Directions: Read the following details carefully to answer the question that follows.
Eight colleagues, P, Q, R, S, T, U, V, and W, are sitting around a circular conference table, all facing towards the center. T sits to the immediate left of S. Only two people sit between T and Q. P sits second to the right of Q. U sits adjacent to both P and Q. V sits opposite to T. R sits adjacent to V but does not sit adjacent to Q. W sits between R and S.
If all the colleagues are arranged in alphabetical order starting from P in the anti-clockwise direction, then the position of how many colleagues will remain unchanged (excluding P)?Correct Answer :
None
Solution :
To solve this seating arrangement puzzle, let us step-by-step determine the positions of all eight colleagues (P, Q, R, S, T, U, V, and W) seated around a circular table facing the center.
There are 8 positions around the circular table. Moving clockwise or anti-clockwise follows the perspectives of the people facing the center:
Step 1: Analyze the given clues to fix positions.
1. "T sits to the immediate left of S."
Let us place S at position 1. Facing the center, immediate left of S is position 2. So, T is at position 2.
2. "V sits opposite to T."
Since there are 8 positions, opposite to position 2 (T) is position 6 (2 + 4 = 6). So, V is at position 6.
3. "Only two people sit between T and Q."
From T (position 2), moving 3 steps in either direction gives position 5 or position 7. Let's check which one works:
- If Q is at position 5: "P sits second to the right of Q". Facing center from position 5, second to the right would be position 3.
- "U sits adjacent to both P and Q". If P is at 3 and Q is at 5, U must be at position 4, which is adjacent to both 3 and 5.
- Let's verify R and W: "R sits adjacent to V (position 6) but does not sit adjacent to Q (position 5)". Thus, R must be at position 7 (adjacent to V at 6, not adjacent to Q at 5).
- "W sits between R and S". Position between R (position 7) and S (position 1) is position 8. So, W is at position 8.
This satisfies all conditions perfectly!
Step 2: Summary of original seating arrangement (clockwise from S at position 1):
Position 1: S
Position 2: T
Position 3: P
Position 4: U
Position 5: Q
Position 6: V
Position 7: R
Position 8: W
Going in anti-clockwise direction starting from P (position 3):
Position 3: P
Position 2: T
Position 1: S
Position 8: W
Position 7: R
Position 6: V
Position 5: Q
Position 4: U
Step 3: Arrange colleagues in alphabetical order starting from P in the anti-clockwise direction:
The alphabetical order starting from P is: P, Q, R, S, T, U, V, W.
Let's map this new alphabetical order anti-clockwise starting at position 3 (P):
- Position 3 (P): P (Original: P) -> Unchanged (excluded as per question)
- Position 2 (T): Q (Original: T) -> Changed
- Position 1 (S): R (Original: S) -> Changed
- Position 8 (W): S (Original: W) -> Changed
- Position 7 (R): T (Original: R) -> Changed
- Position 6 (V): U (Original: V) -> Changed
- Position 5 (Q): V (Original: Q) -> Changed
- Position 4 (U): W (Original: U) -> Changed
Comparing the original anti-clockwise arrangement starting from P with the new alphabetical arrangement:
Original: P, T, S, W, R, V, Q, U
Alphabetical: P, Q, R, S, T, U, V, W
Excluding P, none of the colleagues remain in their original positions.
Therefore, the position of None of the colleagues will remain unchanged.
The correct answer is None.
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