Five friends - David, Ethan, Fred, Gilbert, and Harry were sitting around a circular table facing the center of the table. Harry was sitting next to neither David nor Fred. Gilbert is sitting to the immediate left of Fred. Who among the following is sitting to Fred's immediate right?
David
- Key Information: Five friends (David, Ethan, Fred, Gilbert, Harry) seated at a circular table, facing inwards.
- Clue 1: Gilbert sits immediately to Fred's left.
- Clue 2: Harry is not adjacent to David or Fred.
- Question: Who is sitting immediately to Fred's right?
Understanding Circular Table Arrangements
When people sit at a circular table and face the center, 'left' and 'right' are relative to their own perspective. The person to your immediate left is the one clockwise from you, and the person to your immediate right is the one counter-clockwise from you.
Applying the Clues Step-by-Step
Step 1: Positioning Gilbert relative to Fred
Clue 1 states: "Gilbert is sitting to the immediate left of Fred."
Since they face the center, Gilbert being on Fred's left means Gilbert is positioned immediately clockwise to Fred. We can represent this clockwise sequence as (Fred, Gilbert).
Step 2: Placing Harry based on constraints
We have five positions around the table. Let's denote the clockwise order starting with Fred as F, followed by G (Gilbert), then three other positions for Ethan (E), David (D), and Harry (H).
Current clockwise sequence fragment: F, G, _, _, _
Clue 2 states: "Harry was sitting next to neither David nor Fred."
- Harry (H) cannot be adjacent to Fred (F). In the F, G, _, _, _ sequence, the positions adjacent to F are the one G is in (clockwise) and the last position (counter-clockwise). Since G is already placed, H cannot be in the position counter-clockwise to F.
- The seats available for D, E, and H are the 3rd, 4th, and 5th positions clockwise after F.
- H cannot be in the 5th position (adjacent to F counter-clockwise).
- This leaves the 3rd and 4th positions for H.
- Let's test these positions for H:
- Scenario 1: H is in the 3rd position. The sequence is F, G, H, _, _. The remaining people are D and E for the 4th and 5th positions. The seats adjacent to H are G (2nd) and the 4th position. Clue 2 says H is not next to D. Therefore, D cannot be in the 4th position. D must be in the 5th position, and E must be in the 4th position. The clockwise order is F, G, H, E, D. In this case, H's neighbours are G and E. F is two seats away, and D is two seats away. This satisfies Clue 2.
- Scenario 2: H is in the 4th position. The sequence is F, G, _, H, _. The remaining people are D and E for the 3rd and 5th positions. The seats adjacent to H are the 3rd and 5th positions. Clue 2 says H is not next to D. This means D cannot be in the 3rd or 5th position. However, D must occupy one of these seats. This creates a contradiction, so Scenario 2 is impossible.
Based on this analysis, the only valid clockwise arrangement is: Fred, Gilbert, Harry, Ethan, David.
Step 3: Identifying Fred's Neighbor on the Right
The question asks who is sitting to Fred's immediate right.
In the confirmed clockwise sequence (Fred, Gilbert, Harry, Ethan, David):
- Gilbert is to Fred's immediate left (clockwise).
- David is to Fred's immediate right (counter-clockwise).
Conclusion on Seating Arrangement
The final seating arrangement in clockwise order is Fred, Gilbert, Harry, Ethan, David.
Verification:
- Gilbert is indeed to Fred's immediate left.
- Harry is seated between Gilbert and Ethan, satisfying the condition that Harry is not next to Fred or David.
Therefore, the person sitting to Fred's immediate right is David.
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