(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 ?
Analyzing the Seating Arrangement Clues
This problem requires us to figure out the exact seating positions of five friends on a bench using a set of clues. Let's break down each clue to determine the final arrangement and identify who sits in the middle.
Understanding the Bench Layout
We have five friends sitting on a bench. We can represent the five seats as follows, with seat 1 being the leftmost and seat 5 being the rightmost:
[1] [2] [3] [4] [5]
Applying the Clues Step-by-Step
- Clue (ii): T is on the extreme left hand side of the bench. Placement: This clearly places T in the first position. Current Arrangement: T [2] [3] [4] [5]
- Clue (ii): R is on second position from the right hand side. Placement: The rightmost position is 5, so the second position from the right is position 4. R is placed here. Current Arrangement: T [2] [3] R [5]
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Clue (iv): P and R sitting together.
Deduction: Since R is in position 4, P must be in an adjacent seat, either position 3 or position 5.
- Possibility 1: P is in position 3. Arrangement: T [2] P R [5]
- Possibility 2: P is in position 5. Arrangement: T [2] [3] R P
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Clue (i): R is next to S.
Deduction: We apply this to our possibilities:
- In Possibility 1 (T [2] P R [5]), S must be next to R (position 4). The only available adjacent seat is position 5. Arrangement: T [2] P R S
- In Possibility 2 (T [2] [3] R P), S must be next to R (position 4). The only available adjacent seat is position 3. Arrangement: T [2] S R P
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Clue (ii): S is not sitting with T.
Analysis: Let's check our possibilities against this clue:
- Arrangement T [2] P R S: S is at position 5, T is at position 1. They are not sitting together. This possibility remains valid.
- Arrangement T [2] S R P: S is at position 2, T is at position 1. They are sitting next to each other. This contradicts the clue.
- Clue (iii): P is on the right hand side of Q. Deduction: This means Q must be somewhere to the left of P. In our current structure (T [2] P R S), P is at position 3. The available seats to the left of P are 1 and 2. Seat 1 is occupied by T. Therefore, Q must be in position 2. Current Arrangement: T Q P R S
- Clue (i): P is sitting next to Q. Verification: In the arrangement T Q P R S, Q is at position 2 and P is at position 3. They are indeed next to each other, confirming our arrangement.
- Clue (iii): P is to the right side of T. Verification: In T Q P R S, P is at position 3 and T is at position 1. P is to the right of T, confirming the arrangement.
Final Seating Arrangement
After analyzing all the clues, the confirmed seating order on the bench from left to right is:
T Q P R S
The positions are:
- Position 1: T
- Position 2: Q
- Position 3: P
- Position 4: R
- Position 5: S
Identifying the Middle Person
With five friends seated, the middle position is the 3rd seat.
According to our final arrangement (T Q P R S), the friend sitting in the 3rd position is P.
Therefore, P is sitting exactly in the middle.
Important Questions from Seating Arrangement (Notes)
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?
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?
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?
