Circular Facing Center: Worksheet 6 - Intermediate-Advanced Practice Circular Facing Center INTERMEDIATE ADVANCED

Solution Approach:

Step 1: Draw circular diagram
6 persons facing center. Opposite positions are 3 seats apart.
Number positions 1–6 clockwise.

Step 2: Place definite positions
- Fix E at position 1 (reference point)
- E is second to the LEFT of A → A is 2 clockwise from E
pos[A] = 3
- F sits OPPOSITE E (pos 1) → pos 4
- C sits immediately to the right of F (pos 4) → pos 5

Step 3: Resolve remaining positions
Remaining persons: B, D → remaining seats: [2, 6]
B is NOT adjacent to C (pos 5).
Adjacent to pos 5: pos 4 and pos 6.
Therefore B → pos 2, and D → pos 6.

Final Arrangement (clockwise):
pos1:E → pos2:B → pos3:A → pos4:F → pos5:C → pos6:D
(All facing center)

Opposite pairs: pos1↔pos4, pos2↔pos5, pos3↔pos6

A is at pos 3 → opposite = pos 6 = D

Answer: D sits opposite to A.

Solution Approach:

Step 1: Draw circular diagram
6 persons facing center. Opposite positions are 3 seats apart.
Number positions 1–6 clockwise.

Step 2: Place definite positions
- Fix B at position 1 (reference point)
- B is second to the LEFT of C → C is 2 clockwise from B
pos[C] = 3
- D sits OPPOSITE B (pos 1) → pos 4
- E sits immediately to the right of D (pos 4) → pos 5

Step 3: Resolve remaining positions
Remaining persons: F, A → remaining seats: [2, 6]
F is NOT adjacent to E (pos 5).
Adjacent to pos 5: pos 4 and pos 6.
Therefore F → pos 2, and A → pos 6.

Final Arrangement (clockwise):
pos1:B → pos2:F → pos3:C → pos4:D → pos5:E → pos6:A
(All facing center)

Opposite pairs: pos1↔pos4, pos2↔pos5, pos3↔pos6

C is at pos 3 → opposite = pos 6 = A

Answer: A sits opposite to C.

Solution Approach:

Step 1: Draw circular diagram
6 persons facing center. Opposite positions are 3 seats apart.
Number positions 1–6 clockwise.

Step 2: Place definite positions
- Fix A at position 1 (reference point)
- A is second to the LEFT of C → C is 2 clockwise from A
pos[C] = 3
- F sits OPPOSITE A (pos 1) → pos 4
- B sits immediately to the right of F (pos 4) → pos 5

Step 3: Resolve remaining positions
Remaining persons: D, E → remaining seats: [2, 6]
D is NOT adjacent to B (pos 5).
Adjacent to pos 5: pos 4 and pos 6.
Therefore D → pos 2, and E → pos 6.

Final Arrangement (clockwise):
pos1:A → pos2:D → pos3:C → pos4:F → pos5:B → pos6:E
(All facing center)

Opposite pairs: pos1↔pos4, pos2↔pos5, pos3↔pos6

C is at pos 3 → opposite = pos 6 = E

Answer: E sits opposite to C.

Solution Approach:

Step 1: Draw circular diagram
6 persons facing center. Opposite positions are 3 seats apart.
Number positions 1–6 clockwise.

Step 2: Place definite positions
- Fix E at position 1 (reference point)
- E is second to the LEFT of D → D is 2 clockwise from E
pos[D] = 3
- C sits OPPOSITE E (pos 1) → pos 4
- A sits immediately to the right of C (pos 4) → pos 5

Step 3: Resolve remaining positions
Remaining persons: F, B → remaining seats: [2, 6]
F is NOT adjacent to A (pos 5).
Adjacent to pos 5: pos 4 and pos 6.
Therefore F → pos 2, and B → pos 6.

Final Arrangement (clockwise):
pos1:E → pos2:F → pos3:D → pos4:C → pos5:A → pos6:B
(All facing center)

Opposite pairs: pos1↔pos4, pos2↔pos5, pos3↔pos6

D is at pos 3 → opposite = pos 6 = B

Answer: B sits opposite to D.

