This problem is a logic puzzle involving a seating arrangement around a circular table. We need to determine the exact positions of all 7 people (A, B, C, D, P, Q, R) based on the given clues and then find who is sitting third to the right of A.
Deducing the Seating Arrangement
Let's break down the clues to figure out the seating order:
- Setup: 7 people (A, B, C, D, P, Q, R) are sitting around a circular table facing the center. We can imagine 7 seats numbered 1 to 7 clockwise.
- Clue 4 & 3: "Q sits to the immediate right of B" and "P sits third to the left of B". This gives us a block of people relative to B. If B is at position 0, Q is at +1 (clockwise), and P is at -3 (counter-clockwise). This implies a sequence like P, ?, ?, B, Q.
- Clue 5: "Q sits second to the left of R". This means R is two positions to the right of Q. If Q is at +1 relative to B, R would be at +1 + 2 = +3 relative to B. However, this interpretation might be confusing. Let's use relative positions directly: Q is 2 seats CCW from R. So R is 2 seats CW from Q. In our B=0 structure: B(0), Q(+1). R must be at +3. The partial arrangement based on B is P(-3), ??(-2), ??(-1), B(0), Q(+1), ??(+2), R(+3). This uses all 7 seats.
- Revisiting Clue 5: "Q sits second to the left of R". This means if we start at R and go left (counter-clockwise), the order is R -> Seat 1 -> Q. So, R is 2 seats clockwise from Q. Let's rebuild the relative positions.
- Let B be at position 0.
- Q sits immediate right of B => Q = +1.
- P sits 3rd left of B => P = -3.
- Q sits 2nd left of R => R is 2nd right of Q. R = Q + 2 = +1 + 2 = +3.
- So far, relative to B: P(-3), ??(-2), ??(-1), B(0), Q(+1), ??(+2), R(+3).
- The people placed are P, B, Q, R. The remaining are A, C, D. The empty slots are -2, -1, +2.
- Clue 2: "Only two people sit between R and D when counted from the left of D." R is at position +3. Let's test placing D in the empty slots (-2, -1, +2).
- If D is at -1: Left of D is ??(-2), P(-3). That's 2 people. The next CCW position is A(+3) or ??(+2). Neither is R(+3).
- If D is at -2: Left of D is P(-3), ??(-4 which wraps to +3). That's 2 people (P and R). Wait, R is at +3. This fits! So D must be at position -2.
- Current arrangement: P(-3), D(-2), ??(-1), B(0), Q(+1), ??(+2), R(+3).
- People placed: P, D, B, Q, R. Remaining: A, C. Empty slots: -1, +2.
- The arrangement must be P, D, C, B, Q, A, R or P, D, A, B, Q, C, R.
- Clue 6: "C is not an immediate neighbour of P." P is at -3. Its neighbours are D(-2) and the person at +3 (R). Wait, P's neighbours should be the person at -2 and the person wrapping around from the other side. Let's use numbered seats 1-7.
- Let's restart with a concrete layout based on deductions. From P(-3), ??(-2), ??(-1), B(0), Q(+1), ??(+2), R(+3), let's assign seat numbers. Let B = seat 4.
- B=4 => Q=5, P=1 (3rd left: 3, 2, 1). R=7 (2nd right of Q: 6, 7).
- Arrangement: P(1), ??(2), ??(3), B(4), Q(5), ??(6), R(7).
- People placed: P, B, Q, R. Remaining: A, C, D. Seats left: 2, 3, 6.
- Apply Clue 2: "Only two people sit between R and D when counted from the left of D." R is at 7.
- Try D=3. Left of D: Seat 2, Seat 1(P). That's 2 people. Next is Seat 7(R). This fits! D is at seat 3.
- Arrangement: P(1), ??(2), D(3), B(4), Q(5), ??(6), R(7).
- Remaining seats: 2, 6. Remaining people: A, C.
- Apply Clue 6: "C is not an immediate neighbour of P." P is at 1. Neighbours are R(7) and ??(2). So, Seat 2 cannot be C. Seat 2 must be A.
- Therefore, Seat 6 must be C.
- Final Arrangement (Clockwise): P(1), A(2), D(3), B(4), Q(5), C(6), R(7).
- Verification:
- P(1), A(2), D(3), B(4), Q(5), C(6), R(7)
- Clue 2 (R and D left of D): D=3. Left: A(2), P(1). Count=2. Next is R(7). Correct.
- Clue 3 (P 3rd left of B): B=4. Left: D(3), A(2), P(1). Count=3. Correct.
- Clue 4 (Q immediate right of B): B=4. Right: Q(5). Correct.
- Clue 5 (Q 2nd left of R): R=7. Left: C(6), Q(5). Count=2. Correct.
- Clue 6 (C not neighbour of P): P=1. Neighbours: R(7), A(2). C=6. Correct.
Finding the Person Third to the Right of A
Now that we have the final seating arrangement:
- The arrangement is: P, A, D, B, Q, C, R (clockwise).
- A is at seat 2.
- We need to find who is third to the right (clockwise) of A.
- 1st person to the right of A(2) is D(3).
- 2nd person to the right of A(2) is B(4).
- 3rd person to the right of A(2) is Q(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?
