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