who sits at the third position from the left end of the row?- Seven people, A, B, C, D, E, F and G, are sitting in a row, facing north. Only three people sit between E and D. A sits to the immediate left of D. No one sits to the right of B. Only two people sit between B and A. G sits to the immediate right of F. How many people sit to the right of F?
Seven boxes, A, B, C, D, E, F and G, are kept one over the other but not necessarily in the same order. Only A is kept above F. Only D is kept between F and C. Only E is kept below B. How many boxes are kept below C?
A, B, C, D, J, K and L are sitting around a circular table facing the centre of the table. K sits to the immediate right of B. Only three people sit between K and A when counted from the left of K. Only three people sit between B and L. C sits to the immediate right of D. How many people sit between J and D when counted from the left of D?
