Double Row Facing Each Other: Worksheet 6 - Intermediate-Advanced Practice Double Row Facing Each Other INTERMEDIATE ADVANCED

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
- C sits 4th from the left end of Row 1 → Row 1, pos 4
- D sits at an extreme end: pos 1 or pos 5
- E sits second to the RIGHT of D (south-facing → lower position):
pos[E] = pos[D] - 2
If D at pos 1 → pos[E] = -1 (invalid ✗)
If D at pos 5 → pos[E] = 3 ✓ (pos 3 is free)
∴ D at pos 5, E at pos 3 ✓

Row 1: _ _ E C D
Remaining A,B at pos 1 and 2 (either order — pinned next).

Step 3: Place Row 2 persons
- T faces C (pos 4) → T at Row 2, pos 4
- S sits second to the LEFT of T (north-facing → lower position):
pos[S] = pos[T] - 2 = 2 → S at Row 2 pos 2 ✓
- Q sits at extreme end of Row 2: pos 1 or pos 5
- R is NOT adjacent to T (pos 4): adjacent = pos 3 and pos 5
So R ≠ pos 3 and R ≠ pos 5
Remaining positions for Q,P,R: pos 1, pos 3, pos 5
R not at pos 3 or pos 5 → R at pos 1
Q at extreme → pos 5 (since pos 1 is R) ✓
P fills pos 3 ✓

Row 2: R S P T Q

Final Arrangement:
Position: 1 2 3 4 5
Row 1 (↓): A/B A/B E C D
Row 2 (↑): R S P T Q

Find who faces E:
E is at Row 1, position 3.
Person at Row 2, position 3 = P

Answer: P faces E.

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
- E sits at an extreme end: pos 1 or pos 5
- C sits second to the RIGHT of E (south-facing → lower position):
pos[C] = pos[E] - 2
If E at pos 1 → pos[C] = -1 (invalid ✗)
If E at pos 5 → pos[C] = 3 ✓ (pos 3 is free)
∴ E at pos 5, C at pos 3 ✓

Row 1: _ _ C A E
Remaining B,D at pos 1 and 2 (either order — pinned next).

Step 3: Place Row 2 persons
- P faces A (pos 4) → P at Row 2, pos 4
- Q sits second to the LEFT of P (north-facing → lower position):
pos[Q] = pos[P] - 2 = 2 → Q at Row 2 pos 2 ✓
- S sits at extreme end of Row 2: pos 1 or pos 5
- T is NOT adjacent to P (pos 4): adjacent = pos 3 and pos 5
So T ≠ pos 3 and T ≠ pos 5
Remaining positions for S,R,T: pos 1, pos 3, pos 5
T not at pos 3 or pos 5 → T at pos 1
S at extreme → pos 5 (since pos 1 is T) ✓
R fills pos 3 ✓

Row 2: T Q R P S

Final Arrangement:
Position: 1 2 3 4 5
Row 1 (↓): B/D B/D C A E
Row 2 (↑): T Q R P S

Find who faces C:
C is at Row 1, position 3.
Person at Row 2, position 3 = R

Answer: R faces C.

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
- E sits at an extreme end: pos 1 or pos 5
- C sits second to the RIGHT of E (south-facing → lower position):
pos[C] = pos[E] - 2
If E at pos 1 → pos[C] = -1 (invalid ✗)
If E at pos 5 → pos[C] = 3 ✓ (pos 3 is free)
∴ E at pos 5, C at pos 3 ✓

Row 1: _ _ C A E
Remaining D,B at pos 1 and 2 (either order — pinned next).

Step 3: Place Row 2 persons
- R faces A (pos 4) → R at Row 2, pos 4
- P sits second to the LEFT of R (north-facing → lower position):
pos[P] = pos[R] - 2 = 2 → P at Row 2 pos 2 ✓
- Q sits at extreme end of Row 2: pos 1 or pos 5
- S is NOT adjacent to R (pos 4): adjacent = pos 3 and pos 5
So S ≠ pos 3 and S ≠ pos 5
Remaining positions for Q,T,S: pos 1, pos 3, pos 5
S not at pos 3 or pos 5 → S at pos 1
Q at extreme → pos 5 (since pos 1 is S) ✓
T fills pos 3 ✓

Row 2: S P T R Q

Final Arrangement:
Position: 1 2 3 4 5
Row 1 (↓): D/B D/B C A E
Row 2 (↑): S P T R Q

Find who faces C:
C is at Row 1, position 3.
Person at Row 2, position 3 = T

Answer: T faces C.

