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Linear with Empty Seats - Intermediate Level: tricky scenarios handling Linear with Empty Seats INTERMEDIATE

This expert challenge 📈 worksheet focuses on Linear with Empty Seats - a key topic in Seating Arrangement. You'll solve 20 intermediate-level problems (Worksheet 5 of 10). The primary focus is on tricky scenarios handling. Master how to solve linear with empty seats, linear with empty seats tricks, and linear with empty seats shortcut methods through systematic practice.

📝 Worksheet 5 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate level

What you'll learn in this worksheet:
Your progress through Linear with Empty Seats
Worksheet 5 of 10 (44% complete)

Question 1

There are 10 seats in a row, all facing North. 8 persons G, D, H, F, A, B, C and E are seated, leaving 2 seats empty. G 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. F 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
- G at seat 3
- E 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(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(G) 4(_) 5(_) 6(_) 7(_) 8(E) 9(_) 10(_)

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

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

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

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

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

Verification:
✓ G at seat 3
✓ E at seat 8
✓ Empty at seat 1 (extreme end)
✓ D immediately right of empty seat 1
✓ F fourth to left of E (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 F, G, B, A, D, H, C and E are seated, leaving 2 seats empty. F sits at seat 3. E sits at seat 8. One empty seat is at an extreme end. G sits immediately to the right of an empty seat. A 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
- F at seat 3
- E 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(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(F) 4(_) 5(_) 6(_) 7(_) 8(E) 9(_) 10(_)

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

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

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

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

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

Verification:
✓ F at seat 3
✓ E at seat 8
✓ Empty at seat 1 (extreme end)
✓ G immediately right of empty seat 1
✓ A fourth to left of E (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 A, G, B, D, C, H, F and E are seated, leaving 2 seats empty. A sits at seat 3. E 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 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
- A at seat 3
- E 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(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(A) 4(_) 5(_) 6(_) 7(_) 8(E) 9(_) 10(_)

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

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

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

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

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

Verification:
✓ A at seat 3
✓ E at seat 8
✓ Empty at seat 1 (extreme end)
✓ G immediately right of empty seat 1
✓ D fourth to left of E (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 G, H, C, D, E, B, F and A are seated, leaving 2 seats empty. G sits at seat 3. A 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 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
- G at seat 3
- A 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(A) 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(A) 9(_) 10(_)

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

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

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

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

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

Verification:
✓ G at seat 3
✓ A at seat 8
✓ Empty at seat 1 (extreme end)
✓ H immediately right of empty seat 1
✓ D 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 H, C, F, A, B, D, G 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. C sits immediately to the right of an empty seat. A 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
- C sits immediately to the RIGHT of an empty seat
- Empty at seat 1 → seat 2 = C ✓

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

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

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

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

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

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

Verification:
✓ H at seat 3
✓ E at seat 8
✓ Empty at seat 1 (extreme end)
✓ C immediately right of empty seat 1
✓ A fourth to left of E (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, G, B, D, C, F, A 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. G sits immediately to the right of an empty seat. D 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
- G sits immediately to the RIGHT of an empty seat
- Empty at seat 1 → seat 2 = G ✓

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

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

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

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

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

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

Verification:
✓ E at seat 3
✓ H at seat 8
✓ Empty at seat 1 (extreme end)
✓ G immediately right of empty seat 1
✓ D fourth to left of H (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 C, H, B, F, D, G, E 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. H sits immediately to the right of an empty seat. F 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
- H sits immediately to the RIGHT of an empty seat
- Empty at seat 1 → seat 2 = H ✓

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

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

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

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

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

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

Verification:
✓ C at seat 3
✓ A at seat 8
✓ Empty at seat 1 (extreme end)
✓ H immediately right of empty seat 1
✓ F fourth to left of A (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 B, E, H, C, F, A, G 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. E sits immediately to the right of an empty seat. C 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
- E sits immediately to the RIGHT of an empty seat
- Empty at seat 1 → seat 2 = E ✓

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

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

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

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

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

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

Verification:
✓ B at seat 3
✓ D at seat 8
✓ Empty at seat 1 (extreme end)
✓ E immediately right of empty seat 1
✓ C 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 D, E, H, A, G, F, C and B are seated, leaving 2 seats empty. D sits at seat 3. B sits at seat 8. One empty seat is at an extreme end. E sits immediately to the right of an empty seat. A 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
- D at seat 3
- B at seat 8 (seat 8)
- One empty seat at extreme end → seat 1 is empty