Solution Approach:

Step 1: Draw circular diagram
6 persons facing center. Opposite positions are 3 seats apart.
Number positions 1–6 clockwise.

Step 2: Place definite positions
- Fix E at position 1 (reference point)
- E is second to the LEFT of D → D is 2 clockwise from E
pos[D] = 3
- B sits OPPOSITE E (pos 1) → pos 4
- F sits immediately to the right of B (pos 4) → pos 5

Step 3: Resolve remaining positions
Remaining persons: C, A → remaining seats: [2, 6]
C is NOT adjacent to F (pos 5).
Adjacent to pos 5: pos 4 and pos 6.
Therefore C → pos 2, and A → pos 6.

Final Arrangement (clockwise):
pos1:E → pos2:C → pos3:D → pos4:B → pos5:F → pos6:A
(All facing center)

Opposite pairs: pos1↔pos4, pos2↔pos5, pos3↔pos6

D is at pos 3 → opposite = pos 6 = A

Answer: A sits opposite to D.

Solution Approach:

Step 1: Draw circular diagram
6 persons facing center. Opposite positions are 3 seats apart.
Number positions 1–6 clockwise.

Step 2: Place definite positions
- Fix A at position 1 (reference point)
- A is second to the LEFT of F → F is 2 clockwise from A
pos[F] = 3
- B sits OPPOSITE A (pos 1) → pos 4
- E sits immediately to the right of B (pos 4) → pos 5

Step 3: Resolve remaining positions
Remaining persons: D, C → remaining seats: [2, 6]
D is NOT adjacent to E (pos 5).
Adjacent to pos 5: pos 4 and pos 6.
Therefore D → pos 2, and C → pos 6.

Final Arrangement (clockwise):
pos1:A → pos2:D → pos3:F → pos4:B → pos5:E → pos6:C
(All facing center)

Opposite pairs: pos1↔pos4, pos2↔pos5, pos3↔pos6

F is at pos 3 → opposite = pos 6 = C

Answer: C sits opposite to F.

Solution Approach:

Step 1: Draw circular diagram
6 persons facing center. Opposite positions are 3 seats apart.
Number positions 1–6 clockwise.

Step 2: Place definite positions
- Fix B at position 1 (reference point)
- B is second to the LEFT of D → D is 2 clockwise from B
pos[D] = 3
- A sits OPPOSITE B (pos 1) → pos 4
- E sits immediately to the right of A (pos 4) → pos 5

Step 3: Resolve remaining positions
Remaining persons: F, C → remaining seats: [2, 6]
F is NOT adjacent to E (pos 5).
Adjacent to pos 5: pos 4 and pos 6.
Therefore F → pos 2, and C → pos 6.

Final Arrangement (clockwise):
pos1:B → pos2:F → pos3:D → pos4:A → pos5:E → pos6:C
(All facing center)

Opposite pairs: pos1↔pos4, pos2↔pos5, pos3↔pos6

D is at pos 3 → opposite = pos 6 = C

Answer: C sits opposite to D.

Solution Approach:

Step 1: Draw circular diagram
6 persons facing center. Opposite positions are 3 seats apart.
Number positions 1–6 clockwise.

Step 2: Place definite positions
- Fix D at position 1 (reference point)
- D is second to the LEFT of C → C is 2 clockwise from D
pos[C] = 3
- B sits OPPOSITE D (pos 1) → pos 4
- A sits immediately to the right of B (pos 4) → pos 5

Step 3: Resolve remaining positions
Remaining persons: F, E → remaining seats: [2, 6]
F is NOT adjacent to A (pos 5).
Adjacent to pos 5: pos 4 and pos 6.
Therefore F → pos 2, and E → pos 6.

Final Arrangement (clockwise):
pos1:D → pos2:F → pos3:C → pos4:B → pos5:A → pos6:E
(All facing center)

Opposite pairs: pos1↔pos4, pos2↔pos5, pos3↔pos6

C is at pos 3 → opposite = pos 6 = E

Answer: E sits opposite to C.

