Eight friends, P, Q, R, S, T, U, V and W, are sitting clockwise in the same order around a circular table at equal distances between them, facing the center of the table. If S is sitting in the west, then who is sitting in the south-west direction?
R
Understanding the Circular Seating Arrangement
This problem involves understanding a circular seating arrangement with eight friends and determining their positions based on a given direction.
We are given that eight friends, P, Q, R, S, T, U, V, and W, are sitting around a circular table. They are in a specific order (P to W) clockwise, are equally spaced, and are facing the center.
Mapping Directions in the Circular Setup
A circular table with 8 equally spaced positions can be aligned with the eight primary directions: North, North-East, East, South-East, South, South-West, West, and North-West.
The angle between each adjacent friend is \( \frac{360^\circ}{8} = 45^\circ \).
We are told that S is sitting in the West direction.
The friends are arranged in a clockwise order: P, Q, R, S, T, U, V, W. Since they are in this order clockwise around the table, if we know S's position (West), we can find the position of others relative to S in the clockwise direction.
Starting from S (West) and moving clockwise, the sequence is S, T, U, V, W, P, Q, R. Each step clockwise moves \(45^\circ\) from the current direction.
Let's map the positions starting from S (West):
- S is in the West.
- Moving clockwise \(45^\circ\) from West brings us to North-West. The person after S in the clockwise order is T. So, T is in the North-West.
- Moving clockwise \(45^\circ\) from North-West brings us to North. The person after T is U. So, U is in the North.
- Moving clockwise \(45^\circ\) from North brings us to North-East. The person after U is V. So, V is in the North-East.
- Moving clockwise \(45^\circ\) from North-East brings us to East. The person after V is W. So, W is in the East.
- Moving clockwise \(45^\circ\) from East brings us to South-East. The person after W is P. So, P is in the South-East.
- Moving clockwise \(45^\circ\) from South-East brings us to South. The person after P is Q. So, Q is in the South.
- Moving clockwise \(45^\circ\) from South brings us to South-West. The person after Q is R. So, R is in the South-West.
Let's summarize the positions in a table:
| Friend | Direction |
|---|---|
| S | West |
| T | North-West |
| U | North |
| V | North-East |
| W | East |
| P | South-East |
| Q | South |
| R | South-West |
Identifying the Person in South-West
Based on our mapping, the person sitting in the South-West direction is R.
Revision Table: Key Information Summary
| Aspect | Detail |
|---|---|
| Number of Friends | 8 |
| Friends Order (Clockwise) | P, Q, R, S, T, U, V, W |
| Given Position | S is in the West |
| Angular Separation | \(45^\circ\) between adjacent friends |
| Target Direction | South-West |
| Friend in South-West | R |
Additional Information: Circular Arrangement Basics
Circular arrangement problems are common in logical reasoning. Key points to remember:
- The positions are relative to each other around a circle.
- Clockwise and anti-clockwise directions are crucial for determining relative positions.
- If directions (like North, South, East, West) are involved, assume the standard map orientation unless stated otherwise.
- With N equally spaced items around a circle, the angle between adjacent items is \(360^\circ / N\).
- When a specific item's absolute position (like a direction) is given, it serves as a reference point to fix the positions of all other items.
Understanding how to fix one person's position and then trace the others based on the given order (clockwise or anti-clockwise) and spacing is key to solving these problems.
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