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