Seating Arrangement - Intermediate Level: facing-north-south INTERMEDIATE

Solution Approach:

Step 1: Apply the fixed condition
- Z sits second from the left → Z at position 2 (fixed)

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

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

Step 3: Test each MCQ option

- "Y sits at position 2": ✗ NEVER possible → must be FALSE
- "V sits at position 5": ✓ Possible in at least one valid arrangement
- "W sits at position 1": ✓ Possible in at least one valid arrangement
- "X sits at position 1": ✓ Possible in at least one valid arrangement

Step 4: Conclusion
"Y 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: "Y sits at position 2" must be FALSE.

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 M (faces center) at position 1 (reference point)
- R faces outward, sits third to the RIGHT of M:
M faces center → right = clockwise
3 CW from pos 1 → pos 4
N = pos 4 ✓

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

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

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

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

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

Answer: O sits second to the right of S.

Solution Approach:

Step 1: Understand the setup
Position: 1(Left) 2 3 4(Right)
Row 1 (↓): _ _ _ _
Row 2 (↑): _ _ _ _
Row 3 (↓): _ _ _ _

Facing: Row 1 pos i faces Row 2 pos i; Row 2 pos i faces Row 3 pos i.
(Using viewer's perspective: left=position 1, right=position 4)

Step 2: Apply facing relationships
- D faces R who faces X: all three in the SAME vertical column.
Place at position 2:
Row1: _ D _ _
Row2: _ R _ _
Row3: _ X _ _

Step 3: Apply left-right conditions
- A sits to the left of D(pos 2) in Row 1 → A at position 1
Row1: A D _ _

Step 4: Second facing relationship
- P faces A(Row1 pos1) → P at Row2 position 1
- P faces Y → Y at Row3 position 1
Row1: A D _ _
Row2: P R _ _
Row3: Y X _ _

Step 5: Apply relative positioning in Row 2
- S sits second to the right of P(pos1): 1+2=3 → S at Row2 position 3
Row2: P R S _
S faces Row1 pos3 → C at Row1 pos3 ✓
S faces Row3 pos3 → W at Row3 pos3 ✓

Step 6: Fill remaining positions
Remaining: Row1 pos4=B, Row2 pos4=Q, Row3 pos4=Z

Final Arrangement:
Position: 1 2 3 4
Row 1 (↓): A D C B
Row 2 (↑): P R S Q
Row 3 (↓): Y X W Z

Right extreme of Row 3 = position 4 = Z

Answer: Z

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
- Q sits second to the right of P:
South-facing right = viewer's left = lower position: pos[Q] = pos[P] - 2
Possible: P=3→Q=1, or P=4→Q=2
- T sits immediately to the right of P (viewer's right = higher pos): pos[T] = pos[P] + 1
If P=3 → T=4 ✓ (pos 4 free)
If P=4 → T=5 = S ✗ (conflict)
∴ P=3, Q=1, T=4

Position: Q _ P T S

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

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

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

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

Solution Approach:

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

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

Position: _ [Teacher] Amit Bina _ _
Profsn: _ Teacher Engineer _ _ _

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

Position: _ [Teacher] Amit Bina _ [law]
Profsn: _ Teacher Engineer Lawyer _ Architect

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

Position: _ Chetan Amit Bina _ _
Profsn: _ Teacher Engineer Lawyer _ _

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

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

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

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

Answer: Falguni's profession is Banker.

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

Position: E D A _ _

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: E D A C B

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

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

Solution Approach:

Step 1: Mark total positions
Seats: 1 2 3 4 5 6 7 8 9 10
Total: 10 seats, 8 persons, 2 empty.

Step 2: Place definite positions
- F at seat 3
- B at seat 8 (seat 8)
- One empty seat at extreme end → seat 1 is empty

Seat: 1(_) 2(_) 3(F) 4(_) 5(_) 6(_) 7(_) 8(B) 9(_) 10(_)

Step 3: Apply empty seat adjacency
- D sits immediately to the RIGHT of an empty seat
- Empty at seat 1 → seat 2 = D ✓

Seat: 1(_) 2(D) 3(F) 4(_) 5(_) 6(_) 7(_) 8(B) 9(_) 10(_)

Step 4: Apply "fourth to the left" condition
- H sits fourth to the LEFT of B (seat 8)
- Fourth to left: 8 → 7 → 6 → 5 → 4
- H at seat 4 ✓

Seat: 1(_) 2(D) 3(F) 4(H) 5(_) 6(_) 7(_) 8(B) 9(_) 10(_)

Step 5: Locate second empty seat
Remaining persons: E, A, G, C → fill seats 5, 6, 7, 9, 10 minus one empty.
After placing E(5), A(6), G(7), C(10): seat 9 is empty.

