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Linear with Empty Seats Beginner-Intermediate Worksheet: Focus on common variations practice Linear with Empty Seats BEGINNER INTERMEDIATE

Level up your Linear with Empty Seats skills! You're at Worksheet 4 of 10 (33% through this series). This step-up challenge worksheet features 20 beginner-intermediate-level problems with a focus on common variations practice. Topics covered: linear with empty seats for competitive exams, how to solve linear with empty seats, linear with empty seats tricks.

📝 Worksheet 4 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner Intermediate level

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Your progress through Linear with Empty Seats
Worksheet 4 of 10 (33% complete)

Question 1

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

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

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

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

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

Question 2

There are 10 seats in a row, all facing North. 8 persons H, B, E, A, C, D, F and G are seated, leaving 2 seats empty. H sits at seat 3. G sits at seat 8. One empty seat is at an extreme end. B sits immediately to the right of an empty seat. A 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
- H at seat 3
- G at seat 8 (seat 8)
- One empty seat at extreme end → seat 1 is empty

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

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

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

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

Question 3

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

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

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

Question 4

There are 10 seats in a row, all facing North. 8 persons C, G, D, E, H, B, F and A are seated, leaving 2 seats empty. C sits at seat 3. A sits at seat 8. One empty seat is at an extreme end. G sits immediately to the right of an empty seat. E sits fourth to the left of A. 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
- C at seat 3
- A 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(A) 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(A) 9(_) 10(_)

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

Question 5

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

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

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

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

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

Question 6

There are 10 seats in a row, all facing North. 8 persons E, A, D, G, B, C, H 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. A sits immediately to the right of an empty seat. G 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 → seat 1 is empty

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

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

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

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

Question 7

There are 10 seats in a row, all facing North. 8 persons E, D, F, G, C, A, B and H are seated, leaving 2 seats empty. E sits at seat 3. H sits at seat 8. One empty seat is at an extreme end. D sits immediately to the right of an empty seat. G sits fourth to the left of H. 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
- H 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(H) 9(_) 10(_)

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

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

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

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

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

Verification:
✓ E at seat 3
✓ H at seat 8
✓ Empty at seat 1 (extreme end)
✓ D 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.

Question 8

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

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

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

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

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

Question 9

There are 10 seats in a row, all facing North. 8 persons C, F, G, H, D, A, E and B are seated, leaving 2 seats empty. C sits at seat 3. B sits at seat 8. One empty seat is at an extreme end. F sits immediately to the right of an empty seat. H sits fourth to the left of B. 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
- C at seat 3
- B 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(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(C) 4(_) 5(_) 6(_) 7(_) 8(B) 9(_) 10(_)

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

Question 10

There are 10 seats in a row, all facing North. 8 persons F, C, G, H, E, A, D and B are seated, leaving 2 seats empty. F sits at seat 3. B 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 B. 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
- F at seat 3
- B at seat 8 (seat 8)
- One empty seat at extreme end → seat 1 is empty

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

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

Question 11

There are 10 seats in a row, all facing North. 8 persons C, B, E, H, A, G, D and F are seated, leaving 2 seats empty. C sits at seat 3. F sits at seat 8. One empty seat is at an extreme end. B sits immediately to the right of an empty seat. H 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
- C at seat 3
- F 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(F) 9(_) 10(_)

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

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

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

Question 12

There are 10 seats in a row, all facing North. 8 persons E, A, G, B, C, D, H 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. A sits immediately to the right of an empty seat. B 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 → seat 1 is empty

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

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

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

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

Question 13

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

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

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

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

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

Question 14

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

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

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

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

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

Question 15

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

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

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

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

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

Question 16

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

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

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

Question 17

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

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

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

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

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

Question 18

There are 10 seats in a row, all facing North. 8 persons E, C, A, F, G, B, D and H are seated, leaving 2 seats empty. E sits at seat 3. H sits at seat 8. One empty seat is at an extreme end. C sits immediately to the right of an empty seat. F sits fourth to the left of H. 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
- H 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(H) 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(H) 9(_) 10(_)

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

Question 19

There are 10 seats in a row, all facing North. 8 persons C, D, F, E, B, G, A and H are seated, leaving 2 seats empty. C sits at seat 3. H sits at seat 8. One empty seat is at an extreme end. D sits immediately to the right of an empty seat. E sits fourth to the left of H. 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
- C at seat 3
- H 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(H) 9(_) 10(_)

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

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

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

Question 20

There are 10 seats in a row, all facing North. 8 persons C, F, B, E, G, H, D and A are seated, leaving 2 seats empty. C sits at seat 3. A sits at seat 8. One empty seat is at an extreme end. F sits immediately to the right of an empty seat. E sits fourth to the left of A. 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
- C at seat 3
- A 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(A) 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(C) 4(_) 5(_) 6(_) 7(_) 8(A) 9(_) 10(_)

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.
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