Seating Arrangement - Advanced Level: opposite positions ADVANCED

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

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

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

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

A is at pos 3 → opposite = pos 6 = C

Answer: C sits opposite to A.

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

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 Y → Y at Row3 position 1
Row1: C B _ _
Row2: P S _ _
Row3: Y X _ _

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

Step 6: Fill remaining positions
Remaining: Row1 pos4=A, Row2 pos4=R, Row3 pos4=Z

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

Right extreme of Row 3 = position 4 = Z

Answer: Z

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

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

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

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

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

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

Answer: S sits second to the right of M.

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

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

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

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

Answer: P sits immediately to the left of L.

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 R:
South-facing right = viewer's left = lower position: pos[P] = pos[R] - 2
Possible: R=3→P=1, or R=4→P=2
- Q sits immediately to the right of R (viewer's right = higher pos): pos[Q] = pos[R] + 1
If R=3 → Q=4 ✓ (pos 4 free)
If R=4 → Q=5 = S ✗ (conflict)
∴ R=3, P=1, Q=4

Position: P _ R Q S

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

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

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

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

Solution Approach:

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

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

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

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

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

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

Step 6: Fill remaining positions
Remaining: Row1 pos4=A, Row2 pos4=S, Row3 pos4=Z

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

Right extreme of Row 3 = position 4 = Z

Answer: Z

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

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

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

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

Count persons between empty seats (seat 1 and seat 9):
Seats 2 through 8: B, F, D, A, C, H, 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
✓ D fourth to left of G (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
- 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
- P is NOT adjacent to Q (pos 4): adjacent = pos 3 and pos 5
So P ≠ pos 3 and P ≠ pos 5
Remaining positions for S,R,P: pos 1, pos 3, pos 5
P not at pos 3 or pos 5 → P at pos 1
S at extreme → pos 5 (since pos 1 is P) ✓
R fills pos 3 ✓

Row 2: P T R Q S

Final Arrangement:
Position: 1 2 3 4 5
Row 1 (↓): A/D A/D C E B
Row 2 (↑): P T R Q 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: Create the basic diagram
Draw 5 positions in a row, all facing North (↑):
Position: 1 2 3 4 5

Step 2: Apply direct conditions
- A sits at one extreme end → Place A at position 1
- D sits second to the right of A → D at position 3
- C sits immediately to the left of D → C at position 2

Position: A C D _ _

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

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

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

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

Solution Approach:

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

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

Position: R(↓) _ S(↑) _ _ _

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

Position: R(↓) _ S(↑) Q(↑) T(↓) _

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

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

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

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

Answer: P sits between R and S.

Solution Approach:

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

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

Position: S(↓) _ P(↑) _ _ _

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

Position: S(↓) _ P(↑) Q(↑) T(↓) _

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

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

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

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

Answer: R sits between S and P.

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

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

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

Row 2: P S Q T R

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

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

Answer: Q faces A.

Solution Approach:

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

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

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

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

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

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

Step 6: Fill remaining positions
Remaining: Row1 pos4=D, Row2 pos4=S, Row3 pos4=W

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

Right extreme of Row 3 = position 4 = W

Answer: W

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

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

Row 2: P R T S Q

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

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

Answer: T faces E.

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

Position: _ [Lawyer] Falguni Eshaan _ _
Profsn: _ Lawyer Architect _ _ _

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

Position: _ [Lawyer] Falguni Eshaan _ [law]
Profsn: _ Lawyer Architect Engineer _ Teacher

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

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

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

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

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

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

Answer: Divya's profession is Banker.

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

Step 3: Test each MCQ option

- "V sits at position 1": ✓ Possible in at least one valid arrangement
- "W sits at position 4": ✓ Possible in at least one valid arrangement
- "Z sits at position 1": ✓ Possible in at least one valid arrangement
- "Z sits at position 2": ✗ NEVER possible → must be FALSE

Step 4: Conclusion
"Z 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: "Z 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 P (faces center) at position 1 (reference point)
- Q faces outward, sits third to the RIGHT of P:
P faces center → right = clockwise
3 CW from pos 1 → pos 4
N = pos 4 ✓

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

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

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

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

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

Answer: O sits second to the right of R.

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

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

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

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

C is at pos 3 → opposite = pos 6 = F

Answer: F sits opposite to C.

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

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

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

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

Answer: Three person(s) sit between B and F.

Solution Approach:

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

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

Position: _ [Lawyer] Amit Chetan _ _
Profsn: _ Lawyer Banker _ _ _

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

Position: _ [Lawyer] Amit Chetan _ [law]
Profsn: _ Lawyer Banker Teacher _ Engineer

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

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

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

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

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

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

Answer: Eshaan's profession is Doctor.