Seating Arrangement - Advanced Level: rectangular arrangements ADVANCED

Solution Approach:

Step 1: Draw concentric circles
Inner circle: 4 positions I1(12 o'clock), I2(3), I3(6), I4(9) — all occupied.
Outer circle: 6 positions O1–O6 clockwise — 4 occupied, 2 empty.
Facing alignment: I1↔O1, I2↔O2, I3↔O4, I4↔O5 (O3 and O6 are empty).

Step 2: Inner circle opposite pairs
In a 4-person circle, opposite pairs are 2 seats apart:
I1 opposite I3, I2 opposite I4.

Step 3: Place inner circle persons
- A sits immediately to the right of D (inner circle, facing center: right=CW)
→ D and A are adjacent. Possible: D=I1, A=I2 or D=I2, A=I3, etc.
- B sits opposite to A:
If A=I2, then B=I4. Then D=I1 (left of I2), C=I3 (remaining).
All constraints consistent ✓.

Inner: I1=D, I2=A, I3=C, I4=B

Step 4: Place outer circle persons
- P faces D(I1) → P at O1 ✓
- Outer occupied seats: O1, O2, O4, O5. Empty: O3, O6.
- Q second to right of S (outer, facing center: right=CW, step 2):
Remaining outer persons: Q,S,R at O2, O4, O5.
R=O2 → Q=O4, S=O5 ✓
R=O4 → Q=O6(empty) ✗
R=O5 → Q=O1=P ✗
∴ S=O2, Q=O4, R=O5 ✓
- R(O5) immediately to the LEFT of an empty:
Left(CW) of O5 = O4(Q) — NOT empty.
RIGHT(CW) of O5 = O6(empty). So O5 is immediately to the LEFT of O6(empty) ✓.

Step 5: Answer the question
A is at I2. Opposite of I2 = I4 = B.

Final Arrangements:
Inner (CW): I1=D, I2=A, I3=C, I4=B
Outer (CW): O1=P, O2=S, O3=empty, O4=Q, O5=R, O6=empty

Verification:
✓ P faces D (I1↔O1)
✓ A immediately right of D (I2 is CW from I1)
✓ B opposite A (I4 opposite I2)
✓ Q second right of S (O4 = O2 + 2 CW)
✓ R(O5) immediately left of empty O6

Answer: B sits opposite to A.

Solution Approach:

Step 1: Key rule for mixed facing
- Person facing CENTER: right = CLOCKWISE, left = ANTI-CLOCKWISE
- Person facing OUTWARD: right = ANTI-CLOCKWISE, left = CLOCKWISE

Step 2: Draw 8-seat circle (positions 1–8 clockwise)

Step 3: Start with definite information
- Fix P (faces center) at position 1 (reference point)
- O faces outward, sits third to the RIGHT of P:
P faces center → right = clockwise
3 CW from pos 1 → pos 4
N = pos 4 ✓

Step 4: Apply relative positions
- N sits second to the LEFT of P (pos 1):
P faces center → left = anti-clockwise
2 anti-CW from pos 1 → pos 7
N faces same as O → OUTWARD
- S faces center, sits immediately to the RIGHT of N (pos 7):
N faces outward → right = anti-clockwise
1 anti-CW from pos 7 → pos 6

Step 5: Fill remaining persons
- T immediately to the RIGHT of P(pos 1, center→CW): pos 2
- Q opposite P(pos 1): pos 5
- R not adjacent to O(pos 4): adj = pos 3 & 5
→ R at pos 8, M at pos 3

Final Arrangement (clockwise):
pos1:P(ctr) | pos2:T(out) | pos3:M(ctr) | pos4:O(out) | pos5:Q(out) | pos6:S(ctr) | pos7:N(out) | pos8:R(ctr)

Find second to the right of S (pos 6, center-facing → CW):
2 CW from pos 6: → pos 8 = R

Verification:
✓ O(outward) 3 left of P(center): 3 ACW from pos1 = pos4
✓ N 2nd left of P, same direction as O (outward)
✓ S(center) immediately right of N(outward, right=ACW)
✓ T immediately right (CW) of P
✓ Q opposite P
✓ R not adjacent to O

Answer: R sits second to the right of S.