Solution Approach:

Step 1: Draw circular diagram
6 persons facing center. Opposite positions are 3 seats apart.
Number positions 1–6 clockwise.

Step 2: Place definite positions
- Fix C at position 1 (reference point)
- C is second to the LEFT of B → B is 2 clockwise from C
pos[B] = 3
- F sits OPPOSITE C (pos 1) → pos 4
- D sits immediately to the right of F (pos 4) → pos 5

Step 3: Resolve remaining positions
Remaining persons: A, E → remaining seats: [2, 6]
A is NOT adjacent to D (pos 5).
Adjacent to pos 5: pos 4 and pos 6.
Therefore A → pos 2, and E → pos 6.

Final Arrangement (clockwise):
pos1:C → pos2:A → pos3:B → pos4:F → pos5:D → pos6:E
(All facing center)

Opposite pairs: pos1↔pos4, pos2↔pos5, pos3↔pos6

B is at pos 3 → opposite = pos 6 = E

Answer: E sits opposite to B.

Solution Approach:

Step 1: Draw circular diagram
6 persons facing center. Opposite positions are 3 seats apart.
Number positions 1–6 clockwise.

Step 2: Place definite positions
- Fix C at position 1 (reference point)
- C is second to the LEFT of B → B is 2 clockwise from C
pos[B] = 3
- D sits OPPOSITE C (pos 1) → pos 4
- E sits immediately to the right of D (pos 4) → pos 5

Step 3: Resolve remaining positions
Remaining persons: F, A → remaining seats: [2, 6]
F is NOT adjacent to E (pos 5).
Adjacent to pos 5: pos 4 and pos 6.
Therefore F → pos 2, and A → pos 6.

Final Arrangement (clockwise):
pos1:C → pos2:F → pos3:B → pos4:D → pos5:E → pos6:A
(All facing center)

Opposite pairs: pos1↔pos4, pos2↔pos5, pos3↔pos6

B is at pos 3 → opposite = pos 6 = A

Answer: A sits opposite to B.

Solution Approach:

Step 1: Draw circular diagram
6 persons facing center. Opposite positions are 3 seats apart.
Number positions 1–6 clockwise.

Step 2: Place definite positions
- Fix C at position 1 (reference point)
- C is second to the LEFT of F → F is 2 clockwise from C
pos[F] = 3
- A sits OPPOSITE C (pos 1) → pos 4
- D sits immediately to the right of A (pos 4) → pos 5

Step 3: Resolve remaining positions
Remaining persons: E, B → remaining seats: [2, 6]
E is NOT adjacent to D (pos 5).
Adjacent to pos 5: pos 4 and pos 6.
Therefore E → pos 2, and B → pos 6.

Final Arrangement (clockwise):
pos1:C → pos2:E → pos3:F → pos4:A → pos5:D → pos6:B
(All facing center)

Opposite pairs: pos1↔pos4, pos2↔pos5, pos3↔pos6

F is at pos 3 → opposite = pos 6 = B

Answer: B sits opposite to F.

Solution Approach:

Step 1: Draw circular diagram
6 persons facing center. Opposite positions are 3 seats apart.
Number positions 1–6 clockwise.

Step 2: Place definite positions
- Fix F at position 1 (reference point)
- F is second to the LEFT of B → B is 2 clockwise from F
pos[B] = 3
- A sits OPPOSITE F (pos 1) → pos 4
- D sits immediately to the right of A (pos 4) → pos 5

Step 3: Resolve remaining positions
Remaining persons: C, E → remaining seats: [2, 6]
C is NOT adjacent to D (pos 5).
Adjacent to pos 5: pos 4 and pos 6.
Therefore C → pos 2, and E → pos 6.

Final Arrangement (clockwise):
pos1:F → pos2:C → pos3:B → pos4:A → pos5:D → pos6:E
(All facing center)

Opposite pairs: pos1↔pos4, pos2↔pos5, pos3↔pos6

B is at pos 3 → opposite = pos 6 = E

Answer: E sits opposite to B.

