Circular Table Arrangement Explained
This problem requires us to determine the seating arrangement of seven people (A, B, C, D, P, Q, R) around a circular table, all facing the center. We need to use the given clues to find who sits third to the right of A.
Step-by-Step Solution
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Establishing Initial Positions: We start by using the most definitive clues.
- "Q sits to the immediate right of B." This gives us a block: $B Q$.
- "P sits third to the left of B." If B is at a certain position, counting three positions counter-clockwise lands us on P. This means there are two people between P and B. Combined with the first clue, we get: $P _ _ B Q$.
- "Q sits second to the left of R." This means R is two positions to the right of Q. Adding this to our current arrangement, considering there are 7 seats in total, we get a partial circular arrangement: $P _ _ B Q _ R$. Let's assign tentative positions clockwise: P(1), _(2), _(3), B(4), Q(5), _(6), R(7).
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Placing Remaining People (A, C, D): The empty seats are positions 2, 3, and 6.
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Using the R and D Clue: "Only two people sit between R and D when counted from the left of D." This means if we start at D and move counter-clockwise, we should encounter two people before reaching R. (Order: D -> P1 -> P2 -> R counter-clockwise).
- Let's test the empty seat position 6 for D: $P _ _ B Q D R$.
- Check the condition: D is at position 6. Moving counter-clockwise (left): Q is at 5, B is at 4. The next person would be at position 3. R is at position 7. This arrangement implies the sequence D -> Q -> B -> R (counter-clockwise). There are exactly two people (Q and B) between D and R when counted from D's left. This fits perfectly.
- So, the arrangement clockwise is: P(1), _(2), _(3), B(4), Q(5), D(6), R(7).
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Using the C and P Clue: "C is not an immediate neighbour of P."
- The remaining people are A and C, who must occupy seats 2 and 3.
- P is at seat 1. Its neighbours are R (at seat 7) and the person at seat 2.
- If C were at seat 2, C would be an immediate neighbour of P. This is forbidden.
- Therefore, A must be at seat 2, and C must be at seat 3.
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Final Arrangement: The complete seating arrangement clockwise is:
Position (Clockwise) Person 1 P 2 A 3 C 4 B 5 Q 6 D 7 R
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Answering the Question: "Who sits third to the right of A?"
- A is at position 2.
- Counting three positions clockwise (to the right):
- 1st to the right: C (position 3)
- 2nd to the right: B (position 4)
- 3rd to the right: Q (position 5)
Therefore, Q sits third to the right of A.
Important Questions from Seating Arrangement (Notes)
Read the directions carefully and give the answer from the given options.
P, Q, R, S, T, K, L, M and N are sitting around a circle facing the centre.
K is $4^{th}$ to the right of P and P is $3^{rd}$ to the right of Q.
N is $4^{th}$ to the left of Q and $3^{rd}$ to the right of S.
R is $2^{nd}$ to the right of M and M is the immediate neighbour of P.
T is $2^{nd}$ to the left of L.
Who is to the immediate left of K?
Seven people, F, J, M, L, R, V and X, are sitting in a row, facing north.
Only three people sit to the left of X. Only M sits to the right of R. Only three people sit between R and V. J sits at some place to the left of L but at some place to the right of F.
How many people sit to the left of V?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?
Six people, B, C, D, I, J and K, are sitting around a circular table facing the centre. Only two people sit between B and I when counted from the right of I. K sits to the immediate left of J. I sits to the immediate right of C. Who among the following are the immediate neighbours of D?