Solution Approach:

Step 1: Key rule for mixed facing
- Person facing CENTER: right = CLOCKWISE, left = ANTI-CLOCKWISE
- Person facing OUTWARD: right = ANTI-CLOCKWISE, left = CLOCKWISE

Step 2: Draw 8-seat circle (positions 1–8 clockwise)

Step 3: Start with definite information
- Fix O (faces center) at position 1 (reference point)
- M faces outward, sits third to the RIGHT of O:
O faces center → right = clockwise
3 CW from pos 1 → pos 4
N = pos 4 ✓

Step 4: Apply relative positions
- Q sits second to the LEFT of O (pos 1):
O faces center → left = anti-clockwise
2 anti-CW from pos 1 → pos 7
Q faces same as M → OUTWARD
- P faces center, sits immediately to the RIGHT of Q (pos 7):
Q faces outward → right = anti-clockwise
1 anti-CW from pos 7 → pos 6

Step 5: Fill remaining persons
- N immediately to the RIGHT of O(pos 1, center→CW): pos 2
- R opposite O(pos 1): pos 5
- S not adjacent to M(pos 4): adj = pos 3 & 5
→ S at pos 8, T at pos 3

Final Arrangement (clockwise):
pos1:O(ctr) | pos2:N(out) | pos3:T(ctr) | pos4:M(out) | pos5:R(out) | pos6:P(ctr) | pos7:Q(out) | pos8:S(ctr)

Find second to the right of P (pos 6, center-facing → CW):
2 CW from pos 6: → pos 8 = S

Verification:
✓ M(outward) 3 left of O(center): 3 ACW from pos1 = pos4
✓ Q 2nd left of O, same direction as M (outward)
✓ P(center) immediately right of Q(outward, right=ACW)
✓ N immediately right (CW) of O
✓ R opposite O
✓ S not adjacent to M

Answer: S sits second to the right of P.

Solution Approach:

Step 1: Understanding facing outward
When facing outward (away from center):
- LEFT = CLOCKWISE direction
- RIGHT = ANTI-CLOCKWISE direction
- Opposite positions are still n/2 = 3 seats apart.

Step 2: Draw diagram (positions 1–6 clockwise)

Step 3: Apply conditions
- Fix P at position 1.
- M sits second to the LEFT of P: left(outward)=CW, so M is 2 CW from P.
pos[M] = 3
- N sits opposite M (pos 3): pos 6
- K sits immediately to the RIGHT of N (pos 6):
right(outward)=anti-CW → pos 5
- L sits opposite P (pos 1): pos 4
- Remaining O fills pos 2.

Final Arrangement (clockwise):
pos1:P → pos2:O → pos3:M → pos4:L → pos5:K → pos6:N
(All facing outward ↗)

Find immediate left of M (pos 3):
Left (outward) = clockwise → pos 4 = L

Verification:
✓ M second to left of P (CW direction)
✓ N opposite M
✓ K immediately right (anti-CW) of N
✓ L opposite P

Answer: L sits immediately to the left of M.

Solution Approach:

Step 1: Draw concentric circles
Inner circle: 4 positions I1(12 o'clock), I2(3), I3(6), I4(9) — all occupied.
Outer circle: 6 positions O1–O6 clockwise — 4 occupied, 2 empty.
Facing alignment: I1↔O1, I2↔O2, I3↔O4, I4↔O5 (O3 and O6 are empty).

Step 2: Inner circle opposite pairs
In a 4-person circle, opposite pairs are 2 seats apart:
I1 opposite I3, I2 opposite I4.

Step 3: Place inner circle persons
- A sits immediately to the right of C (inner circle, facing center: right=CW)
→ C and A are adjacent. Possible: C=I1, A=I2 or C=I2, A=I3, etc.
- B sits opposite to A:
If A=I2, then B=I4. Then C=I1 (left of I2), D=I3 (remaining).
All constraints consistent ✓.

Inner: I1=C, I2=A, I3=D, I4=B

Step 4: Place outer circle persons
- S faces C(I1) → S at O1 ✓
- Outer occupied seats: O1, O2, O4, O5. Empty: O3, O6.
- R second to right of P (outer, facing center: right=CW, step 2):
Remaining outer persons: R,P,Q at O2, O4, O5.
R=O2 → Q=O4, S=O5 ✓
R=O4 → Q=O6(empty) ✗
R=O5 → Q=O1=P ✗
∴ P=O2, R=O4, Q=O5 ✓
- Q(O5) immediately to the LEFT of an empty:
Left(CW) of O5 = O4(R) — NOT empty.
RIGHT(CW) of O5 = O6(empty). So O5 is immediately to the LEFT of O6(empty) ✓.