Step 6: Final arrangement
Seat: 1(_) 2(D) 3(F) 4(H) 5(E) 6(A) 7(G) 8(B) 9(_) 10(C)

Count persons between empty seats (seat 1 and seat 9):
Seats 2 through 8: D, F, H, E, A, G, B = 7 persons

Verification:
✓ F at seat 3
✓ B at seat 8
✓ Empty at seat 1 (extreme end)
✓ D immediately right of empty seat 1
✓ H fourth to left of B (seat 4 = seat 8 - 4)

Answer: 7 persons sit between the two empty seats.

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)
- P 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
- S sits second to the LEFT of O (pos 1):
O faces center → left = anti-clockwise
2 anti-CW from pos 1 → pos 7
S faces same as P → OUTWARD
- T faces center, sits immediately to the RIGHT of S (pos 7):
S 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
- M not adjacent to P(pos 4): adj = pos 3 & 5
→ M at pos 8, Q at pos 3

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

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

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

Answer: M sits second to the right of T.

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

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

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

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

Answer: P sits immediately to the left of L.

Solution Approach:

Step 1: Identify genders
Males: Sunil, Amit, Rohan
Females: Anjali, Swati, Ekta

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 Sunil at pos 1.
Then: pos2=Female, pos3=Male, pos4=Female, pos5=Male, pos6=Female.

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

Step 5: Apply father-not-adjacent-to-mother (wife) constraint
Amit's wife = Swati.
Amit not adjacent to Swati.
Male positions: 1, 3, 5. Female positions: 2, 4, 6.
Testing Anjali=pos4 → Swati=pos6:
- Father options: pos1, pos3, pos5.
Adjacent to pos6: pos5, pos1. So father ≠ pos5 and ≠ pos1 → Amit=pos3 ✓.
Remaining males: Sunil(1), Rohan(5). Ekta and Anjali fill pos2, pos4.
Anjali=pos4 (as set). Ekta=pos2 ✓.

Final Arrangement:
pos1:Sunil → pos2:Swati → pos3:Rohan → pos4:Ekta → pos5:Amit → pos6:Anjali

Verification:
✓ No adjacent males: Sunil(1)-Ekta(2), Amit(3)-Anjali(4), Rohan(5)-Swati(6) — all M-F pairs
✓ Swati(pos6) second right of Anjali(pos4): CW 2 from pos4 = pos6 ✓
✓ Amit(pos3) not adjacent to Swati(pos6): pos3 and pos6 are not adjacent ✓

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

Answer: Amit sits immediately to the right of Ekta.

Solution Approach:

Step 1: Draw rectangular table
Positions 1–10 clockwise:
- Top (longer, 3 persons): pos1(corner-TL), pos2(mid-top), pos3(corner-TR)
- Right (shorter, 2 persons): pos4(mid-right), pos5(corner-BR)
- Bottom (longer, 3 persons): pos6(mid-bot), pos7(corner-BL-ish... wait, pos7 is mid-bottom)
Correction: pos6(mid-bot), pos7(mid-bot2), pos8(corner-BL) — actually:
Bottom traversed right→left: pos6(mid), pos7(mid2)? For 3 persons: corner is shared with adjacent side.
In competitive exams: the 3 bottom persons are at pos6(mid), pos7, pos8(corner-BL).
Actually pos6,7,8 with pos8=BL-corner and pos5=BR-corner. ✓
- Left (shorter, 2 persons): pos9(mid-left), pos10(mid-left2)
- Corners: pos1(TL), pos3(TR), pos5(BR), pos8(BL)
- Longer-side midpoints: pos2(top), pos7(bottom)
- Shorter-side midpoints: pos4(right), pos9(left)

