Seating Arrangement - Intermediate-Advanced Level: table arrangement INTERMEDIATE-ADVANCED

Solution Approach:

Step 1: Identify genders
Males: Ankit, Raj, Deepak
Females: Kavya, Heena, 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
Heena sits second to the RIGHT of Kavya (right=CW):
Female positions: 2, 4, 6.
- If Kavya=pos2 → Heena=pos4 ✓ (or pos2+2=pos4)
- If Kavya=pos4 → Heena=pos6 ✓
- If Kavya=pos6 → Heena=pos8%6=pos2 ✓

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

Final Arrangement:
pos1:Ankit → pos2:Heena → pos3:Deepak → pos4:Jyoti → pos5:Raj → pos6:Kavya

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

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

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

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

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

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

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

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

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

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

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
- D 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(D) 9(_) 10(_)

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

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

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

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

Step 3: Test each MCQ option

- "X sits at position 2": ✗ NEVER possible → must be FALSE
- "V sits at position 1": ✓ Possible in at least one valid arrangement
- "V sits at position 4": ✓ Possible in at least one valid arrangement
- "V sits at position 5": ✓ 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: 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 Q (faces center) at position 1 (reference point)
- O faces outward, sits third to the RIGHT of Q:
Q faces center → right = clockwise
3 CW from pos 1 → pos 4
N = pos 4 ✓

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

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

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

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

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

Answer: T sits second to the right of S.

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.
- S second to right of Q (outer, facing center: right=CW, step 2):
Remaining outer persons: S,Q,R at O2, O4, O5.
R=O2 → Q=O4, S=O5 ✓
R=O4 → Q=O6(empty) ✗
R=O5 → Q=O1=P ✗
∴ Q=O2, S=O4, R=O5 ✓
- R(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=D, I2=A, I3=C, I4=B
Outer (CW): O1=P, O2=Q, O3=empty, O4=S, 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)
✓ S second right of Q (O4 = O2 + 2 CW)
✓ R(O5) immediately left of empty O6

Answer: B sits opposite to A.

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

Position: E 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 C remains → C at position 5

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

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

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

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
- Q faces D (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 ✓
- P 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 P,S,R: pos 1, pos 3, pos 5
R not at pos 3 or pos 5 → R at pos 1
P at extreme → pos 5 (since pos 1 is R) ✓
S fills pos 3 ✓

Row 2: R T S Q P

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

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

Answer: S faces A.

Solution Approach:

Step 1: Identify genders
Males: Ankit, Varun, Deepak
Females: Isha, Meera, Gita

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

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

Final Arrangement:
pos1:Ankit → pos2:Meera → pos3:Deepak → pos4:Gita → pos5:Varun → pos6:Isha

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

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

Answer: Varun sits immediately to the right of Gita.

Solution Approach:

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

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

Position: P(↓) _ R(↑) _ _ _

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

Position: P(↓) _ R(↑) T(↑) S(↓) _

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

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

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

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

Answer: Q sits between P and R.

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
- G 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(G) 9(_) 10(_)

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

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

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

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

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

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

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

Verification:
✓ F at seat 3
✓ G at seat 8
✓ Empty at seat 1 (extreme end)
✓ B immediately right of empty seat 1
✓ A fourth to left of G (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.
- K sits second to the LEFT of O: left(outward)=CW, so K is 2 CW from O.
pos[K] = 3
- M sits opposite K (pos 3): pos 6
- L sits immediately to the RIGHT of M (pos 6):
right(outward)=anti-CW → pos 5
- P sits opposite O (pos 1): pos 4
- Remaining N fills pos 2.

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

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

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

Answer: P sits immediately to the left of K.

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

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

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

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

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

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

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

Answer: Deepak sits to the second to the right of Bhanu.

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
- P 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
- S sits immediately to the right of T (viewer's right = higher pos): pos[S] = pos[T] + 1
If T=3 → S=4 ✓ (pos 4 free)
If T=4 → S=5 = P ✗ (conflict)
∴ T=3, R=1, S=4

Position: R _ T S P

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

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

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

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

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

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

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

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

Answer: O sits immediately to the left of L.

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

Row 2: Q T R P S

Final Arrangement:
Position: 1 2 3 4 5
Row 1 (↓): A/B A/B C D E
Row 2 (↑): Q T 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 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 F → F is 2 clockwise from B
pos[F] = 3
- E sits OPPOSITE B (pos 1) → pos 4
- D sits immediately to the right of E (pos 4) → pos 5

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

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

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

F is at pos 3 → opposite = pos 6 = A

Answer: A sits opposite to F.

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

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

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

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

Answer: N sits immediately to the left of P.

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

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

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

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

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

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

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

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

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
- H sits immediately to the RIGHT of an empty seat
- Empty at seat 1 → seat 2 = H ✓

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

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.