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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. Four friends, H, I, J and K, are sitting at the four corners of a square facing towards the centre. H and J are sitting at diagonally opposite corners. I is sitting to the immediate left of H. Who is sitting to the immediate right of J?

  2. Four friends named A, B, C, and D are sitting around a square table in a restaurant. If B is sitting in front of A and diagonally opposite to D, then who is sitting in front of C?

  3. Five persons, A, B, C, D and E, are sitting at each corner of a pentagonal table, facing the centre. C is to the right of A and is second to the left of D. E is not between A and D. Who is sitting third to the left of E?

  4. A group of friends are sitting in an arrangement with one each at the corner of an octagon. All are facing the centre. Medha is sitting diagonally opposite Radha. Medha is on Seema’s left. Raman is next to Seema and opposite Govind. Govind is on Chandra’s right. Shanti is not on Medha’s right but is opposite to Shashi. Who is opposite Chandra?

  5. Who is sitting in front of Tinu?

    A. Ritwik

    B. Kazi

    C. Prem

    D. Sunny

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