Seating Arrangement - Intermediate Level: linear arrangements INTERMEDIATE

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

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

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

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

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

Verification:
✓ C at seat 3
✓ B at seat 8
✓ Empty at seat 1 (extreme end)
✓ G 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.

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

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

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

Row 2: S T R P Q

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

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 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 Aman: opp(pos1) = pos4 → Aman at H4

Step 3: Apply relative positioning
- Esha second to the right of Farhan(pos1):
CW 2: pos1→pos2→pos3
→ Esha 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 Farhan=1, Aman=4, Esha=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 Farhan(pos1):
Adjacent to pos1: pos6 and pos2
→ Charu at pos5 (not adjacent) ✓

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

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

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

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

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

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

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

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

E is at pos 3 → opposite = pos 6 = D

Answer: D sits opposite to E.

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

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

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

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

Verification:
✓ R faces D (I1↔O1)
✓ B immediately right of D (I2 is CW from I1)
✓ C opposite B (I4 opposite I2)
✓ Q 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: 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
- C faces R who faces X: all three in the SAME vertical column.
Place at position 2:
Row1: _ C _ _
Row2: _ R _ _
Row3: _ X _ _

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

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

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

Step 6: Fill remaining positions
Remaining: Row1 pos4=A, Row2 pos4=Q, Row3 pos4=W

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

Right extreme of Row 3 = position 4 = W

Answer: W

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

Position: C A B _ _

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

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

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

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

Solution Approach:

Step 1: Identify genders
Males: Varun, Ankit, Rohan
Females: Anjali, Divya, 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 Varun at pos 1.
Then: pos2=Female, pos3=Male, pos4=Female, pos5=Male, pos6=Female.

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

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

Final Arrangement:
pos1:Varun → pos2:Divya → pos3:Rohan → pos4:Jyoti → pos5:Ankit → pos6:Anjali

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

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

Answer: Ankit sits immediately to the right of Jyoti.

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
- C faces S who faces W: all three in the SAME vertical column.
Place at position 2:
Row1: _ C _ _
Row2: _ S _ _
Row3: _ W _ _

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

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

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 → B at Row1 pos3 ✓
Q faces Row3 pos3 → X at Row3 pos3 ✓

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

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

Right extreme of Row 3 = position 4 = Y

Answer: Y

Solution Approach:

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

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

Position: _ [Architect] Bina Falguni _ _
Profsn: _ Architect Engineer _ _ _

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

Position: _ [Architect] Bina Falguni _ [law]
Profsn: _ Architect Engineer Teacher _ Doctor

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

Position: _ Chetan Bina Falguni _ _
Profsn: _ Architect Engineer Teacher _ _

Step 5: Place E, D, F
Remaining persons: Amit,Eshaan,Divya → positions 1, 5, 6.
- Amit is Banker and NOT adjacent to Bina(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.
- Eshaan is NOT at an extreme end: Eshaan not at pos1 or pos6 → Eshaan at pos5.
- Divya at extreme: pos1 or pos6.
- Doctor at pos6. If F=Doctor, 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 Doctor (pos6)? Not Bina(doc), Falguni(ban), Chetan(eng), Eshaan(remaining profsn), Amit(tea).
Doctor must be Divya. So Divya at pos6 = Doctor. Amit at pos1 = Banker ✓ (not adjacent to Bina).

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

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

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

Answer: Eshaan's profession is Lawyer.

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
- A sits immediately to the left of B → A at position 2

Position: E A B _ _

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

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

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

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

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

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

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

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

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

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

Answer: N sits second to the right of M.

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
- A sits immediately to the left of D → A at position 2

Position: E A D _ _

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 A D C B

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

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

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

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

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

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

A is at pos 3 → opposite = pos 6 = F

Answer: F sits opposite to A.

Solution Approach:

Step 1: Identify genders
Males: Amit, Raj, Rajesh
Females: Gita, Anjali, Farah

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

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

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

Final Arrangement:
pos1:Amit → pos2:Anjali → pos3:Rajesh → pos4:Farah → pos5:Raj → pos6:Gita

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

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

Answer: Raj sits immediately to the right of Farah.

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

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

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

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

Answer: P sits immediately to the left of O.

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

Verification:
✓ R faces D (I1↔O1)
✓ A immediately right of D (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 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
- A sits at an extreme end: pos 1 or pos 5
- E sits second to the RIGHT of A (south-facing → lower position):
pos[E] = pos[A] - 2
If A at pos 1 → pos[E] = -1 (invalid ✗)
If A at pos 5 → pos[E] = 3 ✓ (pos 3 is free)
∴ A at pos 5, E at pos 3 ✓

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

Step 3: Place Row 2 persons
- S faces C (pos 4) → S at Row 2, pos 4
- Q sits second to the LEFT of S (north-facing → lower position):
pos[Q] = pos[S] - 2 = 2 → Q at Row 2 pos 2 ✓
- T sits at extreme end of Row 2: pos 1 or pos 5
- R is NOT adjacent to S (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 Q P S T

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

Find who faces E:
E is at Row 1, position 3.
Person at Row 2, position 3 = P

Answer: P faces E.

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

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

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

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

Answer: E sits second to the left of H.

Solution Approach:

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

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

Position: _ [Engineer] Divya Falguni _ _
Profsn: _ Engineer Lawyer _ _ _

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

Position: _ [Engineer] Divya Falguni _ [law]
Profsn: _ Engineer Lawyer Architect _ Doctor

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

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

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

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

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

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

Answer: Amit's profession is Banker.