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

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

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

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

Question 10

There are 10 seats in a row, all facing North. 8 persons G, A, C, F, D, B, H and E are seated, leaving 2 seats empty. G sits at seat 3. E 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 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
- G at seat 3
- E 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(E) 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(G) 4(_) 5(_) 6(_) 7(_) 8(E) 9(_) 10(_)

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

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

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

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

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

Verification:
✓ G at seat 3
✓ E at seat 8
✓ Empty at seat 1 (extreme end)
✓ A immediately right of empty seat 1
✓ F fourth to left of E (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 G, A, D, H, F, C, E and B are seated, leaving 2 seats empty. G sits at seat 3. B 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 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
- G at seat 3
- B 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(B) 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(G) 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(A) 3(G) 4(H) 5(_) 6(_) 7(_) 8(B) 9(_) 10(_)

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

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

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

Verification:
✓ G at seat 3
✓ B at seat 8
✓ Empty at seat 1 (extreme end)
✓ A 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 12

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

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

Question 13

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

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

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

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

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

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

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

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

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

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

Answer: 7 persons sit between the two empty seats.

Question 14

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

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

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

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

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

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

Verification:
✓ B at seat 3
✓ G at seat 8
✓ Empty at seat 1 (extreme end)
✓ A immediately right of empty seat 1
✓ D fourth to left of G (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 A, C, H, F, D, E, B and G are seated, leaving 2 seats empty. A 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. F 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
- A at seat 3
- G 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(G) 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(A) 4(_) 5(_) 6(_) 7(_) 8(G) 9(_) 10(_)

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

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

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

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

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

Verification:
✓ A at seat 3
✓ G at seat 8
✓ Empty at seat 1 (extreme end)
✓ C immediately right of empty seat 1
✓ F fourth to left of G (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 H, F, D, B, G, E, C and A are seated, leaving 2 seats empty. H 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. B 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
- H at seat 3
- A 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(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(H) 4(_) 5(_) 6(_) 7(_) 8(A) 9(_) 10(_)

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

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

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

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

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

Verification:
✓ H at seat 3
✓ A at seat 8
✓ Empty at seat 1 (extreme end)
✓ F immediately right of empty seat 1
✓ B fourth to left of A (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 D, G, C, B, A, H, F and E are seated, leaving 2 seats empty. D sits at seat 3. E sits at seat 8. One empty seat is at an extreme end. G sits immediately to the right of an empty seat. B 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
- D at seat 3
- E 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(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(D) 4(_) 5(_) 6(_) 7(_) 8(E) 9(_) 10(_)

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

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

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

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

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

Verification:
✓ D at seat 3
✓ E at seat 8
✓ Empty at seat 1 (extreme end)
✓ G immediately right of empty seat 1
✓ B 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 H, C, E, G, B, D, A and F are seated, leaving 2 seats empty. H sits at seat 3. F sits at seat 8. One empty seat is at an extreme end. C 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
- H at seat 3
- F 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(F) 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(H) 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(C) 3(H) 4(G) 5(_) 6(_) 7(_) 8(F) 9(_) 10(_)

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

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

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

Verification:
✓ H at seat 3
✓ F at seat 8
✓ Empty at seat 1 (extreme end)
✓ C 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 19

There are 10 seats in a row, all facing North. 8 persons F, A, G, B, E, H, C 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. A sits immediately to the right of an empty seat. B 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
- A sits immediately to the RIGHT of an empty seat
- Empty at seat 1 → seat 2 = A ✓

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

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

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

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

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

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

Verification:
✓ F at seat 3
✓ D at seat 8
✓ Empty at seat 1 (extreme end)
✓ A immediately right of empty seat 1
✓ B fourth to left of D (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 H, F, A, D, G, E, C and B are seated, leaving 2 seats empty. H 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. 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
- H at seat 3
- B 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(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(H) 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(F) 3(H) 4(D) 5(_) 6(_) 7(_) 8(B) 9(_) 10(_)

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

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

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

Verification:
✓ H at seat 3
✓ B at seat 8
✓ Empty at seat 1 (extreme end)
✓ F 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.
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