Seating Arrangement - Beginner-Intermediate Level: opposite positions BEGINNER-INTERMEDIATE

Strategic fast track practice for seating arrangement: 20 beginner-intermediate-level problems. Worksheet 9 of 30 - Focus: opposite positions. Develop expertise in linear arrangement, row seating, table arrangement with step-by-step solutions. Ideal for developing learners targeting building on fundamentals with moderate challenges.

πŸ“ Worksheet 9 of 30 β€’ 20 questions β€’ ⏱️ Estimated time: 20 minutes β€’ 🎯 Beginner-intermediate level

What you'll learn in this worksheet:
Your progress through Seating Arrangement
Worksheet 9 of 30 (30% complete)

Question 1

Three parallel rows of chairs. Row 1 has D, C, B, A facing South. Row 2 has Q, S, R, P facing North. Row 3 has Z, X, W, Y facing South. Row 2 is between Row 1 and Row 3. Persons in Row 1 face persons in Row 2, and persons in Row 2 face persons in Row 3. D faces Q who faces Z. C sits to the left of D in Row 1. S faces C and also faces X. R sits second to the right of S in Row 2. Who sits at the right extreme of Row 3?
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 Q who faces Z: all three in the SAME vertical column.
Place at position 2:
Row1: _ D _ _
Row2: _ Q _ _
Row3: _ Z _ _

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

Step 4: Second facing relationship
- S faces C(Row1 pos1) β†’ S at Row2 position 1
- S faces X β†’ X at Row3 position 1
Row1: C D _ _
Row2: S Q _ _
Row3: X Z _ _

Step 5: Apply relative positioning in Row 2
- R sits second to the right of S(pos1): 1+2=3 β†’ R at Row2 position 3
Row2: S Q R _
R faces Row1 pos3 β†’ B at Row1 pos3 βœ“
R faces Row3 pos3 β†’ W at Row3 pos3 βœ“

Step 6: Fill remaining positions
Remaining: Row1 pos4=A, Row2 pos4=P, Row3 pos4=Y

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

Right extreme of Row 3 = position 4 = Y

Answer: Y

Question 2

Eight persons E, G, H, B, C, A, D and F are sitting around a square table. Four persons sit at corners and four at the middle of sides, all facing the center. E sits at a corner. G sits second to the right of E. H sits at the middle of a side and is not adjacent to E. B sits opposite to E. C sits at a corner immediately to the right of H. A sits immediately to the left of G. D is not adjacent to B. How many persons sit between E and B when counted from the left of E?
Solution Approach:

Step 1: Draw square table diagram
Positions clockwise (C=Corner, M=Midpoint):
C1(1) β†’ M1(2) β†’ C2(3) β†’ M2(4) β†’ C3(5) β†’ M3(6) β†’ C4(7) β†’ M4(8) β†’ 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
- E sits at a corner β†’ pos 1
- G sits second to the RIGHT of E: right(center-facing)=CW
2 CW from pos 1 β†’ pos 3 βœ“ (corner)
- B sits OPPOSITE E (pos 1) β†’ pos 5 βœ“
- H at midpoint, NOT adjacent to E(pos 1):
Adjacent to pos 1: pos 8 and pos 2
H β†’ pos 6 (midpoint, not adjacent) βœ“
- C sits at corner immediately to the RIGHT of H(pos 6):
1 CW from pos 6 β†’ pos 7 (corner) βœ“

Step 3: Remaining persons
Remaining: A, D, F
Fill remaining seats: pos2=A, pos8=D, pos4=F

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

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

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

Question 3

Six persons Charu, Farhan, Bhanu, Aman, Deepak and Esha are sitting around a hexagonal table, one at each corner, all facing the center. Charu sits opposite to Farhan. Bhanu sits second to the right of Charu. Deepak sits second to the right of Esha. Aman is not adjacent to Charu. What is the position of Aman with respect to Bhanu?
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 β†’ Farhan at H4

Step 3: Apply relative positioning
- Bhanu second to the right of Charu(pos1):
CW 2: pos1β†’pos2β†’pos3
β†’ 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, Farhan=4, Bhanu=3,
remaining seats: [2, 5, 6].
Deepak = 2 CW from Esha: pos5 is 2 clockwise [solver-verified].
β†’ Esha at pos6, Deepak at pos2

