Question 1
Five friends P, Q, S, R and T are sitting in a row facing South.
P sits at the right extreme end. Q sits second to the right of S.
T sits immediately to the right of S (from viewer's perspective).
R is not adjacent to P.
Who sits at the left extreme end?
Solution Approach:
Step 1: Understanding facing South
When persons face South:
- Their right hand points West (viewer's LEFT) — "right" in the question = lower position number
- Viewer's "right" (higher position) = person's left side
Step 2: Set up diagram (viewer's perspective)
Position: 1(left) 2 3 4 5(right)
Step 3: Apply conditions
- P at the right extreme end → Position 5
- Q sits second to the right of S:
South-facing right = viewer's left = lower position: pos[Q] = pos[S] - 2
Possible: S=3→Q=1, or S=4→Q=2
- T sits immediately to the right of S (viewer's right = higher pos): pos[T] = pos[S] + 1
If S=3 → T=4 ✓ (pos 4 free)
If S=4 → T=5 = P ✗ (conflict)
∴ S=3, Q=1, T=4
Position: Q _ S T P
Step 4: Apply constraint
- R not adjacent to P (pos 5): R ≠ pos 4 (taken by T) → R at pos 2 ✓
Final Arrangement (all facing South ↓):
Position: Q R S T P
Verification:
✓ P at right extreme end (pos 5)
✓ Q second to right of S: pos[Q](=1)-2 = 3 = pos[S] (south-facing right=lower)
✓ T immediately right of S (viewer right): pos 3+1 = 4
✓ R not adjacent to P (pos 2, not pos 4)
Answer: Q sits at the left extreme end (position 1).
Step 1: Understanding facing South
When persons face South:
- Their right hand points West (viewer's LEFT) — "right" in the question = lower position number
- Viewer's "right" (higher position) = person's left side
Step 2: Set up diagram (viewer's perspective)
Position: 1(left) 2 3 4 5(right)
Step 3: Apply conditions
- P at the right extreme end → Position 5
- Q sits second to the right of S:
South-facing right = viewer's left = lower position: pos[Q] = pos[S] - 2
Possible: S=3→Q=1, or S=4→Q=2
- T sits immediately to the right of S (viewer's right = higher pos): pos[T] = pos[S] + 1
If S=3 → T=4 ✓ (pos 4 free)
If S=4 → T=5 = P ✗ (conflict)
∴ S=3, Q=1, T=4
Position: Q _ S T P
Step 4: Apply constraint
- R not adjacent to P (pos 5): R ≠ pos 4 (taken by T) → R at pos 2 ✓
Final Arrangement (all facing South ↓):
Position: Q R S T P
Verification:
✓ P at right extreme end (pos 5)
✓ Q second to right of S: pos[Q](=1)-2 = 3 = pos[S] (south-facing right=lower)
✓ T immediately right of S (viewer right): pos 3+1 = 4
✓ R not adjacent to P (pos 2, not pos 4)
Answer: Q sits at the left extreme end (position 1).