Question 1
Five friends P, Q, T, S and R are sitting in a row facing South.
P sits at the right extreme end. Q sits second to the right of T.
R sits immediately to the right of T (from viewer's perspective).
S 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 T:
South-facing right = viewer's left = lower position: pos[Q] = pos[T] - 2
Possible: T=3→Q=1, or T=4→Q=2
- R sits immediately to the right of T (viewer's right = higher pos): pos[R] = pos[T] + 1
If T=3 → R=4 ✓ (pos 4 free)
If T=4 → R=5 = P ✗ (conflict)
∴ T=3, Q=1, R=4
Position: Q _ T R P
Step 4: Apply constraint
- S not adjacent to P (pos 5): S ≠ pos 4 (taken by R) → S at pos 2 ✓
Final Arrangement (all facing South ↓):
Position: Q S T R P
Verification:
✓ P at right extreme end (pos 5)
✓ Q second to right of T: pos[Q](=1)-2 = 3 = pos[T] (south-facing right=lower)
✓ R immediately right of T (viewer right): pos 3+1 = 4
✓ S 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 T:
South-facing right = viewer's left = lower position: pos[Q] = pos[T] - 2
Possible: T=3→Q=1, or T=4→Q=2
- R sits immediately to the right of T (viewer's right = higher pos): pos[R] = pos[T] + 1
If T=3 → R=4 ✓ (pos 4 free)
If T=4 → R=5 = P ✗ (conflict)
∴ T=3, Q=1, R=4
Position: Q _ T R P
Step 4: Apply constraint
- S not adjacent to P (pos 5): S ≠ pos 4 (taken by R) → S at pos 2 ✓
Final Arrangement (all facing South ↓):
Position: Q S T R P
Verification:
✓ P at right extreme end (pos 5)
✓ Q second to right of T: pos[Q](=1)-2 = 3 = pos[T] (south-facing right=lower)
✓ R immediately right of T (viewer right): pos 3+1 = 4
✓ S not adjacent to P (pos 2, not pos 4)
Answer: Q sits at the left extreme end (position 1).