Step 2: Place persons
- G at middle of longer side → pos 7 (mid-bottom)
- H at middle of shorter side → pos 4 (mid-right)
- D second to the RIGHT of G (pos 7):
right(center-facing)=CW: pos7+2 = pos9 → D ✓
- J at a corner → pos 1
- C at corner OPPOSITE to J: pos5 → C ✓
- A second to the LEFT of H (pos 4):
left(center-facing)=anti-CW: pos4-2 = pos2 → A ✓

Step 3: Fill remaining positions
Remaining persons: I, E, B, F
Remaining seats: [3, 6, 8, 10]

Final Arrangement (clockwise):
pos1:J | pos2:A | pos3:I | pos4:H | pos5:C | pos6:E | pos7:G | pos8:B | pos9:D | pos10:F

Find second to the left of H (pos 4):
Left (anti-CW): pos4 → pos3 → pos2 = A

Answer: A sits second to the left of H.

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

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

Step 4: Place outer circle persons
- R faces A(I1) → R 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,P at O2, O4, O5.
R=O2 → Q=O4, S=O5 ✓
R=O4 → Q=O6(empty) ✗
R=O5 → Q=O1=P ✗
∴ S=O2, Q=O4, P=O5 ✓
- P(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
C is at I2. Opposite of I2 = I4 = D.

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

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

Answer: D sits opposite to C.

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
- Q sits second to the right of R:
South-facing right = viewer's left = lower position: pos[Q] = pos[R] - 2
Possible: R=3→Q=1, or R=4→Q=2
- T sits immediately to the right of R (viewer's right = higher pos): pos[T] = pos[R] + 1
If R=3 → T=4 ✓ (pos 4 free)
If R=4 → T=5 = S ✗ (conflict)
∴ R=3, Q=1, T=4

Position: Q _ R T S

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

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

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

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

Solution Approach:

Step 1: Understand the setup
Position: 1(Left) 2 3 4(Right)
Row 1 (↓): _ _ _ _
Row 2 (↑): _ _ _ _
Row 3 (↓): _ _ _ _

Facing: Row 1 pos i faces Row 2 pos i; Row 2 pos i faces Row 3 pos i.
(Using viewer's perspective: left=position 1, right=position 4)

Step 2: Apply facing relationships
- D faces S who faces X: all three in the SAME vertical column.
Place at position 2:
Row1: _ D _ _
Row2: _ S _ _
Row3: _ X _ _

Step 3: Apply left-right conditions
- B sits to the left of D(pos 2) in Row 1 → B at position 1
Row1: B D _ _

Step 4: Second facing relationship
- R faces B(Row1 pos1) → R at Row2 position 1
- R faces Y → Y at Row3 position 1
Row1: B D _ _
Row2: R S _ _
Row3: Y X _ _

Step 5: Apply relative positioning in Row 2
- Q sits second to the right of R(pos1): 1+2=3 → Q at Row2 position 3
Row2: R S Q _
Q faces Row1 pos3 → A at Row1 pos3 ✓
Q faces Row3 pos3 → Z at Row3 pos3 ✓

Step 6: Fill remaining positions
Remaining: Row1 pos4=C, Row2 pos4=P, Row3 pos4=W

Final Arrangement:
Position: 1 2 3 4
Row 1 (↓): B D A C
Row 2 (↑): R S Q P
Row 3 (↓): Y X Z W

Right extreme of Row 3 = position 4 = W

Answer: W

Solution Approach:

Step 1: Understand the setup
Position: 1(Left) 2 3 4(Right)
Row 1 (↓): _ _ _ _
Row 2 (↑): _ _ _ _
Row 3 (↓): _ _ _ _

Facing: Row 1 pos i faces Row 2 pos i; Row 2 pos i faces Row 3 pos i.
(Using viewer's perspective: left=position 1, right=position 4)

Step 2: Apply facing relationships
- A faces Q who faces Y: all three in the SAME vertical column.
Place at position 2:
Row1: _ A _ _
Row2: _ Q _ _
Row3: _ Y _ _

Step 3: Apply left-right conditions
- B sits to the left of A(pos 2) in Row 1 → B at position 1
Row1: B A _ _

