Eight friends K, L, M, N, O, P, Q and R are sitting clockwise in the same sequence around a circular table, facing the centre, at equal distances from each other. If O is sitting in the south-east, then in which direction is R facing?
East
Circular Arrangement Puzzle Solution
The problem describes eight friends K, L, M, N, O, P, Q and R sitting around a circular table. They are arranged in a specific sequence (K to R) clockwise and are facing the centre of the table at equal distances from each other.
Understanding the Setup and Directions
A circular table with 8 equally spaced positions facing the centre can be mapped to the 8 standard compass directions: North, North-East, East, South-East, South, South-West, West, and North-West. Since there are 8 positions equally spaced around 360 degrees, each position is \(360^\circ / 8 = 45^\circ\) away from its neighbours.
We are given that O is sitting in the South-East direction.
Mapping Friend Positions to Directions
The friends are sitting in the clockwise sequence K, L, M, N, O, P, Q, R. If O is in the South-East, we can determine the direction of the other friends by moving around the circle. Since the sequence K to R is clockwise, moving anti-clockwise from O will lead us backwards through the sequence (O, N, M, L, K, R, Q, P).
- O is at South-East.
- Moving 45 degrees anti-clockwise from South-East gives East. N is here.
- Moving 45 degrees anti-clockwise from East gives North-East. M is here.
- Moving 45 degrees anti-clockwise from North-East gives North. L is here.
- Moving 45 degrees anti-clockwise from North gives North-West. K is here.
- Moving 45 degrees anti-clockwise from North-West gives West. R is here.
- Moving 45 degrees anti-clockwise from West gives South-West. Q is here.
- Moving 45 degrees anti-clockwise from South-West gives South. P is here.
We can also think about moving clockwise from O. O is SE. Clockwise from SE is South (45 deg), then South-West (90 deg), then West (135 deg). So, P is at South, Q is at South-West, and R is at West. This confirms R is at the West position.
Here is a summary of the friend positions and their corresponding directions:
| Friend | Direction of Position |
|---|---|
| K | North-West |
| L | North |
| M | North-East |
| N | East |
| O | South-East |
| P | South |
| Q | South-West |
| R | West |
Determining R’s Facing Direction
We need to find the direction R is facing. We have determined that R is sitting at the position corresponding to the West direction.
The problem states that all friends are facing the centre of the table. When a person is located at a certain directional position around a circle and faces the centre, they face the direction opposite to their position.
- If you are at the North position facing the centre, you face South.
- If you are at the East position facing the centre, you face West.
- If you are at the South position facing the centre, you face North.
- If you are at the West position facing the centre, you face East.
- If you are at the North-East position facing the centre, you face South-West.
- If you are at the South-East position facing the centre, you face North-West.
- If you are at the South-West position facing the centre, you face North-East.
- If you are at the North-West position facing the centre, you face South-East.
Since R is sitting at the West position and facing the centre, R is facing the direction opposite to West.
The direction opposite to West is East.
Conclusion
Based on the clockwise arrangement starting from K and O being in the South-East, R is seated in the West direction. As R is facing the centre, R faces the direction opposite to West, which is East.
Revision Table: Circular Seating Arrangement Key Concepts
| Concept | Explanation in Puzzles |
|---|---|
| Circular Arrangement | People or objects placed around a circle. Relative positions (left/right, opposite) are important. |
| Clockwise/Anti-clockwise | Specifies the order or movement direction around the circle. |
| Facing Centre | Individuals are looking towards the middle. The direction they face is opposite to their position direction. |
| Facing Away from Centre | Individuals are looking outwards. The direction they face is the same as their position direction. |
| Equal Distance | Positions are uniformly spaced, often allowing mapping to compass directions. |
Additional Information: Solving Direction & Seating Puzzles
Solving puzzles involving directions and seating arrangements requires careful step-by-step analysis. Here are some tips:
- Draw a diagram: A visual representation of the circular table and positions is very helpful.
- Establish a reference point: Use the given information (like O's position) to anchor your diagram.
- Follow the sequence and direction: Pay close attention to whether the arrangement is clockwise or anti-clockwise.
- Determine facing direction: Clearly distinguish between a person's position direction and the direction they are facing (which depends on whether they face the centre or away).
- Check relative positions: Use terms like 'left'/'right' or 'opposite' based on the perspective of the person at a specific position.
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