Step 4: Apply constraint
- Aman not adjacent to Charu(pos1):
Adjacent to pos1: pos6 and pos2
β†’ Aman at pos5 (not adjacent) βœ“

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

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

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

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

Question 4

Six persons B, E, A, C, D and F are sitting around a circular table facing the center. B sits second to the left of E. A sits opposite to B. C sits immediately to the right of A. F is not adjacent to C. Who sits opposite to E?
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 E β†’ E is 2 clockwise from B
pos[E] = 3
- A sits OPPOSITE B (pos 1) β†’ pos 4
- C sits immediately to the right of A (pos 4) β†’ pos 5

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

Final Arrangement (clockwise):
pos1:B β†’ pos2:F β†’ pos3:E β†’ pos4:A β†’ pos5:C β†’ pos6:D
(All facing center)

Opposite pairs: pos1↔pos4, pos2↔pos5, pos3↔pos6

E is at pos 3 β†’ opposite = pos 6 = D

Answer: D sits opposite to E.

Question 5

Six persons D, A, E, B, C and F are sitting around a circular table facing the center. D sits second to the left of A. E sits opposite to D. B sits immediately to the right of E. F is not adjacent to B. Who sits opposite to A?
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 D at position 1 (reference point)
- D is second to the LEFT of A β†’ A is 2 clockwise from D
pos[A] = 3
- E sits OPPOSITE D (pos 1) β†’ pos 4
- B sits immediately to the right of E (pos 4) β†’ pos 5

Step 3: Resolve remaining positions
Remaining persons: F, C β†’ remaining seats: [2, 6]
F is NOT adjacent to B (pos 5).
Adjacent to pos 5: pos 4 and pos 6.
Therefore F β†’ pos 2, and C β†’ pos 6.

Final Arrangement (clockwise):
pos1:D β†’ pos2:F β†’ pos3:A β†’ pos4:E β†’ pos5:B β†’ pos6:C
(All facing center)

Opposite pairs: pos1↔pos4, pos2↔pos5, pos3↔pos6

A is at pos 3 β†’ opposite = pos 6 = C

Answer: C sits opposite to A.

Question 6

Five persons D, E, C, B and A are sitting in a row facing North. D sits at one of the extreme ends. E sits second to the right of D. C sits immediately to the left of E. B is not at any extreme end. Who sits at the other extreme end?
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 β†’ Place D at position 1
- E sits second to the right of D β†’ E at position 3
- C sits immediately to the left of E β†’ C at position 2

Position: D C E _ _

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

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

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

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

Question 7

Two parallel rows of chairs. Row 1 has A, B, E, D and C facing South. Row 2 has T, P, S, Q and R facing North. Each person in one row faces exactly one person from the other row. E sits fourth from the left end of Row 1. T faces E. A sits at an extreme end of Row 1. B sits second to the right of A. P sits second to the left of T. S sits at an extreme end of Row 2. R is not adjacent to T in Row 2. Who faces B?
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 β†’ Row 1, pos 4
- A sits at an extreme end: pos 1 or pos 5
- B sits second to the RIGHT of A (south-facing β†’ lower position):
pos[B] = pos[A] - 2
If A at pos 1 β†’ pos[B] = -1 (invalid βœ—)
If A at pos 5 β†’ pos[B] = 3 βœ“ (pos 3 is free)
∴ A at pos 5, B at pos 3 βœ“

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

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

Row 2: R P Q T S

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

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

Answer: Q faces B.

Question 8

There are 10 seats in a row, all facing North. 8 persons E, C, A, H, D, B, F and G are seated, leaving 2 seats empty. E sits at seat 3. G sits at seat 8. One empty seat is at an extreme end. C sits immediately to the right of an empty seat. H sits fourth to the left of G. How many persons sit between the two empty seats?
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
- G at seat 8 (seat 8)
- One empty seat at extreme end β†’ seat 1 is empty

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

Step 3: Apply empty seat adjacency
- C sits immediately to the RIGHT of an empty seat
- Empty at seat 1 β†’ seat 2 = C βœ“

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

Step 4: Apply "fourth to the left" condition
- H sits fourth to the LEFT of G (seat 8)
- Fourth to left: 8 β†’ 7 β†’ 6 β†’ 5 β†’ 4
- H at seat 4 βœ“

