Seating Arrangement - Beginner-Intermediate Level: complex arrangements BEGINNER-INTERMEDIATE

Solution Approach:

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

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

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

Step 3: Test each MCQ option

- "X sits at position 4": ✓ Possible in at least one valid arrangement
- "Y sits at position 2": ✗ NEVER possible → must be FALSE
- "Z sits at position 5": ✓ Possible in at least one valid arrangement
- "W sits at position 5": ✓ 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: Create position-person-profession grid
Position: 1 2 3 4 5 6
Person: _ _ _ _ _ _
Profsn: _ _ _ _ _ _

Step 2: Apply direct conditions
- Eshaan is Teacher, 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.)
- Bina sits second to the right of the Architect (pos 2): 2+2 = pos 4 → Bina at position 4

Position: _ [Architect] Eshaan Bina _ _
Profsn: _ Architect Teacher _ _ _

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

Position: _ [Architect] Eshaan Bina _ [law]
Profsn: _ Architect Teacher Banker _ Doctor

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

Position: _ Chetan Eshaan Bina _ _
Profsn: _ Architect Teacher Banker _ _

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

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

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

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

Answer: Falguni's profession is Engineer.

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

Row 1: _ _ A E B
Remaining C,D 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
- R sits second to the LEFT of Q (north-facing → lower position):
pos[R] = pos[Q] - 2 = 2 → R at Row 2 pos 2 ✓
- P sits at extreme end of Row 2: pos 1 or pos 5
- T is NOT adjacent to Q (pos 4): adjacent = pos 3 and pos 5
So T ≠ pos 3 and T ≠ pos 5
Remaining positions for P,S,T: pos 1, pos 3, pos 5
T not at pos 3 or pos 5 → T at pos 1
P at extreme → pos 5 (since pos 1 is T) ✓
S fills pos 3 ✓

Row 2: T R S Q P

Final Arrangement:
Position: 1 2 3 4 5
Row 1 (↓): C/D C/D A E B
Row 2 (↑): T R 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: 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
- E sits at a corner → pos 1
- D sits second to the RIGHT of E: right(center-facing)=CW
2 CW from pos 1 → pos 3 ✓ (corner)
- H sits OPPOSITE E (pos 1) → pos 5 ✓
- B at midpoint, NOT adjacent to E(pos 1):
Adjacent to pos 1: pos 8 and pos 2
B → pos 6 (midpoint, not adjacent) ✓
- C sits at corner immediately to the RIGHT of B(pos 6):
1 CW from pos 6 → pos 7 (corner) ✓

Step 3: Remaining persons
Remaining: F, A, G
Fill remaining seats: pos2=F, pos8=A, pos4=G

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

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

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

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

Position: T _ Q R S

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

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

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

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

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

Row 2: S T P Q R

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

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

Answer: P faces C.

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

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

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

Row 2: T R P S Q

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

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

Answer: P faces A.

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

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

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

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

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

Verification:
✓ C at seat 3
✓ B at seat 8
✓ Empty at seat 1 (extreme end)
✓ F 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: Apply the fixed condition
- Y sits second from the left → Y at position 2 (fixed)

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

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

Step 3: Test each MCQ option

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

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

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

Solution Approach:

Step 1: Identify genders
Males: Amit, Sunil, Deepak
Females: Isha, Swati, Sita

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

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

Final Arrangement:
pos1:Amit → pos2:Swati → pos3:Deepak → pos4:Sita → pos5:Sunil → pos6:Isha

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

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

Answer: Sunil sits immediately to the right of Sita.

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
- Charu second to the right of Bhanu(pos1):
CW 2: pos1→pos2→pos3
→ Charu at H3

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

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

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

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

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

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

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
- R sits immediately to the right of P (viewer's right = higher pos): pos[R] = pos[P] + 1
If P=3 → R=4 ✓ (pos 4 free)
If P=4 → R=5 = S ✗ (conflict)
∴ P=3, Q=1, R=4

Position: Q _ P R S

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

Final Arrangement (all facing South ↓):
Position: Q T P R 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)
✓ R immediately right of P (viewer right): pos 3+1 = 4
✓ T not adjacent to S (pos 2, not pos 4)

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

Solution Approach:

Step 1: Identify genders
Males: Varun, Vikram, Kunal
Females: Meera, Heena, 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 Varun 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 Meera (right=CW):
Female positions: 2, 4, 6.
- If Meera=pos2 → Heena=pos4 ✓ (or pos2+2=pos4)
- If Meera=pos4 → Heena=pos6 ✓
- If Meera=pos6 → Heena=pos8%6=pos2 ✓

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

Final Arrangement:
pos1:Varun → pos2:Heena → pos3:Kunal → pos4:Isha → pos5:Vikram → pos6:Meera

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

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

Answer: Vikram sits immediately to the right of Isha.

Solution Approach:

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

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

Position: P(↓) _ U(↑) _ _ _

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

Position: P(↓) _ U(↑) R(↑) S(↓) _

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

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

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

Person between P (pos 1) and U (pos 3): pos 2 = T

Answer: T sits between P and U.

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

Position: P _ T R S

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

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

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

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

Solution Approach:

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

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

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

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

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

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

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

Answer: D sits opposite to C.

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

Step 3: Test each MCQ option

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

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: 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.
- P sits second to the LEFT of N: left(outward)=CW, so P is 2 CW from N.
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 N (pos 1): pos 4
- Remaining L fills pos 2.

Final Arrangement (clockwise):
pos1:N → pos2:L → 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 N (CW direction)
✓ K opposite P
✓ O immediately right (anti-CW) of K
✓ M opposite N

Answer: M sits immediately to the left of P.

Solution Approach:

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

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

Position: _ [Banker] Falguni Chetan _ _
Profsn: _ Banker Doctor _ _ _

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

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

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

Position: _ Bina Falguni Chetan _ _
Profsn: _ Banker Doctor Teacher _ _

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

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

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

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

Answer: Amit's profession is Architect.

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

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

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

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

C is at pos 3 → opposite = pos 6 = B

Answer: B sits opposite to C.