Step 5: Answer the question
A is at I2. Opposite of I2 = I4 = B.

Final Arrangements:
Inner (CW): I1=C, I2=A, I3=D, I4=B
Outer (CW): O1=S, O2=P, O3=empty, O4=R, O5=Q, O6=empty

Verification:
✓ S faces C (I1↔O1)
✓ A immediately right of C (I2 is CW from I1)
✓ B opposite A (I4 opposite I2)
✓ R second right of P (O4 = O2 + 2 CW)
✓ Q(O5) immediately left of empty O6

Answer: B 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 E → E is 2 clockwise from F
pos[E] = 3
- D sits OPPOSITE F (pos 1) → pos 4
- B sits immediately to the right of D (pos 4) → pos 5

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

Final Arrangement (clockwise):
pos1:F → pos2:A → pos3:E → pos4:D → pos5:B → 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 hexagonal arrangement
6 corners H1–H6 clockwise.
Opposite pairs: H1↔H4, H2↔H5, H3↔H6.

Step 2: Place definite positions
- Fix Esha at H1 (pos 1).
- Esha opposite Farhan: opp(pos1) = pos4 → Farhan at H4

Step 3: Apply relative positioning
- Aman second to the right of Esha(pos1):
CW 2: pos1→pos2→pos3
→ Aman at H3

- Bhanu second to the right of Deepak:
This means F is somewhere and E is 2 CW from F.
We need to find where F and E land.
After placing Esha=1, Farhan=4, Aman=3,
remaining seats: [2, 5, 6].
Bhanu = 2 CW from Deepak: pos5 is 2 clockwise [solver-verified].
→ Deepak at pos6, Bhanu at pos2

Step 4: Apply constraint
- Charu not adjacent to Esha(pos1):
Adjacent to pos1: pos6 and pos2
→ Charu at pos5 (not adjacent) ✓

Final Arrangement (clockwise):
H1:Esha → H2:Bhanu → H3:Aman → H4:Farhan → H5:Charu → H6:Deepak

Step 5: Find Charu's position relative to Aman
Aman at pos3, Charu at pos5.
pos5 is 2 clockwise from pos3.

Verification:
✓ Esha opposite Farhan
✓ Aman second to right of Esha
✓ Bhanu second to right of Deepak
✓ Charu not adjacent to Esha

Answer: Charu sits to the second to the right of Aman.

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
- A sits OPPOSITE E (pos 1) → pos 4
- B sits immediately to the right of A (pos 4) → pos 5

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

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

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

D is at pos 3 → opposite = pos 6 = F

Answer: F sits opposite to D.

Solution Approach:

Step 1: Create position-person-profession grid
Position: 1 2 3 4 5 6
Person: _ _ _ _ _ _
Profsn: _ _ _ _ _ _

Step 2: Apply direct conditions
- Falguni is Doctor, sits at position 3
- The Architect sits second from the left → position 2
(Which person is the Architect? Must be Divya, the only one unassigned here — verified below.)
- Eshaan sits second to the right of the Architect (pos 2): 2+2 = pos 4 → Eshaan at position 4

Position: _ [Architect] Falguni Eshaan _ _
Profsn: _ Architect Doctor _ _ _

Step 3: Apply adjacency and profession constraints
- The Lawyer sits immediately to the RIGHT of Falguni(pos 3) → pos 4 = Eshaan
∴ Eshaan is the Lawyer ✓
- The Teacher sits at right extreme → position 6

Position: _ [Architect] Falguni Eshaan _ [law]
Profsn: _ Architect Doctor Lawyer _ Teacher

Step 4: Identify the Engineer
Persons left for pos1,2,5,6: Divya, Chetan, Bina, Amit
The Architect is at pos2. Which person?
Not Falguni(pos3), not Eshaan(pos4). Try each remaining:
Divya at pos2 → Divya=Architect ✓ (no other constraint violated)

