How many people sit between L and S when counted from the left of S?
Circular Table Seating Arrangement Puzzle Solution
This solution provides a step-by-step deduction to solve the circular table seating puzzle.
1. Understanding the Constraints
- People: L, M, N, O, Q, R, S (7 total)
- Setup: Sitting around a circular table, facing the center.
- Direction Convention (Facing Center): Right = Clockwise, Left = Counter-clockwise.
- Constraint 1: L sits fourth to the right of R. (Implies 3 people between R and L going clockwise: R _ _ _ L)
- Constraint 2: Only two people sit between Q and N when counted from the left of Q. (Implies 2 people between Q and N going counter-clockwise: Q _ _ N)
- Constraint 3: M sits third to the left of O. (Implies 2 people between O and M going counter-clockwise: O _ _ M)
- Constraint 4: S is an immediate neighbor of O and N. (Forms a block: O-S-N or N-S-O)
2. Establishing the Arrangement
We will number the seats 1 to 7 clockwise.
- Place R and L: From Constraint 1 (L is 4th right of R), let R be at position 1. Moving 4 positions clockwise (1 -> 2 -> 3 -> 4 -> 5), L is at position 5.
Arrangement: R(1), _(2), _(3), _(4), L(5), _(6), _(7)
- Place O, S, N block: Constraint 4 requires O, S, N to be adjacent. The only available consecutive slots are (2,3,4) or (6,7,?). Consider the N-S-O block possibility fitting into slots (2,3,4).
Arrangement: R(1), N(2), S(3), O(4), L(5), _(6), _(7)
Check Constraint 3 (M is 3rd left of O): O is at 4. Counter-clockwise: 4 -> 3 -> 2 -> 1. M should be at 1. But R is at 1. This block order (N-S-O clockwise) fails. - Try O-S-N block: Place the O-S-N block in slots (2,3,4).
Arrangement: R(1), O(2), S(3), N(4), L(5), _(6), _(7)
- Place M: Check Constraint 3 (M is 3rd left of O). O is at 2. Counter-clockwise: 2 -> 1 -> 7 -> 6. M is at position 6.
Arrangement: R(1), O(2), S(3), N(4), L(5), M(6), _(7)
- Place Q: The only remaining person is Q, and the only slot is 7. Q is at position 7.
Arrangement: R(1), O(2), S(3), N(4), L(5), M(6), Q(7)
- Verify Constraints:
- L 4th right of R: R(1) -> O(2) -> S(3) -> N(4) -> L(5). Correct.
- 2 between Q and N (from Q's left/counter-clockwise): Q(7) -> M(6) -> L(5) -> N(4). Correct (M and L are between).
- M 3rd left of O: O(2) -> R(1) -> Q(7) -> M(6). Correct (R and Q are between).
- S neighbours O and N: O(2)-S(3)-N(4). Correct.
3. Finding the Number of People Between L and S
The question asks for the number of people between L and S, counted from the left (counter-clockwise) of S.
- Current Arrangement (Clockwise): R(1), O(2), S(3), N(4), L(5), M(6), Q(7)
- S is at position 3. L is at position 5.
- Count from S counter-clockwise:
- Position 2: O (1st person counted)
- Position 1: R (2nd person counted)
- Position 7: Q (3rd person counted)
- Position 6: M (4th person counted)
- Position 5: L (Destination reached)
- The people sitting between S and L in this direction are O, R, Q, and M.
Therefore, there are Four people between L and S when counted from the left of S.
Similar Questions
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Important Questions from Circular Arrangement
Eight students A, B, C, D, E, F, G and Hsit around a circular table, equidistant from each other, facing the centre of the table, not necessarily in the same order. Band Dsit neither adjacent to Cnor opposite to C. Asits in between Eand D, and Fsits in between Band H. Which one of the following is definitely correct?
Akash, Binita, Chandan, Daksh, Ekta & Fatima are standing in a circle. Binita is between Daksh & Chandan. Akash is between Ekta & Chandan. Fatima is to the right of Daksh. Who is between Akash & Fatima?
Six friends A, B, C, D, E and F are sitting around a round table in such a way that A is between E and F, E is opposite to D, and C is not on either side of E. The person opposite to D is
Who among the following is a neighbour of S and R?
Which of the following are not neighbours?