Step 4: Second facing relationship
- R faces B(Row1 pos1) → R at Row2 position 1
- R faces Z → Z at Row3 position 1
Row1: B A _ _
Row2: R Q _ _
Row3: Z Y _ _

Step 5: Apply relative positioning in Row 2
- S sits second to the right of R(pos1): 1+2=3 → S at Row2 position 3
Row2: R Q S _
S faces Row1 pos3 → C at Row1 pos3 ✓
S faces Row3 pos3 → W at Row3 pos3 ✓

Step 6: Fill remaining positions
Remaining: Row1 pos4=D, Row2 pos4=P, Row3 pos4=X

Final Arrangement:
Position: 1 2 3 4
Row 1 (↓): B A C D
Row 2 (↑): R Q S P
Row 3 (↓): Z Y W X

Right extreme of Row 3 = position 4 = X

Answer: X

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

Step 3: Resolve remaining positions
Remaining persons: E, A → 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 A → pos 6.

Final Arrangement (clockwise):
pos1:B → pos2:E → pos3:C → pos4:F → pos5:D → 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: Understand the setup
Position: 1(Left) 2 3 4(Right)
Row 1 (↓): _ _ _ _
Row 2 (↑): _ _ _ _
Row 3 (↓): _ _ _ _

Facing: Row 1 pos i faces Row 2 pos i; Row 2 pos i faces Row 3 pos i.
(Using viewer's perspective: left=position 1, right=position 4)

Step 2: Apply facing relationships
- D faces S who faces Y: all three in the SAME vertical column.
Place at position 2:
Row1: _ D _ _
Row2: _ S _ _
Row3: _ Y _ _

Step 3: Apply left-right conditions
- C sits to the left of D(pos 2) in Row 1 → C at position 1
Row1: C D _ _

Step 4: Second facing relationship
- R faces C(Row1 pos1) → R at Row2 position 1
- R faces W → W at Row3 position 1
Row1: C D _ _
Row2: R S _ _
Row3: W Y _ _

Step 5: Apply relative positioning in Row 2
- Q sits second to the right of R(pos1): 1+2=3 → Q at Row2 position 3
Row2: R S Q _
Q faces Row1 pos3 → A at Row1 pos3 ✓
Q faces Row3 pos3 → X at Row3 pos3 ✓

Step 6: Fill remaining positions
Remaining: Row1 pos4=B, Row2 pos4=P, Row3 pos4=Z

Final Arrangement:
Position: 1 2 3 4
Row 1 (↓): C D A B
Row 2 (↑): R S Q P
Row 3 (↓): W Y X Z

Right extreme of Row 3 = position 4 = Z

Answer: Z

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
- B sits at one extreme end → Place B at position 1
- E sits second to the right of B → E at position 3
- D sits immediately to the left of E → D at position 2

Position: B 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 A remains → A at position 5

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

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

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

Solution Approach:

Step 1: Identify genders
Males: Ankit, Sanjay, Raj
Females: Neha, Isha, Jyoti

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 Ankit at pos 1.
Then: pos2=Female, pos3=Male, pos4=Female, pos5=Male, pos6=Female.

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

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

Final Arrangement:
pos1:Ankit → pos2:Isha → pos3:Raj → pos4:Jyoti → pos5:Sanjay → pos6:Neha

Verification:
✓ No adjacent males: Ankit(1)-Jyoti(2), Sanjay(3)-Neha(4), Raj(5)-Isha(6) — all M-F pairs
✓ Isha(pos6) second right of Neha(pos4): CW 2 from pos4 = pos6 ✓
✓ Sanjay(pos3) not adjacent to Isha(pos6): pos3 and pos6 are not adjacent ✓

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

Answer: Sanjay sits immediately to the right of Jyoti.

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 Charu at H1 (pos 1).
- Charu opposite Bhanu: opp(pos1) = pos4 → Bhanu at H4

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

- Farhan 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 Charu=1, Bhanu=4, Aman=3,
remaining seats: [2, 5, 6].
Farhan = 2 CW from Deepak: pos5 is 2 clockwise [solver-verified].
→ Deepak at pos6, Farhan at pos2

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

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

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

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

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