Seating Arrangement - Expert Level: facing-north-south EXPERT

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

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

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

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

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

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

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

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

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

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

Answer: O sits second to the right of N.

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

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

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 R Q _
Q faces Row1 pos3 → D at Row1 pos3 ✓
Q faces Row3 pos3 → Z at Row3 pos3 ✓

Step 6: Fill remaining positions
Remaining: Row1 pos4=B, Row2 pos4=P, Row3 pos4=W

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

Right extreme of Row 3 = position 4 = W

Answer: W

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

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

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

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

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

Answer: D sits opposite to A.

Solution Approach:

Step 1: Draw rectangular table
Positions 1–10 clockwise:
- Top (longer, 3 persons): pos1(corner-TL), pos2(mid-top), pos3(corner-TR)
- Right (shorter, 2 persons): pos4(mid-right), pos5(corner-BR)
- Bottom (longer, 3 persons): pos6(mid-bot), pos7(corner-BL-ish... wait, pos7 is mid-bottom)
Correction: pos6(mid-bot), pos7(mid-bot2), pos8(corner-BL) — actually:
Bottom traversed right→left: pos6(mid), pos7(mid2)? For 3 persons: corner is shared with adjacent side.
In competitive exams: the 3 bottom persons are at pos6(mid), pos7, pos8(corner-BL).
Actually pos6,7,8 with pos8=BL-corner and pos5=BR-corner. ✓
- Left (shorter, 2 persons): pos9(mid-left), pos10(mid-left2)
- Corners: pos1(TL), pos3(TR), pos5(BR), pos8(BL)
- Longer-side midpoints: pos2(top), pos7(bottom)
- Shorter-side midpoints: pos4(right), pos9(left)

Step 2: Place persons
- J at middle of longer side → pos 7 (mid-bottom)
- E at middle of shorter side → pos 4 (mid-right)
- H second to the RIGHT of J (pos 7):
right(center-facing)=CW: pos7+2 = pos9 → H ✓
- G at a corner → pos 1
- B at corner OPPOSITE to G: pos5 → B ✓
- C second to the LEFT of E (pos 4):
left(center-facing)=anti-CW: pos4-2 = pos2 → C ✓

Step 3: Fill remaining positions
Remaining persons: I, D, A, F
Remaining seats: [3, 6, 8, 10]

Final Arrangement (clockwise):
pos1:G | pos2:C | pos3:I | pos4:E | pos5:B | pos6:D | pos7:J | pos8:A | pos9:H | pos10:F

Find second to the left of E (pos 4):
Left (anti-CW): pos4 → pos3 → pos2 = C

Answer: C sits second to the left of E.

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

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

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

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

Answer: M sits immediately to the left of L.

Solution Approach:

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

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

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

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

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

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

Position: _ Amit Bina Eshaan _ _
Profsn: _ Banker Architect Engineer _ _

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

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

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

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

Answer: Divya's profession is Doctor.

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

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

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

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

Answer: Q sits second to the right of T.

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

Position: B A E _ _

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 C remains → C at position 5

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

Verification:
✓ B at extreme end (pos 1)
✓ E second to the right of B (pos 3)
✓ A immediately to the left of E (pos 2)
✓ D 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 Q (faces center) at position 1 (reference point)
- P faces outward, sits third to the RIGHT of Q:
Q 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 Q (pos 1):
Q faces center → left = anti-clockwise
2 anti-CW from pos 1 → pos 7
R faces same as P → OUTWARD
- M 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 Q(pos 1, center→CW): pos 2
- O opposite Q(pos 1): pos 5
- N not adjacent to P(pos 4): adj = pos 3 & 5
→ N at pos 8, S at pos 3

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

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

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

Answer: N sits second to the right of M.

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

Step 3: Remaining persons
Remaining: D, H, E
Fill remaining seats: pos2=D, pos8=H, pos4=E

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

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

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

Solution Approach:

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

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

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

Step 3: Test each MCQ option

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

Step 4: Conclusion
"X 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: "X sits at position 2" must be FALSE.

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

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
- P faces C(Row1 pos1) → P at Row2 position 1
- P faces Y → Y at Row3 position 1
Row1: C D _ _
Row2: P R _ _
Row3: Y Z _ _

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 R 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=B, Row2 pos4=Q, Row3 pos4=W

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

Right extreme of Row 3 = position 4 = W

Answer: W

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

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

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

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

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

Answer: T sits second to the right of O.