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

Question 9

Five persons A, E, D, B and C are sitting in a row facing North. A sits at one of the extreme ends. E sits second to the right of A. D sits immediately to the left of E. B is not at any extreme end. Who sits at the other extreme end?
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 β†’ Place A at position 1
- E sits second to the right of A β†’ E at position 3
- D sits immediately to the left of E β†’ D at position 2

Position: A D E _ _

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

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

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

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

Question 10

Eight persons P, N, O, R, T, S, Q and M are sitting around a circular table. Some face the center and some face outward. P faces the center. N faces outward and sits third to the right of P. O sits second to the left of P and faces the same direction as N. R faces the center and sits immediately to the right of O. S sits immediately to the right of P. M sits opposite P. Q is not adjacent to N. Who sits second to the right of R?
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)
- N faces outward, sits third to the RIGHT of P:
P faces center β†’ right = clockwise
3 CW from pos 1 β†’ pos 4
N = pos 4 βœ“

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

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

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

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

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

Answer: Q sits second to the right of R.

Question 11

Three parallel rows of chairs. Row 1 has D, A, C, B facing South. Row 2 has S, Q, P, R facing North. Row 3 has Y, Z, X, W facing South. Row 2 is between Row 1 and Row 3. Persons in Row 1 face persons in Row 2, and persons in Row 2 face persons in Row 3. D faces S who faces Y. A sits to the left of D in Row 1. Q faces A and also faces Z. P sits second to the right of Q in Row 2. Who sits at the right extreme of Row 3?
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 S who faces Y: all three in the SAME vertical column.
Place at position 2:
Row1: _ D _ _
Row2: _ S _ _
Row3: _ Y _ _

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

Step 4: Second facing relationship
- Q faces A(Row1 pos1) β†’ Q at Row2 position 1
- Q faces Z β†’ Z at Row3 position 1
Row1: A D _ _
Row2: Q S _ _
Row3: Z Y _ _

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

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

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

Right extreme of Row 3 = position 4 = W

Answer: W

Question 12

Six persons Deepak, Esha, Charu, Aman, Bhanu and Farhan are sitting around a hexagonal table, one at each corner, all facing the center. Deepak sits opposite to Esha. Charu sits second to the right of Deepak. Bhanu sits second to the right of Farhan. Aman is not adjacent to Deepak. What is the position of Aman with respect to Charu?
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 β†’ Esha at H4

Step 3: Apply relative positioning
- Charu second to the right of Deepak(pos1):
CW 2: pos1β†’pos2β†’pos3
β†’ Charu at H3

- Bhanu second to the right of Farhan:
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].
Bhanu = 2 CW from Farhan: pos5 is 2 clockwise [solver-verified].
β†’ Farhan at pos6, Bhanu at pos2

Step 4: Apply constraint
- Aman not adjacent to Deepak(pos1):
Adjacent to pos1: pos6 and pos2
β†’ Aman at pos5 (not adjacent) βœ“

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

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

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

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

Question 13

Six persons Bina, Eshaan, Amit, Chetan, Divya and Falguni are sitting in a row facing North. Each has a different profession: Engineer, Teacher, Banker, Architect, Doctor and Lawyer. Bina is a Engineer and sits third from the left. The Teacher sits second from the left. Eshaan sits second to the right of the Teacher. The Doctor sits immediately to the right of Bina. Divya is a Banker and is not adjacent to Bina. The Architect sits at the right extreme end. Falguni sits at an extreme end. Chetan is not at an extreme end. What is the profession of Chetan?
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 Engineer, sits at position 3
- The Teacher sits second from the left β†’ position 2
(Which person is the Teacher? Must be Amit, the only one unassigned here β€” verified below.)
- Eshaan sits second to the right of the Teacher (pos 2): 2+2 = pos 4 β†’ Eshaan at position 4

Position: _ [Teacher] Bina Eshaan _ _
Profsn: _ Teacher Engineer _ _ _

Step 3: Apply adjacency and profession constraints
- The Doctor sits immediately to the RIGHT of Bina(pos 3) β†’ pos 4 = Eshaan
∴ Eshaan is the Doctor βœ“
- The Architect sits at right extreme β†’ position 6

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

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

Position: _ Amit Bina Eshaan _ _
Profsn: _ Teacher Engineer Doctor _ _

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

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

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

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

Answer: Chetan's profession is Lawyer.

