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