Seating Arrangement - Advanced Level: adjacent seating ADVANCED

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

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

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

Solution Approach:

Step 1: Identify genders
Males: Sanjay, Rohan, Manoj
Females: Pooja, Anjali, Gita

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 Sanjay 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
Rohan's wife = Anjali.
Rohan 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 → Rohan=pos3 ✓.
Remaining males: Sanjay(1), Manoj(5). Gita and Pooja fill pos2, pos4.
Pooja=pos4 (as set). Gita=pos2 ✓.

Final Arrangement:
pos1:Sanjay → pos2:Anjali → pos3:Manoj → pos4:Gita → pos5:Rohan → pos6:Pooja

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

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

Answer: Rohan sits immediately to the right of Gita.

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 R (faces center) at position 1 (reference point)
- O faces outward, sits third to the RIGHT of R:
R 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 R (pos 1):
R faces center → left = anti-clockwise
2 anti-CW from pos 1 → pos 7
T faces same as O → 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 R(pos 1, center→CW): pos 2
- N opposite R(pos 1): pos 5
- S not adjacent to O(pos 4): adj = pos 3 & 5
→ S at pos 8, P at pos 3

Final Arrangement (clockwise):
pos1:R(ctr) | pos2:Q(out) | pos3:P(ctr) | pos4:O(out) | pos5:N(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:
✓ O(outward) 3 left of R(center): 3 ACW from pos1 = pos4
✓ T 2nd left of R, same direction as O (outward)
✓ M(center) immediately right of T(outward, right=ACW)
✓ Q immediately right (CW) of R
✓ N opposite R
✓ S not adjacent to O

Answer: S sits second to the right of M.

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 Charu: opp(pos1) = pos4 → Charu at H4

Step 3: Apply relative positioning
- Deepak second to the right of Bhanu(pos1):
CW 2: pos1→pos2→pos3
→ Deepak at H3

- Farhan second to the right of Aman:
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, Charu=4, Deepak=3,
remaining seats: [2, 5, 6].
Farhan = 2 CW from Aman: pos5 is 2 clockwise [solver-verified].
→ Aman at pos6, Farhan at pos2

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

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

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

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

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

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

Step 3: Apply relative positioning
- Charu second to the right of Deepak(pos1):
CW 2: pos1→pos2→pos3
→ Charu at H3

- Farhan second to the right of Aman:
This means F is somewhere and E is 2 CW from F.
We need to find where F and E land.
After placing Deepak=1, Esha=4, Charu=3,
remaining seats: [2, 5, 6].
Farhan = 2 CW from Aman: pos5 is 2 clockwise [solver-verified].
→ Aman at pos6, Farhan at pos2

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

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

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

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

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

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

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

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

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

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

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

Position: B D A _ _

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 C remains → C at position 5

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

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

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

Solution Approach:

Step 1: Key rule for mixed facing
- Person facing CENTER: right = CLOCKWISE, left = ANTI-CLOCKWISE
- Person facing OUTWARD: right = ANTI-CLOCKWISE, left = CLOCKWISE

Step 2: Draw 8-seat circle (positions 1–8 clockwise)

Step 3: Start with definite information
- Fix P (faces center) at position 1 (reference point)
- M 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
- O sits second to the LEFT of P (pos 1):
P faces center → left = anti-clockwise
2 anti-CW from pos 1 → pos 7
O faces same as M → OUTWARD
- S 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 P(pos 1, center→CW): pos 2
- T opposite P(pos 1): pos 5
- R not adjacent to M(pos 4): adj = pos 3 & 5
→ R at pos 8, Q at pos 3

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

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

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

Answer: R sits second to the right of S.

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
- 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
- T sits immediately to the right of P (viewer's right = higher pos): pos[T] = pos[P] + 1
If P=3 → T=4 ✓ (pos 4 free)
If P=4 → T=5 = Q ✗ (conflict)
∴ P=3, R=1, T=4

Position: R _ P T Q

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

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

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

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

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

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

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

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

Position: B A C _ _

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

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

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

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

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
- H sits at a corner → pos 1
- E sits second to the RIGHT of H: right(center-facing)=CW
2 CW from pos 1 → pos 3 ✓ (corner)
- D sits OPPOSITE H (pos 1) → pos 5 ✓
- B at midpoint, NOT adjacent to H(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: A, F, G
Fill remaining seats: pos2=A, pos8=F, pos4=G

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

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

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

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 Aman: opp(pos1) = pos4 → Aman at H4

Step 3: Apply relative positioning
- Bhanu second to the right of Charu(pos1):
CW 2: pos1→pos2→pos3
→ Bhanu at H3

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

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

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

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

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

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

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

Position: C E A _ _

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 B remains → B at position 5

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

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

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

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

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

Row 2: R T P Q S

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

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

Answer: P faces B.

Solution Approach:

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

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

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

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

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 D _ _
Row2: Q P _ _
Row3: Y Z _ _

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

Step 6: Fill remaining positions
Remaining: Row1 pos4=C, Row2 pos4=R, Row3 pos4=W

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

Right extreme of Row 3 = position 4 = W

Answer: W

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 (↓)
- R sits immediately to the left of T (pos 5) facing North (↑) → Position 4

Position: P(↓) _ S(↑) R(↑) T(↓) _

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

Final Arrangement:
Pos: P(↓) Q(↑) S(↑) R(↑) 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
✓ R at pos 4 (immediately left of T), facing North

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

Answer: Q sits between P and S.

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

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

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

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

Answer: Q sits second to the right of S.

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

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

Step 4: Place outer circle persons
- Q faces C(I1) → Q at O1 ✓
- Outer occupied seats: O1, O2, O4, O5. Empty: O3, O6.
- S second to right of R (outer, facing center: right=CW, step 2):
Remaining outer persons: S,R,P at O2, O4, O5.
R=O2 → Q=O4, S=O5 ✓
R=O4 → Q=O6(empty) ✗
R=O5 → Q=O1=P ✗
∴ R=O2, S=O4, P=O5 ✓
- P(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
D is at I2. Opposite of I2 = I4 = A.

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

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

Answer: A sits opposite to D.

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

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

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

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

Answer: N sits immediately to the left of K.