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Question

Eight boys, P, Q, R, S, T, U, V and W, are seated around a round table, not necessarily in same order, but with equal spacing between them and all facing the centre of the table. S is seated exactly opposite to P, who has U and R as his immediate neighbours. T is seated immediately next to V, who is to the immediate right of S. Q is exactly opposite to T and does not have R as his immediate neighbour. With this information, which of the following statements is correct?

The correct answer is

R is seated exactly opposite to W

This question involves arranging eight boys around a round table based on a set of clues. We need to deduce the correct seating order and then verify which of the given statements is true.

Understanding the Round Table Seating Arrangement

In a round table arrangement where everyone is facing the center, "immediate right" and "immediate left" are relative to the person's perspective. Opposite positions divide the table into two equal halves.

Step-by-Step Solution to the Seating Puzzle

Let's build the seating arrangement step-by-step using the provided clues:

  1. We have 8 boys: P, Q, R, S, T, U, V, W. They are around a round table with equal spacing.
  2. Clue 1: S is seated exactly opposite to P. Let's place P anywhere. S must be in the position directly across from P.
  3. Clue 2: P has U and R as his immediate neighbours. This means U and R are on either side of P. Let's assume, for now, U is to P's immediate right (clockwise) and R is to P's immediate left (counter-clockwise). We can adjust this later if needed.
  4. Clue 3: V is to the immediate right of S. If we look at S (facing the center), the person to S's immediate right will be in the clockwise direction from S. So, V is clockwise from S.
  5. Clue 4: T is seated immediately next to V. Since V is to the immediate right of S (clockwise from S), T must be next to V. This means V is between S and T in the clockwise direction. So, we have a sequence S - V - T sitting together clockwise.
  6. Clue 5: Q is exactly opposite to T. We can place Q directly across from T.
  7. Clue 6: Q does not have R as his immediate neighbour. We will use this clue to check our arrangement or decide between possible arrangements (like the initial choice of U and R's sides relative to P).

Let's try to sketch the arrangement based on these clues. We can list the positions in clockwise order starting from P:

  1. Start with P. Position 1: P
  2. S is opposite P. In an 8-person arrangement, opposite means 4 positions away. So, Position 5: S
  3. U and R are neighbours of P (Positions 2 and 8). Let's place U at Position 2 and R at Position 8.
  4. V is immediate right of S. From S (Position 5), the immediate right is Position 6. Position 6: V
  5. T is next to V. Since V is at Position 6, T must be at Position 7 (in the clockwise sequence S-V-T). Position 7: T
  6. Q is opposite T. T is at Position 7. Opposite Position 7 is Position 3. Position 3: Q

So far, the arrangement is (clockwise starting from P): P, U, Q, ?, S, V, T, R. The positions are:

  • Position 1: P
  • Position 2: U
  • Position 3: Q
  • Position 4: ?
  • Position 5: S
  • Position 6: V
  • Position 7: T
  • Position 8: R

The only remaining person is W, and the only remaining position is Position 4. So, W must be at Position 4.

The complete clockwise arrangement starting from P is: P, U, Q, W, S, V, T, R.

Let's verify all clues with this arrangement:

  • S opposite P: P at 1, S at 5. Yes.
  • P neighbours U and R: U at 2, R at 8. Yes.
  • V immediate right of S: S at 5, V at 6 (clockwise). Yes.
  • T next to V: V at 6, T at 7. Yes (T is also next to R at 8).
  • Q opposite T: Q at 3, T at 7. Yes.
  • Q does not have R as neighbour: Q at 3. Neighbours are U at 2 and W at 4. R is at 8. Yes.

All clues are satisfied by the arrangement: P - U - Q - W - S - V - T - R (clockwise).

Let's list who is opposite whom in this arrangement:

  • P is opposite S
  • U is opposite V
  • Q is opposite T
  • W is opposite R

Verifying the Statements

Now we check each given statement based on our derived seating arrangement.

  1. R is seated exactly opposite to W.

    In our arrangement, W is opposite R. This statement is true.

  2. S and U are the immediate neighbours of W.

    W is seated between Q and S. W's immediate neighbours are Q and S. U is a neighbour of P and Q. This statement is false.

  3. Q and U are not the neighbours of each other.

    Q is seated between U and W. Q's immediate neighbours are U and W. U is a neighbour of P and Q. U and Q are immediate neighbours. This statement is false.

  4. T is seated immediately next to V but not next to R.

    T's immediate neighbours are V and R. T is next to V and also next to R. The statement says T is not next to R, which is false.

Conclusion

Based on the detailed seating arrangement derived from the clues, only the first statement is correct.

Position (Clockwise from P) Person Opposite Person Immediate Neighbours
1 P S R, U
2 U V P, Q
3 Q T U, W
4 W R Q, S
5 S P W, V
6 V U S, T
7 T Q V, R
8 R W T, P

Revision Table: Seating Arrangement Puzzle

Key concepts used in solving this round table puzzle include understanding relative positions (left/right from a person's perspective facing the center) and opposite positions in a circular arrangement. Always start with a fixed position and build the arrangement step-by-step, verifying each clue as you go. Pay close attention to the wording like "immediate neighbour" and "exactly opposite".

Additional Information: Types of Seating Arrangements

Seating arrangement problems are common in logical reasoning tests. They can involve:

  • Linear Arrangement: People or objects arranged in a straight line (single row or double row).
  • Circular Arrangement: People or objects arranged around a circle (facing center, facing outwards, or mixed).
  • Rectangular/Square Arrangement: People or objects around a table with sides (corners, middle of sides).

Solving these problems often requires deductive reasoning, careful interpretation of clues, and systematic diagramming or listing of possibilities.

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Important Questions from Polygon Arrangement

  1. A, B, C, D, E, F, G and H are sitting around a square table facing the centre of the table. Some of them are sitting at the corners while some are sitting at the exact centre of the sides.

    G sits second to the right of F. B sits second to the right of A. C sits third to the right of H. E sits third to the right of F. C is not the immediate neighbour of A. Who sits second to the right of B?

  2. 6 persons A, B, C, D, E and F are sitting around a rectangular table, facing towards the centre (not necessarily in the same order). One person is sitting on each of the smaller sides. Two persons are sitting on each of the bigger sides. No person is sitting at the corners. C and F are sitting on the same side. B is sitting opposite to A. F is the immediate neighbour of B. A is sitting second to the left of D.

    Counting towards the left of D, how many persons are sitting between A and D?

  3. Seven friends, A, B, C, D, E, F, and G are seating around a square table, facing towards the centre. Some of them are sitting at the corners while some are sitting at the exact centre of the sides of the table. One seat is left vacant. D is sitting exactly at the centre of one of the sides of the table. C is sitting at a corner, third to the left of B. There are exactly two people sitting between C and D. F is an immediate neighbour of both B and D. A is second to the right of F. E is not an immediate neighbour of A, but third to the left of F. G is an immediate neighbour of C. Where is the vacant seat?

  4. Rashmi, Sunita, Mona and Sakshi are sitting around a square table. Rashmi is to the right of Sunita. Mona is to the left of Sakshi. Which of the persons mentioned in the options is sitting opposite to each other?

  5. V, W, X, Y, Z, A, B and C were sitting around a square table facing the centre. Some of these were sitting at corners and some were sitting at exact centre of the sides. C was to the immediate right of W. B was third to the left of Z. A was the immediate neighbour of X and C. Z, not at any corner, was the immediate neighbour of W and Y. Who among the following was sitting third to the right of A?

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