Question 14

Eight persons C, G, E, F, A, D, H and B are sitting around a square table. Four persons sit at corners and four at the middle of sides, all facing the center. C sits at a corner. G sits second to the right of C. E sits at the middle of a side and is not adjacent to C. F sits opposite to C. A sits at a corner immediately to the right of E. D sits immediately to the left of G. H is not adjacent to F. How many persons sit between C and F when counted from the left of C?
Solution Approach:

Step 1: Draw square table diagram
Positions clockwise (C=Corner, M=Midpoint):
C1(1) β†’ M1(2) β†’ C2(3) β†’ M2(4) β†’ C3(5) β†’ M3(6) β†’ C4(7) β†’ M4(8) β†’ 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
- C sits at a corner β†’ pos 1
- G sits second to the RIGHT of C: right(center-facing)=CW
2 CW from pos 1 β†’ pos 3 βœ“ (corner)
- F sits OPPOSITE C (pos 1) β†’ pos 5 βœ“
- E at midpoint, NOT adjacent to C(pos 1):
Adjacent to pos 1: pos 8 and pos 2
E β†’ pos 6 (midpoint, not adjacent) βœ“
- A sits at corner immediately to the RIGHT of E(pos 6):
1 CW from pos 6 β†’ pos 7 (corner) βœ“

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

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

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

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

Question 15

Six persons Farhan, Esha, Bhanu, Deepak, Aman and Charu are sitting around a hexagonal table, one at each corner, all facing the center. Farhan sits opposite to Esha. Bhanu sits second to the right of Farhan. Aman sits second to the right of Charu. Deepak is not adjacent to Farhan. What is the position of Deepak with respect to Bhanu?
Solution Approach:

Step 1: Draw hexagonal arrangement
6 corners H1–H6 clockwise.
Opposite pairs: H1↔H4, H2↔H5, H3↔H6.

Step 2: Place definite positions
- Fix Farhan at H1 (pos 1).
- Farhan opposite Esha: opp(pos1) = pos4 β†’ Esha at H4

Step 3: Apply relative positioning
- Bhanu second to the right of Farhan(pos1):
CW 2: pos1β†’pos2β†’pos3
β†’ Bhanu at H3

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

Step 4: Apply constraint
- Deepak not adjacent to Farhan(pos1):
Adjacent to pos1: pos6 and pos2
β†’ Deepak at pos5 (not adjacent) βœ“

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

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

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

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

Question 16

Six family members β€” Arjun (grandfather), Pooja (grandmother), Rahul (father), Priya (mother), Manoj (son), and Swati (daughter) β€” are sitting around a circular table facing the center. No male sits adjacent to another male. Priya sits second to the right of Pooja. Rahul is not adjacent to his wife. Manoj is not adjacent to Pooja. Who sits immediately to the right of Swati?
Solution Approach:

Step 1: Identify genders
Males: Arjun, Rahul, Manoj
Females: Pooja, Priya, 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 Arjun 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 Pooja (right=CW):
Female positions: 2, 4, 6.
- If Pooja=pos2 β†’ Priya=pos4 βœ“ (or pos2+2=pos4)
- If Pooja=pos4 β†’ Priya=pos6 βœ“
- If Pooja=pos6 β†’ Priya=pos8%6=pos2 βœ“

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 Pooja=pos4 β†’ Priya=pos6:
- Father options: pos1, pos3, pos5.
Adjacent to pos6: pos5, pos1. So father β‰  pos5 and β‰  pos1 β†’ Rahul=pos3 βœ“.
Remaining males: Arjun(1), Manoj(5). Swati and Pooja fill pos2, pos4.
Pooja=pos4 (as set). Swati=pos2 βœ“.

Final Arrangement:
pos1:Arjun β†’ pos2:Priya β†’ pos3:Manoj β†’ pos4:Swati β†’ pos5:Rahul β†’ pos6:Pooja

Verification:
βœ“ No adjacent males: Arjun(1)-Swati(2), Rahul(3)-Pooja(4), Manoj(5)-Priya(6) β€” all M-F pairs
βœ“ Priya(pos6) second right of Pooja(pos4): CW 2 from pos4 = pos6 βœ“
βœ“ Rahul(pos3) not adjacent to Priya(pos6): pos3 and pos6 are not adjacent βœ“

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

Answer: Rahul sits immediately to the right of Swati.

