Problem Setup
Analyze the given constraints for the circular table arrangement:
- There are 7 people: A, B, C, D, E, F, and G.
- They are seated around a circular table facing the center.
- Constraint 1: Exactly 2 people sit between F and C when counting clockwise from F.
- Constraint 2: Exactly 2 people sit between C and A when counting clockwise from C.
- Constraint 3: Exactly 3 people sit between F and G when counting clockwise from F.
- Constraint 4: E sits immediately to the left of D (meaning E is counter-clockwise to D, or E D in clockwise order).
- The question asks for the number of people between D and F when counting clockwise from D.
Step-by-Step Solution
Step 1: Determine the relative positions of F, C, and A.
- Imagine 7 seats numbered 1 to 7 clockwise. Let F be at seat 1.
- From Constraint 1 (F _ _ C), C is 3 seats clockwise from F. So, C is at seat 1 + 3 = 4.
- From Constraint 2 (C _ _ A), A is 3 seats clockwise from C. So, A is at seat 4 + 3 = 7.
- The arrangement so far (clockwise) is: F(1), Seat 2, Seat 3, C(4), Seat 5, Seat 6, A(7).
Step 2: Determine the position of G.
- From Constraint 3 (F _ _ _ G), G is 4 seats clockwise from F. So, G is at seat 1 + 4 = 5.
- The arrangement is now: F(1), Seat 2, Seat 3, C(4), G(5), Seat 6, A(7).
Step 3: Place D and E using Constraint 4.
- The remaining seats are 2, 3, and 6.
- The remaining people are B, D, and E.
- Constraint 4 states E is immediately left (counter-clockwise) of D. This means in clockwise order, they appear as E D.
- The only adjacent pair of empty seats that fits the E D clockwise pattern is Seat 2 (for E) and Seat 3 (for D).
- Arrangement: F(1), E(2), D(3), C(4), G(5), Seat 6, A(7).
Step 4: Place the remaining person B.
- The only empty seat left is Seat 6. B must be at Seat 6.
- The final clockwise arrangement is: F, E, D, C, G, B, A.
Step 5: Answer the question.
- The question asks for the number of people between D and F, counted clockwise from D.
- D is at Seat 3. F is at Seat 1.
- Counting clockwise from D: The sequence is D -> C(4) -> G(5) -> B(6) -> A(7) -> F(1).
- The people sitting between D and F in this direction are C, G, B, and A.
- There are 4 people between D and F.
Important Questions from Circular Arrangement
- A, B, C, D, E and F are sitting around a circular table facing the centre. D sits third to the right of C. A sits second to the left of C. E sits second to the right of F. B sits to the immediate right of E. How many people sit between A and F when counted from the left of A?
A, B, C, D, E and F are sitting around a circular table, facing the centre. A and D are immediate neighbours of C. E is to the immediate left of D. A and F are not immediate neighbours. Who sits third to the right of A?
- Six colleagues - Hussain, Anita, Manshaad, Emily, Sunita, and Shanti - are sitting around a circular table facing the centre. Hussain is sitting second to the right of Anita. Manshaad is an immediate neighbour of both Emily and Anita. Sunita is sitting second to the left of Manshaad. Who is sitting second to the left of Shanti?
A, B, C, D, E and F are sitting around a circular table, facing the centre. D sits third to the right of C. A sits second to the left of C. E sits second to the right of F. B sits to the immediate right of E. How many people sit between A and F, when counted from the left of A?
- A, B, C, D, E and F are sitting around a circular table, facing the centre. B sits third to the right of C. C sits second to the left of A. F sits third to the right of D. D sits to the immediate left of E. How many people sit between E and B, when counted from the left of E?