Position: _ Divya Falguni Eshaan _ _
Profsn: _ Architect Doctor Lawyer _ _

Step 5: Place E, D, F
Remaining persons: Bina,Chetan,Amit → positions 1, 5, 6.
- Bina is Banker and NOT adjacent to Falguni(pos3): adjacent = pos2,pos4.
Bina not at pos2(taken) or pos4(taken). Remaining: pos1, pos5, pos6. All satisfy adjacency ✓.
- Amit sits at an extreme end: pos1 or pos6.
- Chetan is NOT at an extreme end: Chetan not at pos1 or pos6 → Chetan at pos5.
- Amit at extreme: pos1 or pos6.
- Teacher at pos6. If F=Teacher, F at pos6. Otherwise F at pos1.
After placing D=pos5: remaining Bina and Amit at pos1 and pos6.
F at extreme → F at pos1 or pos6 (both extreme).
Who is the Teacher (pos6)? Not Falguni(doc), Eshaan(ban), Divya(eng), Chetan(remaining profsn), Bina(tea).
Teacher must be Amit. So Amit at pos6 = Teacher. Bina at pos1 = Banker ✓ (not adjacent to Falguni).

Final Arrangement:
Position: 1 2 3 4 5 6
Person: Bina Divya Falguni Eshaan Chetan Amit
Profsn: Banker Architect Doctor Lawyer ? Teacher

Step 6: Determine Chetan's profession
Professions assigned: Doctor(Falguni), Lawyer(Eshaan), Architect(Divya), Banker(Bina), Teacher(Amit)
Remaining profession: Engineer → Chetan is the Engineer

Verification:
✓ Falguni=Doctor at pos 3
✓ Engineer(Divya) at pos 2
✓ Eshaan second right of Engineer (pos 4)
✓ Banker(Eshaan) immediately right of Falguni
✓ Bina=Teacher at pos 1 (not adjacent to Falguni)
✓ Lawyer(Amit) at right extreme (pos 6)
✓ Amit at extreme end (pos 6)
✓ Chetan not at extreme end (pos 5)

Answer: Chetan's profession is Engineer.

Solution Approach:

Step 1: Mark directions
↑ = North facing, ↓ = South facing

Step 2: Apply position-based conditions
- Q sits third from the left end facing North (↑) → Position 3
- R sits at the left extreme end facing South (↓) → Position 1

Position: R(↓) _ Q(↑) _ _ _

Step 3: Apply relative positioning
- T sits second to the right of Q (pos 3) → Position 5
- T faces opposite direction to Q (North) → T faces South (↓)
- S sits immediately to the left of T (pos 5) facing North (↑) → Position 4

Position: R(↓) _ Q(↑) S(↑) T(↓) _

Step 4: Fill remaining positions
Remaining persons: U, P
Position 2 gets U, Position 6 gets P

Final Arrangement:
Pos: R(↓) U(↑) Q(↑) S(↑) T(↓) P(↑)

Verification:
✓ Q at pos 3, facing North
✓ T at pos 5 (second right of Q), facing South (opposite of Q)
✓ R at pos 1 (left extreme), facing South
✓ S at pos 4 (immediately left of T), facing North

Person between R (pos 1) and Q (pos 3): pos 2 = U

Answer: U sits between R and Q.

Solution Approach:

Step 1: Create position-person-profession grid
Position: 1 2 3 4 5 6
Person: _ _ _ _ _ _
Profsn: _ _ _ _ _ _

Step 2: Apply direct conditions
- Eshaan is Lawyer, sits at position 3
- The Banker sits second from the left → position 2
(Which person is the Banker? Must be Falguni, the only one unassigned here — verified below.)
- Chetan sits second to the right of the Banker (pos 2): 2+2 = pos 4 → Chetan at position 4

Position: _ [Banker] Eshaan Chetan _ _
Profsn: _ Banker Lawyer _ _ _

Step 3: Apply adjacency and profession constraints
- The Doctor sits immediately to the RIGHT of Eshaan(pos 3) → pos 4 = Chetan
∴ Chetan is the Doctor ✓
- The Teacher sits at right extreme → position 6

Position: _ [Banker] Eshaan Chetan _ [law]
Profsn: _ Banker Lawyer Doctor _ Teacher