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
- E sits at an extreme end: pos 1 or pos 5
- B sits second to the RIGHT of E (south-facing → lower position):
pos[B] = pos[E] - 2
If E at pos 1 → pos[B] = -1 (invalid ✗)
If E at pos 5 → pos[B] = 3 ✓ (pos 3 is free)
∴ E at pos 5, B at pos 3 ✓

Row 1: _ _ B A E
Remaining C,D 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
- R sits second to the LEFT of S (north-facing → lower position):
pos[R] = pos[S] - 2 = 2 → R at Row 2 pos 2 ✓
- Q sits at extreme end of Row 2: pos 1 or pos 5
- T is NOT adjacent to S (pos 4): adjacent = pos 3 and pos 5
So T ≠ pos 3 and T ≠ pos 5
Remaining positions for Q,P,T: pos 1, pos 3, pos 5
T not at pos 3 or pos 5 → T at pos 1
Q at extreme → pos 5 (since pos 1 is T) ✓
P fills pos 3 ✓

Row 2: T R P S Q

Final Arrangement:
Position: 1 2 3 4 5
Row 1 (↓): C/D C/D B A E
Row 2 (↑): T R P S Q

Find who faces B:
B is at Row 1, position 3.
Person at Row 2, position 3 = P

Answer: P faces B.

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
- D sits 4th from the left end of Row 1 → Row 1, pos 4
- E sits at an extreme end: pos 1 or pos 5
- B sits second to the RIGHT of E (south-facing → lower position):
pos[B] = pos[E] - 2
If E at pos 1 → pos[B] = -1 (invalid ✗)
If E at pos 5 → pos[B] = 3 ✓ (pos 3 is free)
∴ E at pos 5, B at pos 3 ✓

Row 1: _ _ B D E
Remaining A,C at pos 1 and 2 (either order — pinned next).

Step 3: Place Row 2 persons
- P faces D (pos 4) → P at Row 2, pos 4
- T sits second to the LEFT of P (north-facing → lower position):
pos[T] = pos[P] - 2 = 2 → T at Row 2 pos 2 ✓
- Q sits at extreme end of Row 2: pos 1 or pos 5
- S is NOT adjacent to P (pos 4): adjacent = pos 3 and pos 5
So S ≠ pos 3 and S ≠ pos 5
Remaining positions for Q,R,S: pos 1, pos 3, pos 5
S not at pos 3 or pos 5 → S at pos 1
Q at extreme → pos 5 (since pos 1 is S) ✓
R fills pos 3 ✓

Row 2: S T R P Q

Final Arrangement:
Position: 1 2 3 4 5
Row 1 (↓): A/C A/C B D E
Row 2 (↑): S T R P Q

Find who faces B:
B is at Row 1, position 3.
Person at Row 2, position 3 = R

Answer: R faces B.

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
- D sits 4th from the left end of Row 1 → Row 1, pos 4
- E sits at an extreme end: pos 1 or pos 5
- C sits second to the RIGHT of E (south-facing → lower position):
pos[C] = pos[E] - 2
If E at pos 1 → pos[C] = -1 (invalid ✗)
If E at pos 5 → pos[C] = 3 ✓ (pos 3 is free)
∴ E at pos 5, C at pos 3 ✓

Row 1: _ _ C D E
Remaining B,A at pos 1 and 2 (either order — pinned next).

Step 3: Place Row 2 persons
- S faces D (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 ✓
- Q sits at extreme end of Row 2: pos 1 or pos 5
- P is NOT adjacent to S (pos 4): adjacent = pos 3 and pos 5
So P ≠ pos 3 and P ≠ pos 5
Remaining positions for Q,R,P: pos 1, pos 3, pos 5
P not at pos 3 or pos 5 → P at pos 1
Q at extreme → pos 5 (since pos 1 is P) ✓
R fills pos 3 ✓

Row 2: P T R S Q

Final Arrangement:
Position: 1 2 3 4 5
Row 1 (↓): B/A B/A C D E
Row 2 (↑): P T R S Q

Find who faces C:
C is at Row 1, position 3.
Person at Row 2, position 3 = R

Answer: R faces C.

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
- C sits 4th from the left end of Row 1 → Row 1, pos 4
- D sits at an extreme end: pos 1 or pos 5
- B sits second to the RIGHT of D (south-facing → lower position):
pos[B] = pos[D] - 2
If D at pos 1 → pos[B] = -1 (invalid ✗)
If D at pos 5 → pos[B] = 3 ✓ (pos 3 is free)
∴ D at pos 5, B at pos 3 ✓

Row 1: _ _ B C D
Remaining E,A at pos 1 and 2 (either order — pinned next).

