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

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
- E 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(E) 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(E) 9(_) 10(_)

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

Solution Approach:

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

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

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

Step 3: Test each MCQ option

- "V sits at position 1": ✓ Possible in at least one valid arrangement
- "Z sits at position 2": ✗ NEVER possible → must be FALSE
- "V sits at position 5": ✓ Possible in at least one valid arrangement
- "X sits at position 1": ✓ Possible in at least one valid arrangement

Step 4: Conclusion
"Z sits at position 2" is impossible in ALL 7 valid arrangement(s) — it must be FALSE.
All other options occur in at least one valid arrangement.

Answer: "Z sits at position 2" must be FALSE.

Solution Approach:

Step 1: Identify genders
Males: Sunil, Rajesh, Amit
Females: Isha, Neha, Pooja

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

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

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

Final Arrangement:
pos1:Sunil → pos2:Neha → pos3:Amit → pos4:Pooja → pos5:Rajesh → pos6:Isha

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

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

Answer: Rajesh sits immediately to the right of Pooja.

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

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

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

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

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

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

Right extreme of Row 3 = position 4 = Y

Answer: Y

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
- S faces B(Row1 pos1) → S at Row2 position 1
- S faces W → W at Row3 position 1
Row1: B D _ _
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 → A at Row1 pos3 ✓
Q faces Row3 pos3 → Y at Row3 pos3 ✓

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

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

Right extreme of Row 3 = position 4 = X

Answer: X

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

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

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

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

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

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

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

Solution Approach:

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

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

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

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

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

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

Row 2: Q T S P R

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

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

Answer: S faces E.

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

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

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

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

Answer: J sits second to the left of H.

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

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

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

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

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

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

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

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

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

Solution Approach:

Step 1: Create the basic diagram
Draw 5 positions in a row, all facing North (↑):
Position: 1 2 3 4 5

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

Position: D A 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 C remains → C at position 5

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

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

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

Position: R _ S T Q

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

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

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

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

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
- P 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 = P ✗ (conflict)
∴ R=3, S=1, Q=4

Position: S _ R Q P

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

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

Verification:
✓ P 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
✓ T not adjacent to P (pos 2, not pos 4)

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

Solution Approach:

Step 1: Identify genders
Males: Rahul, Sunil, Vikram
Females: Pooja, 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 Pooja (right=CW):
Female positions: 2, 4, 6.
- If Pooja=pos2 → Isha=pos4 ✓ (or pos2+2=pos4)
- If Pooja=pos4 → Isha=pos6 ✓
- If Pooja=pos6 → Isha=pos8%6=pos2 ✓

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

Final Arrangement:
pos1:Rahul → pos2:Isha → pos3:Vikram → pos4:Swati → pos5:Sunil → pos6:Pooja

Verification:
✓ No adjacent males: Rahul(1)-Swati(2), Sunil(3)-Pooja(4), Vikram(5)-Isha(6) — all M-F pairs
✓ Isha(pos6) second right of Pooja(pos4): CW 2 from pos4 = pos6 ✓
✓ Sunil(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 = Sunil.

Answer: Sunil sits immediately to the right of Swati.

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

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

Step 4: Second facing relationship
- Q faces A(Row1 pos1) → Q at Row2 position 1
- Q faces W → W at Row3 position 1
Row1: A C _ _
Row2: Q P _ _
Row3: W 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 → B at Row1 pos3 ✓
S faces Row3 pos3 → X at Row3 pos3 ✓

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

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

Right extreme of Row 3 = position 4 = Y

Answer: Y

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
- 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(H) 9(_) 10(_)

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

Solution Approach:

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

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

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

Step 3: Test each MCQ option

- "Z sits at position 4": ✓ Possible in at least one valid arrangement
- "X sits at position 2": ✗ NEVER possible → must be FALSE
- "V sits at position 1": ✓ Possible in at least one valid arrangement
- "Z sits at position 5": ✓ 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: Identify genders
Males: Sanjay, Rajesh, Raj
Females: Jyoti, Gita, Priya

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
Gita sits second to the RIGHT of Jyoti (right=CW):
Female positions: 2, 4, 6.
- If Jyoti=pos2 → Gita=pos4 ✓ (or pos2+2=pos4)
- If Jyoti=pos4 → Gita=pos6 ✓
- If Jyoti=pos6 → Gita=pos8%6=pos2 ✓

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

Final Arrangement:
pos1:Sanjay → pos2:Gita → pos3:Raj → pos4:Priya → pos5:Rajesh → pos6:Jyoti

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

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

Answer: Rajesh sits immediately to the right of Priya.

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

Step 3: Test each MCQ option

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

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

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

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

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

Answer: L sits immediately to the left of O.