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