Let's carefully analyze the seating arrangement based on the clues provided.
Problem Restatement
- Persons: o, p, q, r, s, t, u, v, w, x, y, z
- They are seated around a triangle-shaped chair arrangement.
- Each edge of the triangle has 3 people seated.
- Each corner has 1 person seated.
- Total seats = 3 edges × 3 people per edge + 3 corners = 9 + 3 = 12 seats (matches 12 persons).
Key Points and Clues
- Edges and corners:
- Each edge has 3 people.
- Each corner has 1 person.
- So, on each edge, the middle person is "in the middle" of the edge.
- Positions of o, p, q:
- o, p, q are seated in the middle of each edge.
- Positions of x and w:
- Only 5 people sit between x and w.
- Neither x nor w sits at corners.
- t is second to the left of w.
- t is immediate left of r.
- u is immediate neighbor of x.
- Only 2 people sit between t and u.
- Positions of s, z, v:
- s sits at one of the corners.
- s is third to the right of w.
- s is immediate neighbor to both z and v.
- v is immediate neighbor to p.
- Positions of y and o:
- Two people sit between y and o.
- o doesn’t sit near w.
Step-by-Step Deduction
Step 1: Triangle Seating Setup
Label the corners as C1, C2, C3. Between corners, edges have 3 people each:
- Edge1: C1 - a - b - C2
- Edge2: C2 - c - d - C3
- Edge3: C3 - e - f - C1
Total seats: 3 corners + 3 edges × 3 seats = 12 seats.
Step 2: Place o, p, q in the middle of edges
Since o, p, q are in the middle of edges, they must be in positions a, d, or f (the middle seats on each edge). Assign:
- o at a (middle of edge C1-C2)
- p at d (middle of edge C2-C3)
- q at f (middle of edge C3-C1)
Step 3: v is immediate neighbor of p
p is at d (middle of edge C2-C3). Neighbors of p are c and e (the seats adjacent to d). So v is either c or e.
Step 4: s sits at one corner and is immediate neighbor to both z and v
- s is at a corner (C1, C2, or C3).
- s neighbors z and v.
- Since corners have 2 neighbors (one on each side), z and v must be the two neighbors of s.
Step 5: s is third to the right of w
- w is not at a corner.
- s is third to the right of w.
The seating is around the triangle, so "third to the right" means counting 3 seats clockwise from w to s.
Step 6: x and w are not at corners
- x and w are somewhere on edges but not corners.
- 5 people sit between x and w.
Step 7: t is second to left of w and immediate left of r
- t is second to the left of w.
- t is immediate left of r.
- Only 2 people sit between t and u.
- u is immediate neighbor of x.
Step 8: Two people sit between y and o, and o doesn’t sit near w
- y and o have two people between them.
- o is at a (middle of edge C1-C2).
- w is not near o.
Final Deduction: Who sits at the corners?
- s sits at one corner.
- The other two corners must be assigned to the remaining persons who fit the constraints.
Since s is at a corner and neighbors z and v, and v neighbors p, the corners are:
- s at one corner
- The other two corners must be assigned to persons who are neighbors to the edges and fit the constraints.
Answer to the Question:
Who among the following sit at the corner?
- s (confirmed corner)
- The other two corners are not explicitly named in the clues, but since x and w are not at corners, and o, p, q are in the middle of edges, the remaining corners are likely to be:
- The corners adjacent to s, which are neighbors to z and v.
Thus, s is definitely at a corner.
Summary:
- s sits at a corner.
- The other corners are not explicitly named but are neighbors of s, likely z and possibly another person.
- From the clues, only s is explicitly confirmed to be at a corner.
If you provide the list of options, I can specify exactly who among them sits at the corner.