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
- E at seat 3
- A at seat 8 (seat 8)
- One empty seat at extreme end → seat 1 is empty

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

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

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

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

Solution Approach:

Step 1: Draw rectangular table
Positions 1–10 clockwise:
- Top (longer, 3 persons): pos1(corner-TL), pos2(mid-top), pos3(corner-TR)
- Right (shorter, 2 persons): pos4(mid-right), pos5(corner-BR)
- Bottom (longer, 3 persons): pos6(mid-bot), pos7(corner-BL-ish... wait, pos7 is mid-bottom)
Correction: pos6(mid-bot), pos7(mid-bot2), pos8(corner-BL) — actually:
Bottom traversed right→left: pos6(mid), pos7(mid2)? For 3 persons: corner is shared with adjacent side.
In competitive exams: the 3 bottom persons are at pos6(mid), pos7, pos8(corner-BL).
Actually pos6,7,8 with pos8=BL-corner and pos5=BR-corner. ✓
- Left (shorter, 2 persons): pos9(mid-left), pos10(mid-left2)
- Corners: pos1(TL), pos3(TR), pos5(BR), pos8(BL)
- Longer-side midpoints: pos2(top), pos7(bottom)
- Shorter-side midpoints: pos4(right), pos9(left)

Step 2: Place persons
- A at middle of longer side → pos 7 (mid-bottom)
- D at middle of shorter side → pos 4 (mid-right)
- B second to the RIGHT of A (pos 7):
right(center-facing)=CW: pos7+2 = pos9 → B ✓
- E at a corner → pos 1
- C at corner OPPOSITE to E: pos5 → C ✓
- H second to the LEFT of D (pos 4):
left(center-facing)=anti-CW: pos4-2 = pos2 → H ✓

Step 3: Fill remaining positions
Remaining persons: I, F, J, G
Remaining seats: [3, 6, 8, 10]

Final Arrangement (clockwise):
pos1:E | pos2:H | pos3:I | pos4:D | pos5:C | pos6:F | pos7:A | pos8:J | pos9:B | pos10:G

Find second to the left of D (pos 4):
Left (anti-CW): pos4 → pos3 → pos2 = H

Answer: H sits second to the left of D.

Solution Approach:

Step 1: Identify genders
Males: Raj, Rahul, Manoj
Females: Ekta, Priya, 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 Raj at pos 1.
Then: pos2=Female, pos3=Male, pos4=Female, pos5=Male, pos6=Female.

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

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

Final Arrangement:
pos1:Raj → pos2:Priya → pos3:Manoj → pos4:Kavya → pos5:Rahul → pos6:Ekta

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

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

Answer: Rahul sits immediately to the right of Kavya.

Solution Approach:

Step 1: Draw rectangular table
Positions 1–10 clockwise:
- Top (longer, 3 persons): pos1(corner-TL), pos2(mid-top), pos3(corner-TR)
- Right (shorter, 2 persons): pos4(mid-right), pos5(corner-BR)
- Bottom (longer, 3 persons): pos6(mid-bot), pos7(corner-BL-ish... wait, pos7 is mid-bottom)
Correction: pos6(mid-bot), pos7(mid-bot2), pos8(corner-BL) — actually:
Bottom traversed right→left: pos6(mid), pos7(mid2)? For 3 persons: corner is shared with adjacent side.
In competitive exams: the 3 bottom persons are at pos6(mid), pos7, pos8(corner-BL).
Actually pos6,7,8 with pos8=BL-corner and pos5=BR-corner. ✓
- Left (shorter, 2 persons): pos9(mid-left), pos10(mid-left2)
- Corners: pos1(TL), pos3(TR), pos5(BR), pos8(BL)
- Longer-side midpoints: pos2(top), pos7(bottom)
- Shorter-side midpoints: pos4(right), pos9(left)

Step 2: Place persons
- G at middle of longer side → pos 7 (mid-bottom)
- C at middle of shorter side → pos 4 (mid-right)
- J second to the RIGHT of G (pos 7):
right(center-facing)=CW: pos7+2 = pos9 → J ✓
- B at a corner → pos 1
- F at corner OPPOSITE to B: pos5 → F ✓
- H second to the LEFT of C (pos 4):
left(center-facing)=anti-CW: pos4-2 = pos2 → H ✓

Step 3: Fill remaining positions
Remaining persons: A, E, I, D
Remaining seats: [3, 6, 8, 10]

Final Arrangement (clockwise):
pos1:B | pos2:H | pos3:A | pos4:C | pos5:F | pos6:E | pos7:G | pos8:I | pos9:J | pos10:D

Find second to the left of C (pos 4):
Left (anti-CW): pos4 → pos3 → pos2 = H

Answer: H sits second to the left of C.

Solution Approach:

Step 1: Draw the double row setup
Row 1 faces South (↓), Row 2 faces North (↑)
Person at position i in Row 1 faces person at position i in Row 2.

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

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

Step 2: Place Row 1 persons
- E sits 4th from the left end of Row 1 → Row 1, pos 4
- C sits at an extreme end: pos 1 or pos 5
- D sits second to the RIGHT of C (south-facing → lower position):
pos[D] = pos[C] - 2
If C at pos 1 → pos[D] = -1 (invalid ✗)
If C at pos 5 → pos[D] = 3 ✓ (pos 3 is free)
∴ C at pos 5, D at pos 3 ✓

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

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

Row 2: R T S P Q

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

Find who faces D:
D is at Row 1, position 3.
Person at Row 2, position 3 = S

Answer: S faces D.

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

Position: A B D _ _

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

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

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

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