Step 3: Place Row 2 persons
- Q faces C (pos 4) → Q at Row 2, pos 4
- T sits second to the LEFT of Q (north-facing → lower position):
pos[T] = pos[Q] - 2 = 2 → T at Row 2 pos 2 ✓
- R sits at extreme end of Row 2: pos 1 or pos 5
- S is NOT adjacent to Q (pos 4): adjacent = pos 3 and pos 5
So S ≠ pos 3 and S ≠ pos 5
Remaining positions for R,P,S: pos 1, pos 3, pos 5
S not at pos 3 or pos 5 → S at pos 1
R at extreme → pos 5 (since pos 1 is S) ✓
P fills pos 3 ✓

Row 2: S T P Q R

Final Arrangement:
Position: 1 2 3 4 5
Row 1 (↓): E/A E/A B C D
Row 2 (↑): S T P Q R

Find who faces B:
B is at Row 1, position 3.
Person at Row 2, position 3 = P

Answer: P faces B.

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
- E 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 E C
Remaining B,A at pos 1 and 2 (either order — pinned next).

Step 3: Place Row 2 persons
- T faces E (pos 4) → T at Row 2, pos 4
- R sits second to the LEFT of T (north-facing → lower position):
pos[R] = pos[T] - 2 = 2 → R at Row 2 pos 2 ✓
- Q sits at extreme end of Row 2: pos 1 or pos 5
- P is NOT adjacent to T (pos 4): adjacent = pos 3 and pos 5
So P ≠ pos 3 and P ≠ pos 5
Remaining positions for Q,S,P: pos 1, pos 3, pos 5
P not at pos 3 or pos 5 → P at pos 1
Q at extreme → pos 5 (since pos 1 is P) ✓
S fills pos 3 ✓

Row 2: P R S T Q

Final Arrangement:
Position: 1 2 3 4 5
Row 1 (↓): B/A B/A D E C
Row 2 (↑): P R S T Q

Find who faces D:
D is at Row 1, position 3.
Person at Row 2, position 3 = S

Answer: S 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
- D sits 4th from the left end of Row 1 → Row 1, pos 4
- E sits at an extreme end: pos 1 or pos 5
- B sits second to the RIGHT of E (south-facing → lower position):
pos[B] = pos[E] - 2
If E at pos 1 → pos[B] = -1 (invalid ✗)
If E at pos 5 → pos[B] = 3 ✓ (pos 3 is free)
∴ E at pos 5, B at pos 3 ✓

Row 1: _ _ B D E
Remaining A,C at pos 1 and 2 (either order — pinned next).

Step 3: Place Row 2 persons
- P faces D (pos 4) → P at Row 2, pos 4
- S sits second to the LEFT of P (north-facing → lower position):
pos[S] = pos[P] - 2 = 2 → S at Row 2 pos 2 ✓
- R sits at extreme end of Row 2: pos 1 or pos 5
- T is NOT adjacent to P (pos 4): adjacent = pos 3 and pos 5
So T ≠ pos 3 and T ≠ pos 5
Remaining positions for R,Q,T: pos 1, pos 3, pos 5
T not at pos 3 or pos 5 → T at pos 1
R at extreme → pos 5 (since pos 1 is T) ✓
Q fills pos 3 ✓

Row 2: T S Q P R

Final Arrangement:
Position: 1 2 3 4 5
Row 1 (↓): A/C A/C B D E
Row 2 (↑): T S Q P R

Find who faces B:
B is at Row 1, position 3.
Person at Row 2, position 3 = Q

Answer: Q faces B.

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
- 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 A C
Remaining B,E at pos 1 and 2 (either order — pinned next).

Step 3: Place Row 2 persons
- Q faces A (pos 4) → Q at Row 2, pos 4
- R sits second to the LEFT of Q (north-facing → lower position):
pos[R] = pos[Q] - 2 = 2 → R at Row 2 pos 2 ✓
- S sits at extreme end of Row 2: pos 1 or pos 5
- T is NOT adjacent to Q (pos 4): adjacent = pos 3 and pos 5
So T ≠ pos 3 and T ≠ pos 5
Remaining positions for S,P,T: pos 1, pos 3, pos 5
T not at pos 3 or pos 5 → T at pos 1
S at extreme → pos 5 (since pos 1 is T) ✓
P fills pos 3 ✓