Solution Approach:

Step 1: Draw circular diagram
6 persons facing center. Opposite positions are 3 seats apart.
Number positions 1–6 clockwise.

Step 2: Place definite positions
- Fix B at position 1 (reference point)
- B is second to the LEFT of A → A is 2 clockwise from B
pos[A] = 3
- E sits OPPOSITE B (pos 1) → pos 4
- C sits immediately to the right of E (pos 4) → pos 5

Step 3: Resolve remaining positions
Remaining persons: F, D → remaining seats: [2, 6]
F is NOT adjacent to C (pos 5).
Adjacent to pos 5: pos 4 and pos 6.
Therefore F → pos 2, and D → pos 6.

Final Arrangement (clockwise):
pos1:B → pos2:F → pos3:A → pos4:E → pos5:C → pos6:D
(All facing center)

Opposite pairs: pos1↔pos4, pos2↔pos5, pos3↔pos6

A is at pos 3 → opposite = pos 6 = D

Answer: D sits opposite to A.

Solution Approach:

Step 1: Draw circular diagram
6 persons facing center. Opposite positions are 3 seats apart.
Number positions 1–6 clockwise.

Step 2: Place definite positions
- Fix F at position 1 (reference point)
- F is second to the LEFT of B → B is 2 clockwise from F
pos[B] = 3
- C sits OPPOSITE F (pos 1) → pos 4
- E sits immediately to the right of C (pos 4) → pos 5

Step 3: Resolve remaining positions
Remaining persons: A, D → remaining seats: [2, 6]
A is NOT adjacent to E (pos 5).
Adjacent to pos 5: pos 4 and pos 6.
Therefore A → pos 2, and D → pos 6.

Final Arrangement (clockwise):
pos1:F → pos2:A → pos3:B → pos4:C → pos5:E → pos6:D
(All facing center)

Opposite pairs: pos1↔pos4, pos2↔pos5, pos3↔pos6

B is at pos 3 → opposite = pos 6 = D

Answer: D sits opposite to B.

Solution Approach:

Step 1: Draw circular diagram
6 persons facing center. Opposite positions are 3 seats apart.
Number positions 1–6 clockwise.

Step 2: Place definite positions
- Fix A at position 1 (reference point)
- A is second to the LEFT of E → E is 2 clockwise from A
pos[E] = 3
- D sits OPPOSITE A (pos 1) → pos 4
- F sits immediately to the right of D (pos 4) → pos 5

Step 3: Resolve remaining positions
Remaining persons: B, C → remaining seats: [2, 6]
B is NOT adjacent to F (pos 5).
Adjacent to pos 5: pos 4 and pos 6.
Therefore B → pos 2, and C → pos 6.

Final Arrangement (clockwise):
pos1:A → pos2:B → pos3:E → pos4:D → pos5:F → pos6:C
(All facing center)

Opposite pairs: pos1↔pos4, pos2↔pos5, pos3↔pos6

E is at pos 3 → opposite = pos 6 = C

Answer: C sits opposite to E.

Solution Approach:

Step 1: Draw circular diagram
6 persons facing center. Opposite positions are 3 seats apart.
Number positions 1–6 clockwise.

Step 2: Place definite positions
- Fix A at position 1 (reference point)
- A is second to the LEFT of C → C is 2 clockwise from A
pos[C] = 3
- E sits OPPOSITE A (pos 1) → pos 4
- F sits immediately to the right of E (pos 4) → pos 5

Step 3: Resolve remaining positions
Remaining persons: D, B → remaining seats: [2, 6]
D is NOT adjacent to F (pos 5).
Adjacent to pos 5: pos 4 and pos 6.
Therefore D → pos 2, and B → pos 6.

Final Arrangement (clockwise):
pos1:A → pos2:D → pos3:C → pos4:E → pos5:F → pos6:B
(All facing center)

Opposite pairs: pos1↔pos4, pos2↔pos5, pos3↔pos6

C is at pos 3 → opposite = pos 6 = B

Answer: B sits opposite to C.

