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

Solution Approach:

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

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

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

Step 3: Test each MCQ option

- "Y sits at position 2": ✗ NEVER possible → must be FALSE
- "Y sits at position 5": ✓ Possible in at least one valid arrangement
- "V sits at position 1": ✓ Possible in at least one valid arrangement
- "V 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: Draw the double row setup
Row 1 faces South (↓), Row 2 faces North (↑)
Person at position i in Row 1 faces person at position i in Row 2.

Position: 1 2 3 4 5
Row 1 (↓): _ _ _ _ _
Row 2 (↑): _ _ _ _ _

Key direction rule:
- Row 1 (South-facing): "right" = viewer's LEFT (lower position numbers)
- Row 2 (North-facing): "right" = viewer's RIGHT (higher position numbers)

Step 2: Place Row 1 persons
- B sits 4th from the left end of Row 1 → Row 1, pos 4
- 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 B E
Remaining D,A at pos 1 and 2 (either order — pinned next).

Step 3: Place Row 2 persons
- T faces B (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 (↓): D/A D/A C B E
Row 2 (↑): P S Q T R

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

Answer: Q faces C.

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

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

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

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

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

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

Answer: T sits second to the right of P.

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
- F 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(F) 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(F) 9(_) 10(_)

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

Solution Approach:

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

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

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

Step 3: Test each MCQ option

- "Y sits at position 2": ✗ NEVER possible → must be FALSE
- "Y sits at position 1": ✓ Possible in at least one valid arrangement
- "X sits at position 1": ✓ Possible in at least one valid arrangement
- "V 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: 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
- T at the right extreme end → Position 5
- P sits second to the right of S:
South-facing right = viewer's left = lower position: pos[P] = pos[S] - 2
Possible: S=3→P=1, or S=4→P=2
- Q sits immediately to the right of S (viewer's right = higher pos): pos[Q] = pos[S] + 1
If S=3 → Q=4 ✓ (pos 4 free)
If S=4 → Q=5 = T ✗ (conflict)
∴ S=3, P=1, Q=4

Position: P _ S Q T

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

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

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

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

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
- P sits at the left extreme end facing South (↓) → Position 1

Position: P(↓) _ S(↑) _ _ _

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

Position: P(↓) _ S(↑) R(↑) Q(↓) _

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

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

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

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

Answer: T sits between P and S.

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
- A 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(A) 9(_) 10(_)

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

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

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

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

Position: _ [Architect] Eshaan Chetan _ _
Profsn: _ Architect Banker _ _ _

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

Position: _ [Architect] Eshaan Chetan _ [law]
Profsn: _ Architect Banker Doctor _ Lawyer

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

Position: _ Divya Eshaan Chetan _ _
Profsn: _ Architect Banker Doctor _ _

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

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

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

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

Answer: Bina's profession is Engineer.

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

- Esha 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 Farhan=1, Aman=4, Bhanu=3,
remaining seats: [2, 5, 6].
Esha = 2 CW from Charu: pos5 is 2 clockwise [solver-verified].
→ Charu 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:Aman → H5:Deepak → H6:Charu

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

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

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

Solution Approach:

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

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

Position: T(↓) _ Q(↑) _ _ _

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

Position: T(↓) _ Q(↑) U(↑) P(↓) _

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

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

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

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

Answer: R sits between T and Q.

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
- D sits at one extreme end → Place D at position 1
- B sits second to the right of D → B at position 3
- E sits immediately to the left of B → E at position 2

Position: D E B _ _

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

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

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

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

Solution Approach:

Step 1: Identify genders
Males: Rohan, Varun, Raj
Females: Anjali, Pooja, Divya

Step 2: Apply no-adjacent-males constraint
With 3 males and 3 females in a circle of 6, "no two males adjacent" forces strict alternation:
M, F, M, F, M, F (clockwise)

Step 3: Build the arrangement
Position 1: a Male. Let Rohan at pos 1.
Then: pos2=Female, pos3=Male, pos4=Female, pos5=Male, pos6=Female.

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

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

Final Arrangement:
pos1:Rohan → pos2:Pooja → pos3:Raj → pos4:Divya → pos5:Varun → pos6:Anjali

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

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

Answer: Varun sits immediately to the right of Divya.

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
- H at seat 3
- F at seat 8 (seat 8)
- One empty seat at extreme end → seat 1 is empty

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

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

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

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

Solution Approach:

Step 1: Identify genders
Males: Manoj, Kunal, Vikram
Females: Sita, Anjali, Meera

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

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

Final Arrangement:
pos1:Manoj → pos2:Anjali → pos3:Vikram → pos4:Meera → pos5:Kunal → pos6:Sita

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

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

Answer: Kunal sits immediately to the right of Meera.

Solution Approach:

Step 1: Identify genders
Males: Vikram, Rohan, Ankit
Females: Ekta, Isha, Kavya

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

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

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

Final Arrangement:
pos1:Vikram → pos2:Isha → pos3:Ankit → pos4:Kavya → pos5:Rohan → pos6:Ekta

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

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

Answer: Rohan sits immediately to the right of Kavya.

Solution Approach:

Step 1: Identify genders
Males: Kunal, Raj, Varun
Females: Pooja, Anjali, Heena

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 Kunal 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 Pooja (right=CW):
Female positions: 2, 4, 6.
- If Pooja=pos2 → Anjali=pos4 ✓ (or pos2+2=pos4)
- If Pooja=pos4 → Anjali=pos6 ✓
- If Pooja=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 Pooja=pos4 → Anjali=pos6:
- Father options: pos1, pos3, pos5.
Adjacent to pos6: pos5, pos1. So father ≠ pos5 and ≠ pos1 → Raj=pos3 ✓.
Remaining males: Kunal(1), Varun(5). Heena and Pooja fill pos2, pos4.
Pooja=pos4 (as set). Heena=pos2 ✓.

Final Arrangement:
pos1:Kunal → pos2:Anjali → pos3:Varun → pos4:Heena → pos5:Raj → pos6:Pooja

Verification:
✓ No adjacent males: Kunal(1)-Heena(2), Raj(3)-Pooja(4), Varun(5)-Anjali(6) — all M-F pairs
✓ Anjali(pos6) second right of Pooja(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 Heena:
Heena at pos 4. Right (CW) = pos 5 = Raj.

Answer: Raj sits immediately to the right of Heena.

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

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

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

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

Answer: P sits immediately to the left of O.

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

- Bhanu second to the right of Esha:
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, Deepak=3,
remaining seats: [2, 5, 6].
Bhanu = 2 CW from Esha: pos5 is 2 clockwise [solver-verified].
→ Esha 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:Deepak → H4:Aman → H5:Charu → H6:Esha

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

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

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

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
- P sits at the left extreme end facing South (↓) → Position 1

Position: P(↓) _ 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: P(↓) _ S(↑) Q(↑) T(↓) _

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

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

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

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

Answer: R sits between P and S.