Row 2: T R P Q S

Final Arrangement:
Position: 1 2 3 4 5
Row 1 (↓): B/E B/E D A C
Row 2 (↑): T R P Q S

Find who faces D:
D is at Row 1, position 3.
Person at Row 2, position 3 = P

Answer: P 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 ✓
- P sits at extreme end of Row 2: pos 1 or pos 5
- T is NOT adjacent to R (pos 4): adjacent = pos 3 and pos 5
So T ≠ pos 3 and T ≠ pos 5
Remaining positions for P,Q,T: pos 1, pos 3, pos 5
T not at pos 3 or pos 5 → T at pos 1
P at extreme → pos 5 (since pos 1 is T) ✓
Q fills pos 3 ✓

Row 2: T S Q R P

Final Arrangement:
Position: 1 2 3 4 5
Row 1 (↓): E/A E/A D B C
Row 2 (↑): T S Q R P

Find who faces D:
D is at Row 1, position 3.
Person at Row 2, position 3 = Q

Answer: Q 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
- E 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 E C
Remaining B,A at pos 1 and 2 (either order — pinned next).

Step 3: Place Row 2 persons
- T faces E (pos 4) → T at Row 2, pos 4
- Q sits second to the LEFT of T (north-facing → lower position):
pos[Q] = pos[T] - 2 = 2 → Q at Row 2 pos 2 ✓
- S sits at extreme end of Row 2: pos 1 or pos 5
- P is NOT adjacent to T (pos 4): adjacent = pos 3 and pos 5
So P ≠ pos 3 and P ≠ pos 5
Remaining positions for S,R,P: pos 1, pos 3, pos 5
P not at pos 3 or pos 5 → P at pos 1
S at extreme → pos 5 (since pos 1 is P) ✓
R fills pos 3 ✓

Row 2: P Q R T S

Final Arrangement:
Position: 1 2 3 4 5
Row 1 (↓): B/A B/A D E C
Row 2 (↑): P Q R T S

Find who faces D:
D is at Row 1, position 3.
Person at Row 2, position 3 = R

Answer: R 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
- D sits 4th from the left end of Row 1 → Row 1, pos 4
- C sits at an extreme end: pos 1 or pos 5
- B sits second to the RIGHT of C (south-facing → lower position):
pos[B] = pos[C] - 2
If C at pos 1 → pos[B] = -1 (invalid ✗)
If C at pos 5 → pos[B] = 3 ✓ (pos 3 is free)
∴ C at pos 5, B at pos 3 ✓

Row 1: _ _ B D C
Remaining A,E at pos 1 and 2 (either order — pinned next).

Step 3: Place Row 2 persons
- P faces D (pos 4) → P at Row 2, pos 4
- R sits second to the LEFT of P (north-facing → lower position):
pos[R] = pos[P] - 2 = 2 → R at Row 2 pos 2 ✓
- S sits at extreme end of Row 2: pos 1 or pos 5
- T is NOT adjacent to P (pos 4): adjacent = pos 3 and pos 5
So T ≠ pos 3 and T ≠ pos 5
Remaining positions for S,Q,T: pos 1, pos 3, pos 5
T not at pos 3 or pos 5 → T at pos 1
S at extreme → pos 5 (since pos 1 is T) ✓
Q fills pos 3 ✓

Row 2: T R Q P S

Final Arrangement:
Position: 1 2 3 4 5
Row 1 (↓): A/E A/E B D C
Row 2 (↑): T R Q P S

Find who faces B:
B is at Row 1, position 3.
Person at Row 2, position 3 = Q

Answer: Q faces B.

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
- D sits 4th from the left end of Row 1 → Row 1, pos 4
- B sits at an extreme end: pos 1 or pos 5
- E sits second to the RIGHT of B (south-facing → lower position):
pos[E] = pos[B] - 2
If B at pos 1 → pos[E] = -1 (invalid ✗)
If B at pos 5 → pos[E] = 3 ✓ (pos 3 is free)
∴ B at pos 5, E at pos 3 ✓

Row 1: _ _ E D B
Remaining C,A at pos 1 and 2 (either order — pinned next).

