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
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Six persons A, B, C, D, E and Fare sitting equidistant from each other around a circular table (facing the centre of the table).
Consider the Question and two Statements given below :
Question : Who is sitting on the immediate left of A?
Statement-1 : Bis sitting opposite to Cand Dis sitting opposite to E.
Statement-2 : Fis sitting on the immediate left of B.
Which one of the following is correct in respect of the Question and the Statements?
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