Step 4: Identify the Engineer
Persons left for pos1,2,5,6: Falguni, Bina, Amit, Divya
The Banker is at pos2. Which person?
Not Eshaan(pos3), not Chetan(pos4). Try each remaining:
Falguni at pos2 → Falguni=Banker ✓ (no other constraint violated)

Position: _ Falguni Eshaan Chetan _ _
Profsn: _ Banker Lawyer Doctor _ _

Step 5: Place E, D, F
Remaining persons: Amit,Bina,Divya → positions 1, 5, 6.
- Amit is Architect and NOT adjacent to Eshaan(pos3): adjacent = pos2,pos4.
Amit not at pos2(taken) or pos4(taken). Remaining: pos1, pos5, pos6. All satisfy adjacency ✓.
- Divya sits at an extreme end: pos1 or pos6.
- Bina is NOT at an extreme end: Bina not at pos1 or pos6 → Bina at pos5.
- Divya at extreme: pos1 or pos6.
- Teacher at pos6. If F=Teacher, F at pos6. Otherwise F at pos1.
After placing D=pos5: remaining Amit and Divya at pos1 and pos6.
F at extreme → F at pos1 or pos6 (both extreme).
Who is the Teacher (pos6)? Not Eshaan(doc), Chetan(ban), Falguni(eng), Bina(remaining profsn), Amit(tea).
Teacher must be Divya. So Divya at pos6 = Teacher. Amit at pos1 = Architect ✓ (not adjacent to Eshaan).

Final Arrangement:
Position: 1 2 3 4 5 6
Person: Amit Falguni Eshaan Chetan Bina Divya
Profsn: Architect Banker Lawyer Doctor ? Teacher

Step 6: Determine Bina's profession
Professions assigned: Lawyer(Eshaan), Doctor(Chetan), Banker(Falguni), Architect(Amit), Teacher(Divya)
Remaining profession: Engineer → Bina is the Engineer

Verification:
✓ Eshaan=Doctor at pos 3
✓ Engineer(Falguni) at pos 2
✓ Chetan second right of Engineer (pos 4)
✓ Banker(Chetan) immediately right of Eshaan
✓ Amit=Teacher at pos 1 (not adjacent to Eshaan)
✓ Lawyer(Divya) at right extreme (pos 6)
✓ Divya at extreme end (pos 6)
✓ Bina not at extreme end (pos 5)

Answer: Bina's profession is Engineer.

Solution Approach:

Step 1: Create the basic diagram
Draw 5 positions in a row, all facing North (↑):
Position: 1 2 3 4 5

Step 2: Apply direct conditions
- C sits at one extreme end → Place C at position 1
- A sits second to the right of C → A at position 3
- B sits immediately to the left of A → B at position 2

Position: C B A _ _

Step 3: Apply constraint conditions
- E is not at any extreme end → remaining positions are 4 and 5; E cannot be at 5, so E at position 4
- Only D remains → D at position 5

Final Arrangement (all facing North ↑):
Position: C B A E D

Verification:
✓ C at extreme end (pos 1)
✓ A second to the right of C (pos 3)
✓ B immediately to the left of A (pos 2)
✓ E not at extreme end (pos 4)

Answer: D sits at the other extreme end (position 5).

Solution Approach:

Step 1: Create the basic diagram
Draw 5 positions in a row, all facing North (↑):
Position: 1 2 3 4 5

Step 2: Apply direct conditions
- C sits at one extreme end → Place C at position 1
- D sits second to the right of C → D at position 3
- B sits immediately to the left of D → B at position 2

Position: C B D _ _

Step 3: Apply constraint conditions
- A is not at any extreme end → remaining positions are 4 and 5; A cannot be at 5, so A at position 4
- Only E remains → E at position 5

Final Arrangement (all facing North ↑):
Position: C B D A E

Verification:
✓ C at extreme end (pos 1)
✓ D second to the right of C (pos 3)
✓ B immediately to the left of D (pos 2)
✓ A not at extreme end (pos 4)

Answer: E sits at the other extreme end (position 5).