Step 3: Place Row 2 persons
- T faces D (pos 4) → T at Row 2, pos 4
- Q sits second to the LEFT of T (north-facing → lower position):
pos[Q] = pos[T] - 2 = 2 → Q at Row 2 pos 2 ✓
- S sits at extreme end of Row 2: pos 1 or pos 5
- P is NOT adjacent to T (pos 4): adjacent = pos 3 and pos 5
So P ≠ pos 3 and P ≠ pos 5
Remaining positions for S,R,P: pos 1, pos 3, pos 5
P not at pos 3 or pos 5 → P at pos 1
S at extreme → pos 5 (since pos 1 is P) ✓
R fills pos 3 ✓

Row 2: P Q R T S

Final Arrangement:
Position: 1 2 3 4 5
Row 1 (↓): C/A C/A E D B
Row 2 (↑): P Q R T S

Find who faces E:
E is at Row 1, position 3.
Person at Row 2, position 3 = R

Answer: R faces E.

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
- S faces B (pos 4) → S at Row 2, pos 4
- R sits second to the LEFT of S (north-facing → lower position):
pos[R] = pos[S] - 2 = 2 → R at Row 2 pos 2 ✓
- P sits at extreme end of Row 2: pos 1 or pos 5
- Q is NOT adjacent to S (pos 4): adjacent = pos 3 and pos 5
So Q ≠ pos 3 and Q ≠ pos 5
Remaining positions for P,T,Q: pos 1, pos 3, pos 5
Q not at pos 3 or pos 5 → Q at pos 1
P at extreme → pos 5 (since pos 1 is Q) ✓
T fills pos 3 ✓

Row 2: Q R T S P

Final Arrangement:
Position: 1 2 3 4 5
Row 1 (↓): E/A E/A D B C
Row 2 (↑): Q R T S P

Find who faces D:
D is at Row 1, position 3.
Person at Row 2, position 3 = T

Answer: T 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
- D sits at an extreme end: pos 1 or pos 5
- B sits second to the RIGHT of D (south-facing → lower position):
pos[B] = pos[D] - 2
If D at pos 1 → pos[B] = -1 (invalid ✗)
If D at pos 5 → pos[B] = 3 ✓ (pos 3 is free)
∴ D at pos 5, B at pos 3 ✓

Row 1: _ _ B A D
Remaining C,E at pos 1 and 2 (either order — pinned next).

Step 3: Place Row 2 persons
- T faces A (pos 4) → T at Row 2, pos 4
- S sits second to the LEFT of T (north-facing → lower position):
pos[S] = pos[T] - 2 = 2 → S at Row 2 pos 2 ✓
- R sits at extreme end of Row 2: pos 1 or pos 5
- P is NOT adjacent to T (pos 4): adjacent = pos 3 and pos 5
So P ≠ pos 3 and P ≠ pos 5
Remaining positions for R,Q,P: pos 1, pos 3, pos 5
P not at pos 3 or pos 5 → P at pos 1
R at extreme → pos 5 (since pos 1 is P) ✓
Q fills pos 3 ✓

Row 2: P S Q T R

Final Arrangement:
Position: 1 2 3 4 5
Row 1 (↓): C/E C/E B A D
Row 2 (↑): P S Q T R

Find who faces B:
B is at Row 1, position 3.
Person at Row 2, position 3 = Q

Answer: Q faces B.

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
- D sits 4th from the left end of Row 1 → Row 1, pos 4
- C sits at an extreme end: pos 1 or pos 5
- A sits second to the RIGHT of C (south-facing → lower position):
pos[A] = pos[C] - 2
If C at pos 1 → pos[A] = -1 (invalid ✗)
If C at pos 5 → pos[A] = 3 ✓ (pos 3 is free)
∴ C at pos 5, A at pos 3 ✓

Row 1: _ _ A D C
Remaining B,E at pos 1 and 2 (either order — pinned next).

Step 3: Place Row 2 persons
- T faces D (pos 4) → T at Row 2, pos 4
- S sits second to the LEFT of T (north-facing → lower position):
pos[S] = pos[T] - 2 = 2 → S at Row 2 pos 2 ✓
- P sits at extreme end of Row 2: pos 1 or pos 5
- Q is NOT adjacent to T (pos 4): adjacent = pos 3 and pos 5
So Q ≠ pos 3 and Q ≠ pos 5
Remaining positions for P,R,Q: pos 1, pos 3, pos 5
Q not at pos 3 or pos 5 → Q at pos 1
P at extreme → pos 5 (since pos 1 is Q) ✓
R fills pos 3 ✓

Row 2: Q S R T P

Final Arrangement:
Position: 1 2 3 4 5
Row 1 (↓): B/E B/E A D C
Row 2 (↑): Q S R T P

Find who faces A:
A is at Row 1, position 3.
Person at Row 2, position 3 = R

Answer: R faces A.

