Seating Arrangement - Intermediate-Advanced Level: relative positions INTERMEDIATE-ADVANCED

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

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

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

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

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

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

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

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

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

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

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

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

Answer: M sits immediately to the left of P.

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

Step 3: Test each MCQ option

- "X sits at position 2": ✗ NEVER possible → must be FALSE
- "Y sits at position 3": ✓ Possible in at least one valid arrangement
- "V sits at position 4": ✓ Possible in at least one valid arrangement
- "Y sits at position 4": ✓ Possible in at least one valid arrangement

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

Solution Approach:

Step 1: Draw square table diagram
Positions clockwise (C=Corner, M=Midpoint):
C1(1) → M1(2) → C2(3) → M2(4) → C3(5) → M3(6) → C4(7) → M4(8) → back to C1
Corner positions: 1, 3, 5, 7
Midpoint positions: 2, 4, 6, 8
Opposite corners: pos1↔pos5, pos3↔pos7

Step 2: Place persons systematically
- A sits at a corner → pos 1
- E sits second to the RIGHT of A: right(center-facing)=CW
2 CW from pos 1 → pos 3 ✓ (corner)
- H sits OPPOSITE A (pos 1) → pos 5 ✓
- B at midpoint, NOT adjacent to A(pos 1):
Adjacent to pos 1: pos 8 and pos 2
B → pos 6 (midpoint, not adjacent) ✓
- F sits at corner immediately to the RIGHT of B(pos 6):
1 CW from pos 6 → pos 7 (corner) ✓

Step 3: Remaining persons
Remaining: D, C, G
Fill remaining seats: pos2=D, pos8=C, pos4=G

Final Arrangement (clockwise):
pos1:A → pos2:D → pos3:E → pos4:G → pos5:H → pos6:B → pos7:F → pos8:C

Step 4: Count from LEFT of A to H
Left = anti-clockwise direction from A(pos 1):
pos1(A) → pos8(C) → pos7(F) → pos6(B) → pos5(H)
Persons between (excluding A and H): pos8(C), pos7(F), pos6(B)
Count = 3 person(s)

Answer: Three person(s) sit between A and H.

Solution Approach:

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

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

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

Step 3: Test each MCQ option

- "V sits at position 5": ✓ Possible in at least one valid arrangement
- "V sits at position 4": ✓ Possible in at least one valid arrangement
- "X sits at position 3": ✓ Possible in at least one valid arrangement
- "V sits at position 2": ✗ NEVER possible → must be FALSE

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

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

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

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

Row 2: R S P Q T

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

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: 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
- B at seat 3
- D at seat 8 (seat 8)
- One empty seat at extreme end → seat 1 is empty

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

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

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

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

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

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

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

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

Answer: L sits immediately to the left of P.

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
- R faces C(I1) → R at O1 ✓
- Outer occupied seats: O1, O2, O4, O5. Empty: O3, O6.
- S second to right of P (outer, facing center: right=CW, step 2):
Remaining outer persons: S,P,Q at O2, O4, O5.
R=O2 → Q=O4, S=O5 ✓
R=O4 → Q=O6(empty) ✗
R=O5 → Q=O1=P ✗
∴ P=O2, S=O4, Q=O5 ✓
- Q(O5) immediately to the LEFT of an empty:
Left(CW) of O5 = O4(S) — 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=R, O2=P, O3=empty, O4=S, O5=Q, O6=empty

Verification:
✓ R faces C (I1↔O1)
✓ A immediately right of C (I2 is CW from I1)
✓ B opposite A (I4 opposite I2)
✓ S 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 D at position 1 (reference point)
- D is second to the LEFT of E → E is 2 clockwise from D
pos[E] = 3
- F sits OPPOSITE D (pos 1) → pos 4
- B 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 B (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:E → pos4:F → pos5:B → pos6:A
(All facing center)

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

E is at pos 3 → opposite = pos 6 = A

Answer: A sits opposite to E.