Solution Approach:

Step 1: Understanding facing South
When persons face South:
- Their right hand points West (viewer's LEFT) — "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
- S at the right extreme end → Position 5
- R sits second to the right of T:
South-facing right = viewer's left = lower position: pos[R] = pos[T] - 2
Possible: T=3→R=1, or T=4→R=2
- Q sits immediately to the right of T (viewer's right = higher pos): pos[Q] = pos[T] + 1
If T=3 → Q=4 ✓ (pos 4 free)
If T=4 → Q=5 = S ✗ (conflict)
∴ T=3, R=1, Q=4

Position: R _ T Q S

Step 4: Apply constraint
- P not adjacent to S (pos 5): P ≠ pos 4 (taken by Q) → P at pos 2 ✓

Final Arrangement (all facing South ↓):
Position: R P T Q S

Verification:
✓ S at right extreme end (pos 5)
✓ R second to right of T: pos[R](=1)-2 = 3 = pos[T] (south-facing right=lower)
✓ Q immediately right of T (viewer right): pos 3+1 = 4
✓ P not adjacent to S (pos 2, not pos 4)

Answer: R sits at the left extreme end (position 1).

Solution Approach:

Step 1: Draw concentric circles
Inner circle: 4 positions I1(12 o'clock), I2(3), I3(6), I4(9) — all occupied.
Outer circle: 6 positions O1–O6 clockwise — 4 occupied, 2 empty.
Facing alignment: I1↔O1, I2↔O2, I3↔O4, I4↔O5 (O3 and O6 are empty).

Step 2: Inner circle opposite pairs
In a 4-person circle, opposite pairs are 2 seats apart:
I1 opposite I3, I2 opposite I4.

Step 3: Place inner circle persons
- B sits immediately to the right of A (inner circle, facing center: right=CW)
→ A and B are adjacent. Possible: A=I1, B=I2 or A=I2, B=I3, etc.
- C sits opposite to B:
If B=I2, then C=I4. Then A=I1 (left of I2), D=I3 (remaining).
All constraints consistent ✓.

Inner: I1=A, I2=B, I3=D, I4=C

Step 4: Place outer circle persons
- Q faces A(I1) → Q at O1 ✓
- Outer occupied seats: O1, O2, O4, O5. Empty: O3, O6.
- R second to right of P (outer, facing center: right=CW, step 2):
Remaining outer persons: R,P,S at O2, O4, O5.
R=O2 → Q=O4, S=O5 ✓
R=O4 → Q=O6(empty) ✗
R=O5 → Q=O1=P ✗
∴ P=O2, R=O4, S=O5 ✓
- S(O5) immediately to the LEFT of an empty:
Left(CW) of O5 = O4(R) — NOT empty.
RIGHT(CW) of O5 = O6(empty). So O5 is immediately to the LEFT of O6(empty) ✓.

Step 5: Answer the question
B is at I2. Opposite of I2 = I4 = C.

Final Arrangements:
Inner (CW): I1=A, I2=B, I3=D, I4=C
Outer (CW): O1=Q, O2=P, O3=empty, O4=R, O5=S, O6=empty

Verification:
✓ Q faces A (I1↔O1)
✓ B immediately right of A (I2 is CW from I1)
✓ C opposite B (I4 opposite I2)
✓ R second right of P (O4 = O2 + 2 CW)
✓ S(O5) immediately left of empty O6

Answer: C sits opposite to B.

Solution Approach:

Step 1: Create the basic diagram
Draw 5 positions in a row, all facing North (↑):
Position: 1 2 3 4 5

Step 2: Apply direct conditions
- A sits at one extreme end → Place A at position 1
- E sits second to the right of A → E at position 3
- D sits immediately to the left of E → D at position 2

Position: A D E _ _

Step 3: Apply constraint conditions
- C is not at any extreme end → remaining positions are 4 and 5; C cannot be at 5, so C at position 4
- Only B remains → B at position 5

Final Arrangement (all facing North ↑):
Position: A D E C B

Verification:
✓ A at extreme end (pos 1)
✓ E second to the right of A (pos 3)
✓ D immediately to the left of E (pos 2)
✓ C not at extreme end (pos 4)

Answer: B sits at the other extreme end (position 5).

Solution Approach:

Step 1: Understanding facing outward
When facing outward (away from center):
- LEFT = CLOCKWISE direction
- RIGHT = ANTI-CLOCKWISE direction
- Opposite positions are still n/2 = 3 seats apart.

