Question 1
Two parallel rows of chairs. Row 1 has B, D, A, C and E facing South.
Row 2 has S, T, P, Q and R facing North. Each person in one row faces exactly one person from the other row.
A sits fourth from the left end of Row 1. S faces A.
B sits at an extreme end of Row 1. D sits second to the right of B.
T sits second to the left of S. P sits at an extreme end of Row 2.
R is not adjacent to S in Row 2.
Who faces D?
Solution Approach:
Step 1: Draw the double row setup
Row 1 faces South (↓), Row 2 faces North (↑)
Person at position i in Row 1 faces person at position i in Row 2.
Position: 1 2 3 4 5
Row 1 (↓): _ _ _ _ _
Row 2 (↑): _ _ _ _ _
Key direction rule:
- Row 1 (South-facing): "right" = viewer's LEFT (lower position numbers)
- Row 2 (North-facing): "right" = viewer's RIGHT (higher position numbers)
Step 2: Place Row 1 persons
- A sits 4th from the left end of Row 1 → Row 1, pos 4
- B sits at an extreme end: pos 1 or pos 5
- D sits second to the RIGHT of B (south-facing → lower position):
pos[D] = pos[B] - 2
If B at pos 1 → pos[D] = -1 (invalid ✗)
If B at pos 5 → pos[D] = 3 ✓ (pos 3 is free)
∴ B at pos 5, D at pos 3 ✓
Row 1: _ _ D A B
Remaining C,E at pos 1 and 2 (either order — pinned next).
Step 3: Place Row 2 persons
- S faces A (pos 4) → S at Row 2, pos 4
- T sits second to the LEFT of S (north-facing → lower position):
pos[T] = pos[S] - 2 = 2 → T at Row 2 pos 2 ✓
- P sits at extreme end of Row 2: pos 1 or pos 5
- R is NOT adjacent to S (pos 4): adjacent = pos 3 and pos 5
So R ≠ pos 3 and R ≠ pos 5
Remaining positions for P,Q,R: pos 1, pos 3, pos 5
R not at pos 3 or pos 5 → R at pos 1
P at extreme → pos 5 (since pos 1 is R) ✓
Q fills pos 3 ✓
Row 2: R T Q S P
Final Arrangement:
Position: 1 2 3 4 5
Row 1 (↓): C/E C/E D A B
Row 2 (↑): R T Q S P
Find who faces D:
D is at Row 1, position 3.
Person at Row 2, position 3 = Q
Answer: Q faces D.
Step 1: Draw the double row setup
Row 1 faces South (↓), Row 2 faces North (↑)
Person at position i in Row 1 faces person at position i in Row 2.
Position: 1 2 3 4 5
Row 1 (↓): _ _ _ _ _
Row 2 (↑): _ _ _ _ _
Key direction rule:
- Row 1 (South-facing): "right" = viewer's LEFT (lower position numbers)
- Row 2 (North-facing): "right" = viewer's RIGHT (higher position numbers)
Step 2: Place Row 1 persons
- A sits 4th from the left end of Row 1 → Row 1, pos 4
- B sits at an extreme end: pos 1 or pos 5
- D sits second to the RIGHT of B (south-facing → lower position):
pos[D] = pos[B] - 2
If B at pos 1 → pos[D] = -1 (invalid ✗)
If B at pos 5 → pos[D] = 3 ✓ (pos 3 is free)
∴ B at pos 5, D at pos 3 ✓
Row 1: _ _ D A B
Remaining C,E at pos 1 and 2 (either order — pinned next).
Step 3: Place Row 2 persons
- S faces A (pos 4) → S at Row 2, pos 4
- T sits second to the LEFT of S (north-facing → lower position):
pos[T] = pos[S] - 2 = 2 → T at Row 2 pos 2 ✓
- P sits at extreme end of Row 2: pos 1 or pos 5
- R is NOT adjacent to S (pos 4): adjacent = pos 3 and pos 5
So R ≠ pos 3 and R ≠ pos 5
Remaining positions for P,Q,R: pos 1, pos 3, pos 5
R not at pos 3 or pos 5 → R at pos 1
P at extreme → pos 5 (since pos 1 is R) ✓
Q fills pos 3 ✓
Row 2: R T Q S P
Final Arrangement:
Position: 1 2 3 4 5
Row 1 (↓): C/E C/E D A B
Row 2 (↑): R T Q S P
Find who faces D:
D is at Row 1, position 3.
Person at Row 2, position 3 = Q
Answer: Q faces D.