Solution Approach:

Step 1: Draw square table diagram
Positions clockwise (C=Corner, M=Midpoint):
C1(1) → M1(2) → C2(3) → M2(4) → C3(5) → M3(6) → C4(7) → M4(8) → back to C1
Corner positions: 1, 3, 5, 7
Midpoint positions: 2, 4, 6, 8
Opposite corners: pos1↔pos5, pos3↔pos7

Step 2: Place persons systematically
- C sits at a corner → pos 1
- E sits second to the RIGHT of C: right(center-facing)=CW
2 CW from pos 1 → pos 3 ✓ (corner)
- D sits OPPOSITE C (pos 1) → pos 5 ✓
- G at midpoint, NOT adjacent to C(pos 1):
Adjacent to pos 1: pos 8 and pos 2
G → pos 6 (midpoint, not adjacent) ✓
- A sits at corner immediately to the RIGHT of G(pos 6):
1 CW from pos 6 → pos 7 (corner) ✓

Step 3: Remaining persons
Remaining: B, F, H
Fill remaining seats: pos2=B, pos8=F, pos4=H

Final Arrangement (clockwise):
pos1:C → pos2:B → pos3:E → pos4:H → pos5:D → pos6:G → pos7:A → pos8:F

Step 4: Count from LEFT of C to D
Left = anti-clockwise direction from C(pos 1):
pos1(C) → pos8(F) → pos7(A) → pos6(G) → pos5(D)
Persons between (excluding C and D): pos8(F), pos7(A), pos6(G)
Count = 3 person(s)

Answer: Three person(s) sit between C and D.

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

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

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

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

Answer: H sits second to the left of 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
- B faces R who faces W: all three in the SAME vertical column.
Place at position 2:
Row1: _ B _ _
Row2: _ R _ _
Row3: _ W _ _

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

Step 4: Second facing relationship
- P faces C(Row1 pos1) → P at Row2 position 1
- P faces X → X at Row3 position 1
Row1: C B _ _
Row2: P R _ _
Row3: X W _ _

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 → A at Row1 pos3 ✓
S faces Row3 pos3 → Y at Row3 pos3 ✓

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

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

Right extreme of Row 3 = position 4 = Z

Answer: Z

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

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

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

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

Answer: O sits immediately to the left of K.

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

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

Step 4: Place outer circle persons
- Q faces B(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
A is at I2. Opposite of I2 = I4 = C.

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

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

Answer: C sits opposite to 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
- 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 E C
Remaining D,A at pos 1 and 2 (either order — pinned next).

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

Row 2: R T P Q S

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

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: Identify genders
Males: Rohan, Varun, Kunal
Females: Priya, Swati, Isha

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 Rohan 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 Priya (right=CW):
Female positions: 2, 4, 6.
- If Priya=pos2 → Swati=pos4 ✓ (or pos2+2=pos4)
- If Priya=pos4 → Swati=pos6 ✓
- If Priya=pos6 → Swati=pos8%6=pos2 ✓

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

Final Arrangement:
pos1:Rohan → pos2:Swati → pos3:Kunal → pos4:Isha → pos5:Varun → pos6:Priya

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

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

Answer: Varun sits immediately to the right of Isha.

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
- A at seat 3
- E at seat 8 (seat 8)
- One empty seat at extreme end → seat 1 is empty

Seat: 1(_) 2(_) 3(A) 4(_) 5(_) 6(_) 7(_) 8(E) 9(_) 10(_)

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

Seat: 1(_) 2(G) 3(A) 4(_) 5(_) 6(_) 7(_) 8(E) 9(_) 10(_)

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

Seat: 1(_) 2(G) 3(A) 4(C) 5(_) 6(_) 7(_) 8(E) 9(_) 10(_)

Step 5: Locate second empty seat
Remaining persons: F, B, H, D → fill seats 5, 6, 7, 9, 10 minus one empty.
After placing F(5), B(6), H(7), D(10): seat 9 is empty.

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

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

Verification:
✓ A at seat 3
✓ E at seat 8
✓ Empty at seat 1 (extreme end)
✓ G immediately right of empty seat 1
✓ C fourth to left of E (seat 4 = seat 8 - 4)

Answer: 7 persons sit between the two empty seats.

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
- B sits second to the right of E → B at position 3
- C sits immediately to the left of B → C at position 2

Position: E C B _ _

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 D remains → D at position 5

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

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

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

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.
- C sits opposite to A:
If A=I2, then C=I4. Then D=I1 (left of I2), B=I3 (remaining).
All constraints consistent ✓.

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

Step 4: Place outer circle persons
- S faces D(I1) → S at O1 ✓
- Outer occupied seats: O1, O2, O4, O5. Empty: O3, O6.
- Q second to right of P (outer, facing center: right=CW, step 2):
Remaining outer persons: Q,P,R at O2, O4, O5.
R=O2 → Q=O4, S=O5 ✓
R=O4 → Q=O6(empty) ✗
R=O5 → Q=O1=P ✗
∴ P=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 = C.

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

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

Answer: C sits opposite to A.