The problem asks to identify the person sitting between Sam and Rachel based on a set of clues about six friends seated around a circular table.
Analyzing Seating Arrangement Clues
- Constraint 1: Olivia is to the immediate right of Peter. This gives us a block [Peter -> Olivia] in clockwise order.
- Constraint 2: Peter and Toby are neighbours. Since Olivia is to Peter's right, Toby must be to Peter's left. This forms the block [Toby - Peter -> Olivia].
- Constraint 3: Victoria is to the immediate right of Sam. This gives us a block [Sam -> Victoria] in clockwise order.
- Constraint 4: Sam is not sitting next to Rachel.
- Constraint 5: Sam is not sitting next to Toby.
Deducing the Arrangement
We have the blocks [Toby - Peter -> Olivia] and [Sam -> Victoria]. The sixth person is Rachel.
Let's combine these blocks considering the circular arrangement and the remaining constraints:
- Start with the [Toby - Peter -> Olivia] block.
- We need to place the [Sam -> Victoria] block and Rachel (R) into the remaining three spots.
- Scenario 1: Place [Sam -> Victoria] next to Olivia, followed by Rachel.
- Clockwise Order: Toby - Peter - Olivia - Sam - Victoria - Rachel.
- Check Constraints:
- Olivia right of Peter: Yes.
- Peter/Toby neighbors: Yes.
- Victoria right of Sam: Yes.
- Sam not next to Rachel: Sam's neighbors are Olivia and Victoria. Rachel's neighbors are Victoria and Toby. Yes, Sam is not next to Rachel.
- Sam not next to Toby: Sam's neighbors are Olivia and Victoria. Toby's neighbors are Rachel and Peter. Yes, Sam is not next to Toby.
- In this arrangement, Sam's neighbours are Olivia and Victoria. Rachel's neighbours are Victoria and Toby. The common neighbour is Victoria.
- Scenario 2: Place Rachel next to Olivia, followed by the [Sam -> Victoria] block.
- Clockwise Order: Toby - Peter - Olivia - Rachel - Sam - Victoria.
- Check Constraints:
- Sam not next to Rachel: Sam's neighbours are Rachel and Victoria. This violates the constraint.
- This scenario is invalid.
- Other placements involving splitting the blocks or placing Rachel between Peter and Toby would violate adjacency rules or create conflicts with Sam's neighbours. For example, placing Sam next to Toby (Toby - Peter - Olivia - Rachel - Victoria - Sam) violates Constraint 5.
Identifying the Common Neighbour
Based on the valid arrangement (Toby - Peter - Olivia - Sam - Victoria - Rachel, clockwise), we analyze the neighbours:
- Sam's neighbours: Olivia and Victoria.
- Rachel's neighbours: Victoria and Toby.
The person who is the immediate neighbour of both Sam and Rachel is Victoria.
Important Questions from Seating arrangement
Seven people A, B, C, D, E, F and G are sitting around a circular table, facing the centre (but not necessarily in the same order). A is sitting second to the right of E. Only one person is sitting between D and A. B is sitting third to the right of G. F is an immediate neighbour of B. How many people are sitting between D and E when counted from the left of E?
Seven people A, B, C, D, E, F, and G are sitting around a circular table, facing the center (but not necessarily in the same order). C is sitting to the immediate right of E. D is sitting third to the left of C. A is the immediate neighbor of B and C. F is not the immediate neighbor of E. What is the position of G with respect to A?
P, Q, R, S, T, U, V and W are sitting around a circular table facing the centre (but not necessarily in the same order).
P is sitting to the immediate right of V and third to the left of U.
S is sitting fourth to the right of Q, who is not an immediate neighbour of P and T.
Q is sitting to the second right of U.
R is sitting to the immediate right of Q and second to the left of P.
How many people are sitting between R and T when counted from the left of T?
Rajan, Pragyan, Kamal, Sachin, Ashok, Narendra, and Laksh are sitting around a circular table, facing the centre (but not necessarily in the same order).
Rajan sits 3rd to the right of Narendra. Kamal sits 2nd to the right of Rajan.
Ashok is an immediate neighbour of Narendra. Pragyan sits to the immediate right of Sachin.
Who is sitting 3rd to the left of Narendra?
P got married 15 years ago. Today her age is 13⁄5 times her age at the time of her marriage. At present her son’s age is 1⁄5 of her age. What was her son’s age 4 years ago as a fraction of P’s age at that time?