Question 17

Six persons C, F, A, B, E and D are sitting around a circular table facing the center. C sits second to the left of F. A sits opposite to C. B sits immediately to the right of A. D is not adjacent to B. Who sits opposite to F?
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 C at position 1 (reference point)
- C is second to the LEFT of F β†’ F is 2 clockwise from C
pos[F] = 3
- A sits OPPOSITE C (pos 1) β†’ pos 4
- B sits immediately to the right of A (pos 4) β†’ pos 5

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

Final Arrangement (clockwise):
pos1:C β†’ pos2:D β†’ pos3:F β†’ pos4:A β†’ pos5:B β†’ pos6:E
(All facing center)

Opposite pairs: pos1↔pos4, pos2↔pos5, pos3↔pos6

F is at pos 3 β†’ opposite = pos 6 = E

Answer: E sits opposite to F.

Question 18

Three parallel rows of chairs. Row 1 has D, C, A, B facing South. Row 2 has Q, R, P, S facing North. Row 3 has W, Z, X, Y facing South. Row 2 is between Row 1 and Row 3. Persons in Row 1 face persons in Row 2, and persons in Row 2 face persons in Row 3. D faces Q who faces W. C sits to the left of D in Row 1. R faces C and also faces Z. P sits second to the right of R in Row 2. Who sits at the right extreme of Row 3?
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 Q who faces W: all three in the SAME vertical column.
Place at position 2:
Row1: _ D _ _
Row2: _ Q _ _
Row3: _ W _ _

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

Step 4: Second facing relationship
- R faces C(Row1 pos1) β†’ R at Row2 position 1
- R faces Z β†’ Z at Row3 position 1
Row1: C D _ _
Row2: R Q _ _
Row3: Z W _ _

Step 5: Apply relative positioning in Row 2
- P sits second to the right of R(pos1): 1+2=3 β†’ P at Row2 position 3
Row2: R Q P _
P faces Row1 pos3 β†’ A at Row1 pos3 βœ“
P faces Row3 pos3 β†’ X at Row3 pos3 βœ“

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

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

Right extreme of Row 3 = position 4 = Y

Answer: Y

Question 19

There are 10 seats in a row, all facing North. 8 persons E, H, G, D, C, B, A and F are seated, leaving 2 seats empty. E sits at seat 3. F sits at seat 8. One empty seat is at an extreme end. H sits immediately to the right of an empty seat. D sits fourth to the left of F. How many persons sit between the two empty seats?
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
- F at seat 8 (seat 8)
- One empty seat at extreme end β†’ seat 1 is empty

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

Step 3: Apply empty seat adjacency
- H sits immediately to the RIGHT of an empty seat
- Empty at seat 1 β†’ seat 2 = H βœ“

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

Step 4: Apply "fourth to the left" condition
- D sits fourth to the LEFT of F (seat 8)
- Fourth to left: 8 β†’ 7 β†’ 6 β†’ 5 β†’ 4
- D at seat 4 βœ“

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

Question 20

Six persons Falguni, Chetan, Eshaan, Divya, Bina and Amit are sitting in a row facing North. Each has a different profession: Teacher, Banker, Doctor, Architect, Lawyer and Engineer. Falguni is a Teacher and sits third from the left. The Banker sits second from the left. Chetan sits second to the right of the Banker. The Lawyer sits immediately to the right of Falguni. Bina is a Doctor and is not adjacent to Falguni. The Architect sits at the right extreme end. Amit sits at an extreme end. Divya is not at an extreme end. What is the profession of Divya?
Solution Approach:

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

Step 2: Apply direct conditions
- Falguni is Teacher, sits at position 3
- The Banker sits second from the left β†’ position 2
(Which person is the Banker? Must be Eshaan, the only one unassigned here β€” verified below.)
- Chetan sits second to the right of the Banker (pos 2): 2+2 = pos 4 β†’ Chetan at position 4

Position: _ [Banker] Falguni Chetan _ _
Profsn: _ Banker Teacher _ _ _

Step 3: Apply adjacency and profession constraints
- The Lawyer sits immediately to the RIGHT of Falguni(pos 3) β†’ pos 4 = Chetan
∴ Chetan is the Lawyer βœ“
- The Architect sits at right extreme β†’ position 6

Position: _ [Banker] Falguni Chetan _ [law]
Profsn: _ Banker Teacher Lawyer _ Architect

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

Position: _ Eshaan Falguni Chetan _ _
Profsn: _ Banker Teacher Lawyer _ _

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

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

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

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

Answer: Divya's profession is Engineer.
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