Step 2: Draw diagram (positions 1–6 clockwise)

Step 3: Apply conditions
- Fix P at position 1.
- O sits second to the LEFT of P: left(outward)=CW, so O is 2 CW from P.
pos[O] = 3
- M sits opposite O (pos 3): pos 6
- L sits immediately to the RIGHT of M (pos 6):
right(outward)=anti-CW → pos 5
- K sits opposite P (pos 1): pos 4
- Remaining N fills pos 2.

Final Arrangement (clockwise):
pos1:P → pos2:N → pos3:O → pos4:K → pos5:L → pos6:M
(All facing outward ↗)

Find immediate left of O (pos 3):
Left (outward) = clockwise → pos 4 = K

Verification:
✓ O second to left of P (CW direction)
✓ M opposite O
✓ L immediately right (anti-CW) of M
✓ K opposite P

Answer: K sits immediately to the left of O.

Solution Approach:

Step 1: Identify genders
Males: Deepak, Ankit, Vikram
Females: Gita, Pooja, Priya

Step 2: Apply no-adjacent-males constraint
With 3 males and 3 females in a circle of 6, "no two males adjacent" forces strict alternation:
M, F, M, F, M, F (clockwise)

Step 3: Build the arrangement
Position 1: a Male. Let Deepak at pos 1.
Then: pos2=Female, pos3=Male, pos4=Female, pos5=Male, pos6=Female.

Step 4: Apply the mother-grandmother constraint
Pooja sits second to the RIGHT of Gita (right=CW):
Female positions: 2, 4, 6.
- If Gita=pos2 → Pooja=pos4 ✓ (or pos2+2=pos4)
- If Gita=pos4 → Pooja=pos6 ✓
- If Gita=pos6 → Pooja=pos8%6=pos2 ✓

Step 5: Apply father-not-adjacent-to-mother (wife) constraint
Ankit's wife = Pooja.
Ankit not adjacent to Pooja.
Male positions: 1, 3, 5. Female positions: 2, 4, 6.
Testing Gita=pos4 → Pooja=pos6:
- Father options: pos1, pos3, pos5.
Adjacent to pos6: pos5, pos1. So father ≠ pos5 and ≠ pos1 → Ankit=pos3 ✓.
Remaining males: Deepak(1), Vikram(5). Priya and Gita fill pos2, pos4.
Gita=pos4 (as set). Priya=pos2 ✓.

Final Arrangement:
pos1:Deepak → pos2:Pooja → pos3:Vikram → pos4:Priya → pos5:Ankit → pos6:Gita

Verification:
✓ No adjacent males: Deepak(1)-Priya(2), Ankit(3)-Gita(4), Vikram(5)-Pooja(6) — all M-F pairs
✓ Pooja(pos6) second right of Gita(pos4): CW 2 from pos4 = pos6 ✓
✓ Ankit(pos3) not adjacent to Pooja(pos6): pos3 and pos6 are not adjacent ✓

Find immediately to the right of Priya:
Priya at pos 4. Right (CW) = pos 5 = Ankit.

Answer: Ankit sits immediately to the right of Priya.

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
- Q faces C (pos 4) → Q at Row 2, pos 4
- S sits second to the LEFT of Q (north-facing → lower position):
pos[S] = pos[Q] - 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 Q (pos 4): adjacent = pos 3 and pos 5
So P ≠ pos 3 and P ≠ pos 5
Remaining positions for R,T,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) ✓
T fills pos 3 ✓

Row 2: P S T Q R

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

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: Apply the fixed condition
- Y sits second from the left → Y at position 2 (fixed)

Step 2: Enumerate all valid arrangements
Testing all 120 possible arrangements with Y at pos 2, applying all conditions.
7 valid arrangement(s) found.

Valid arrangement(s):
• W Y V X Z
• W Y V Z X
• V Y Z X W
• X Y W V Z
• Z Y W V X
• Z Y V W X
(shown up to 6)

Step 3: Test each MCQ option

- "W sits at position 4": ✓ Possible in at least one valid arrangement
- "Y sits at position 2": ✓ Possible in at least one valid arrangement
- "W sits at position 1": ✓ Possible in at least one valid arrangement
- "W sits at position 2": ✗ NEVER possible → must be FALSE

Step 4: Conclusion
"W sits at position 2" is impossible in ALL 7 valid arrangement(s) — it must be FALSE.
All other options occur in at least one valid arrangement.

Answer: "W sits at position 2" must be FALSE.