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
- D sits 4th from the left end of Row 1 → Row 1, pos 4
- C sits at an extreme end: pos 1 or pos 5
- E sits second to the RIGHT of C (south-facing → lower position):
pos[E] = pos[C] - 2
If C at pos 1 → pos[E] = -1 (invalid ✗)
If C at pos 5 → pos[E] = 3 ✓ (pos 3 is free)
∴ C at pos 5, E at pos 3 ✓

Row 1: _ _ E D C
Remaining A,B at pos 1 and 2 (either order — pinned next).

Step 3: Place Row 2 persons
- S faces D (pos 4) → S at Row 2, pos 4
- R sits second to the LEFT of S (north-facing → lower position):
pos[R] = pos[S] - 2 = 2 → R at Row 2 pos 2 ✓
- Q sits at extreme end of Row 2: pos 1 or pos 5
- P is NOT adjacent to S (pos 4): adjacent = pos 3 and pos 5
So P ≠ pos 3 and P ≠ pos 5
Remaining positions for Q,T,P: pos 1, pos 3, pos 5
P not at pos 3 or pos 5 → P at pos 1
Q at extreme → pos 5 (since pos 1 is P) ✓
T fills pos 3 ✓

Row 2: P R T S Q

Final Arrangement:
Position: 1 2 3 4 5
Row 1 (↓): A/B A/B E D C
Row 2 (↑): P R T S Q

Find who faces E:
E is at Row 1, position 3.
Person at Row 2, position 3 = T

Answer: T faces E.

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
- C sits 4th from the left end of Row 1 → Row 1, pos 4
- D sits at an extreme end: pos 1 or pos 5
- A sits second to the RIGHT of D (south-facing → lower position):
pos[A] = pos[D] - 2
If D at pos 1 → pos[A] = -1 (invalid ✗)
If D at pos 5 → pos[A] = 3 ✓ (pos 3 is free)
∴ D at pos 5, A at pos 3 ✓

Row 1: _ _ A C D
Remaining E,B at pos 1 and 2 (either order — pinned next).

Step 3: Place Row 2 persons
- P faces C (pos 4) → P at Row 2, pos 4
- R sits second to the LEFT of P (north-facing → lower position):
pos[R] = pos[P] - 2 = 2 → R at Row 2 pos 2 ✓
- T sits at extreme end of Row 2: pos 1 or pos 5
- S is NOT adjacent to P (pos 4): adjacent = pos 3 and pos 5
So S ≠ pos 3 and S ≠ pos 5
Remaining positions for T,Q,S: pos 1, pos 3, pos 5
S not at pos 3 or pos 5 → S at pos 1
T at extreme → pos 5 (since pos 1 is S) ✓
Q fills pos 3 ✓

Row 2: S R Q P T

Final Arrangement:
Position: 1 2 3 4 5
Row 1 (↓): E/B E/B A C D
Row 2 (↑): S R Q P T

Find who faces A:
A is at Row 1, position 3.
Person at Row 2, position 3 = Q

Answer: Q faces A.

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
- E sits 4th from the left end of Row 1 → Row 1, pos 4
- C sits at an extreme end: pos 1 or pos 5
- A sits second to the RIGHT of C (south-facing → lower position):
pos[A] = pos[C] - 2
If C at pos 1 → pos[A] = -1 (invalid ✗)
If C at pos 5 → pos[A] = 3 ✓ (pos 3 is free)
∴ C at pos 5, A at pos 3 ✓

Row 1: _ _ A E C
Remaining B,D at pos 1 and 2 (either order — pinned next).

Step 3: Place Row 2 persons
- P faces E (pos 4) → P at Row 2, pos 4
- R sits second to the LEFT of P (north-facing → lower position):
pos[R] = pos[P] - 2 = 2 → R at Row 2 pos 2 ✓
- Q sits at extreme end of Row 2: pos 1 or pos 5
- T is NOT adjacent to P (pos 4): adjacent = pos 3 and pos 5
So T ≠ pos 3 and T ≠ pos 5
Remaining positions for Q,S,T: pos 1, pos 3, pos 5
T not at pos 3 or pos 5 → T at pos 1
Q at extreme → pos 5 (since pos 1 is T) ✓
S fills pos 3 ✓

Row 2: T R S P Q

Final Arrangement:
Position: 1 2 3 4 5
Row 1 (↓): B/D B/D A E C
Row 2 (↑): T R S P Q

Find who faces A:
A is at Row 1, position 3.
Person at Row 2, position 3 = S

Answer: S faces A.