Solution Approach:

Step 1: Draw circular diagram
6 persons facing center. Opposite positions are 3 seats apart.
Number positions 1–6 clockwise.

Step 2: Place definite positions
- Fix D at position 1 (reference point)
- D is second to the LEFT of B → B is 2 clockwise from D
pos[B] = 3
- F sits OPPOSITE D (pos 1) → pos 4
- A sits immediately to the right of F (pos 4) → pos 5

Step 3: Resolve remaining positions
Remaining persons: E, C → remaining seats: [2, 6]
E is NOT adjacent to A (pos 5).
Adjacent to pos 5: pos 4 and pos 6.
Therefore E → pos 2, and C → pos 6.

Final Arrangement (clockwise):
pos1:D → pos2:E → pos3:B → pos4:F → pos5:A → pos6:C
(All facing center)

Opposite pairs: pos1↔pos4, pos2↔pos5, pos3↔pos6

B is at pos 3 → opposite = pos 6 = C

Answer: C sits opposite to B.

Solution Approach:

Step 1: Draw circular diagram
6 persons facing center. Opposite positions are 3 seats apart.
Number positions 1–6 clockwise.

Step 2: Place definite positions
- Fix D at position 1 (reference point)
- D is second to the LEFT of B → B is 2 clockwise from D
pos[B] = 3
- F sits OPPOSITE D (pos 1) → pos 4
- E sits immediately to the right of F (pos 4) → pos 5

Step 3: Resolve remaining positions
Remaining persons: C, A → remaining seats: [2, 6]
C is NOT adjacent to E (pos 5).
Adjacent to pos 5: pos 4 and pos 6.
Therefore C → pos 2, and A → pos 6.

Final Arrangement (clockwise):
pos1:D → pos2:C → pos3:B → pos4:F → pos5:E → pos6:A
(All facing center)

Opposite pairs: pos1↔pos4, pos2↔pos5, pos3↔pos6

B is at pos 3 → opposite = pos 6 = A

Answer: A sits opposite to B.

Solution Approach:

Step 1: Draw circular diagram
6 persons facing center. Opposite positions are 3 seats apart.
Number positions 1–6 clockwise.

Step 2: Place definite positions
- Fix C at position 1 (reference point)
- C is second to the LEFT of A → A is 2 clockwise from C
pos[A] = 3
- B sits OPPOSITE C (pos 1) → pos 4
- F sits immediately to the right of B (pos 4) → pos 5

Step 3: Resolve remaining positions
Remaining persons: E, D → remaining seats: [2, 6]
E is NOT adjacent to F (pos 5).
Adjacent to pos 5: pos 4 and pos 6.
Therefore E → pos 2, and D → pos 6.

Final Arrangement (clockwise):
pos1:C → pos2:E → pos3:A → pos4:B → pos5:F → pos6:D
(All facing center)

Opposite pairs: pos1↔pos4, pos2↔pos5, pos3↔pos6

A is at pos 3 → opposite = pos 6 = D

Answer: D sits opposite to A.

Solution Approach:

Step 1: Draw circular diagram
6 persons facing center. Opposite positions are 3 seats apart.
Number positions 1–6 clockwise.

Step 2: Place definite positions
- Fix B at position 1 (reference point)
- B is second to the LEFT of D → D is 2 clockwise from B
pos[D] = 3
- E sits OPPOSITE B (pos 1) → pos 4
- A sits immediately to the right of E (pos 4) → pos 5

Step 3: Resolve remaining positions
Remaining persons: F, C → remaining seats: [2, 6]
F is NOT adjacent to A (pos 5).
Adjacent to pos 5: pos 4 and pos 6.
Therefore F → pos 2, and C → pos 6.

Final Arrangement (clockwise):
pos1:B → pos2:F → pos3:D → pos4:E → pos5:A → pos6:C
(All facing center)

Opposite pairs: pos1↔pos4, pos2↔pos5, pos3↔pos6

D is at pos 3 → opposite = pos 6 = C

Answer: C sits opposite to D.