Seating Arrangement - Advanced Level: square arrangements ADVANCED

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

Position: C E 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 A remains → A at position 5

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

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

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

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

Position: S _ R Q T

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

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

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

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

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)
- P 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
- S sits second to the LEFT of T (pos 1):
T faces center → left = anti-clockwise
2 anti-CW from pos 1 → pos 7
S faces same as P → OUTWARD
- Q 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
- O immediately to the RIGHT of T(pos 1, center→CW): pos 2
- M opposite T(pos 1): pos 5
- R not adjacent to P(pos 4): adj = pos 3 & 5
→ R at pos 8, N at pos 3

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

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

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

Answer: R sits second to the right of Q.

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

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

Step 4: Place outer circle persons
- P faces C(I1) → P at O1 ✓
- Outer occupied seats: O1, O2, O4, O5. Empty: O3, O6.
- S second to right of Q (outer, facing center: right=CW, step 2):
Remaining outer persons: S,Q,R at O2, O4, O5.
R=O2 → Q=O4, S=O5 ✓
R=O4 → Q=O6(empty) ✗
R=O5 → Q=O1=P ✗
∴ Q=O2, S=O4, R=O5 ✓
- R(O5) immediately to the LEFT of an empty:
Left(CW) of O5 = O4(S) — NOT empty.
RIGHT(CW) of O5 = O6(empty). So O5 is immediately to the LEFT of O6(empty) ✓.

Step 5: Answer the question
B is at I2. Opposite of I2 = I4 = A.

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

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

Answer: A sits opposite to B.

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

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

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

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

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

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

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

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

Final Arrangement:
Position: 1 2 3 4
Row 1 (↓): A B C D
Row 2 (↑): P Q S R
Row 3 (↓): X Y 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 M (faces center) at position 1 (reference point)
- Q faces outward, sits third to the RIGHT of M:
M 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 M (pos 1):
M faces center → left = anti-clockwise
2 anti-CW from pos 1 → pos 7
T faces same as Q → OUTWARD
- P 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
- R immediately to the RIGHT of M(pos 1, center→CW): pos 2
- O opposite M(pos 1): pos 5
- S not adjacent to Q(pos 4): adj = pos 3 & 5
→ S at pos 8, N at pos 3

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

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

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

Answer: S sits second to the right of P.

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

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

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

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

Answer: R sits second to the right of M.

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

Position: Q _ T P R

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

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

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

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

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

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

Final Arrangement (clockwise):
pos1:B → pos2:E → pos3:C → pos4:A → pos5:D → 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 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.
- C sits opposite to A:
If A=I2, then C=I4. Then D=I1 (left of I2), B=I3 (remaining).
All constraints consistent ✓.

Inner: I1=D, I2=A, I3=B, 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
A is at I2. Opposite of I2 = I4 = C.

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

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

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
- A faces Q who faces Z: all three in the SAME vertical column.
Place at position 2:
Row1: _ A _ _
Row2: _ Q _ _
Row3: _ Z _ _

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

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 A _ _
Row2: R Q _ _
Row3: X Z _ _

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 → Y 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 (↓): C A B D
Row 2 (↑): R Q P S
Row 3 (↓): X Z 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
- D sits immediately to the left of B → D at position 2

Position: C D B _ _

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 A remains → A at position 5

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

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

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

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

Position: P _ S R Q

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

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

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

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

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

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

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

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

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

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

Solution Approach:

Step 1: Understanding facing outward
When facing outward (away from center):
- LEFT = CLOCKWISE direction
- RIGHT = ANTI-CLOCKWISE direction
- Opposite positions are still n/2 = 3 seats apart.

Step 2: Draw diagram (positions 1–6 clockwise)

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

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

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

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

Answer: N sits immediately to the left of K.

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 P who faces Z: all three in the SAME vertical column.
Place at position 2:
Row1: _ A _ _
Row2: _ P _ _
Row3: _ Z _ _

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

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

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

Step 6: Fill remaining positions
Remaining: Row1 pos4=B, Row2 pos4=R, Row3 pos4=Y

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

Right extreme of Row 3 = position 4 = Y

Answer: Y

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

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

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

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

Answer: M sits immediately to the left of P.

Solution Approach:

Step 1: Identify genders
Males: Rahul, Arjun, Varun
Females: Neha, Isha, Swati

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

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

Final Arrangement:
pos1:Rahul → pos2:Isha → pos3:Varun → pos4:Swati → pos5:Arjun → pos6:Neha

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

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

Answer: Arjun sits immediately to the right of Swati.

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

Position: R _ P Q T

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

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

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

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