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Temporal Box Movement - Intermediate Level: tricky scenarios handling Temporal Box Movement INTERMEDIATE

This expert challenge 📈 worksheet focuses on Temporal Box Movement - a key topic in Box Stack Puzzles. You'll solve 20 intermediate-level problems (Worksheet 5 of 10). The primary focus is on tricky scenarios handling. Master how to solve temporal box movement, temporal box movement tricks, and temporal box movement 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 Temporal Box Movement
Worksheet 5 of 10 (44% complete)

Question 1

Initially, five boxes A, B, C, D, and E are in Stack 1 (positions 1-5, bottom to top): A at position 1, B at 2, C at 3, D at 4, E at 5. A series of operations is performed: Operation 1: Move the top box of Stack 1 to a new Stack 2 Operation 2: Move the box at position 2 of Stack 1 to top of Stack 2 Operation 3: Move the top box of Stack 1 to top of Stack 2 After these operations, which box is at the bottom of Stack 2?
Step-by-step Solution:
1. Initial State:
- Stack 1 (bottom to top): A(1), B(2), C(3), D(4), E(5)
- Stack 2: Empty

2. Operation 1: Move top box of Stack 1 to Stack 2
- Remove E from Stack 1 (was at position 5)
- Stack 1 after: A(1), B(2), C(3), D(4)
- Stack 2 after: E(1)

3. Operation 2: Move box at position 2 of Stack 1 to top of Stack 2
- Box at position 2 is B
- Remove B from Stack 1
- Stack 1 after: A(1), C(2), D(3) [positions renumber]
- Stack 2 after: E(1), B(2) [B placed on top]

4. Operation 3: Move top box of Stack 1 to top of Stack 2
- Top box of Stack 1 is D (position 3)
- Remove D from Stack 1
- Stack 1 after: A(1), C(2)
- Stack 2 after: E(1), B(2), D(3) [D placed on top]

5. Final Stack 2 (bottom to top): E, B, D

6. Answer: Box E is at the bottom of Stack 2

Question 2

Initially, five boxes A, B, C, D, and E are in Stack 1 (positions 1-5, bottom to top): A at position 1, B at 2, C at 3, D at 4, E at 5. A series of operations is performed: Operation 1: Move the top box of Stack 1 to a new Stack 2 Operation 2: Move the box at position 2 of Stack 1 to top of Stack 2 Operation 3: Move the top box of Stack 1 to top of Stack 2 After these operations, which box is at the bottom of Stack 2?
Step-by-step Solution:
1. Initial State:
- Stack 1 (bottom to top): A(1), B(2), C(3), D(4), E(5)
- Stack 2: Empty

2. Operation 1: Move top box of Stack 1 to Stack 2
- Remove E from Stack 1 (was at position 5)
- Stack 1 after: A(1), B(2), C(3), D(4)
- Stack 2 after: E(1)

3. Operation 2: Move box at position 2 of Stack 1 to top of Stack 2
- Box at position 2 is B
- Remove B from Stack 1
- Stack 1 after: A(1), C(2), D(3) [positions renumber]
- Stack 2 after: E(1), B(2) [B placed on top]

4. Operation 3: Move top box of Stack 1 to top of Stack 2
- Top box of Stack 1 is D (position 3)
- Remove D from Stack 1
- Stack 1 after: A(1), C(2)
- Stack 2 after: E(1), B(2), D(3) [D placed on top]

5. Final Stack 2 (bottom to top): E, B, D

6. Answer: Box E is at the bottom of Stack 2

Question 3

Initially, five boxes A, B, C, D, and E are in Stack 1 (positions 1-5, bottom to top): A at position 1, B at 2, C at 3, D at 4, E at 5. A series of operations is performed: Operation 1: Move the top box of Stack 1 to a new Stack 2 Operation 2: Move the box at position 2 of Stack 1 to top of Stack 2 Operation 3: Move the top box of Stack 1 to top of Stack 2 After these operations, which box is at the bottom of Stack 2?
Step-by-step Solution:
1. Initial State:
- Stack 1 (bottom to top): A(1), B(2), C(3), D(4), E(5)
- Stack 2: Empty

2. Operation 1: Move top box of Stack 1 to Stack 2
- Remove E from Stack 1 (was at position 5)
- Stack 1 after: A(1), B(2), C(3), D(4)
- Stack 2 after: E(1)

3. Operation 2: Move box at position 2 of Stack 1 to top of Stack 2
- Box at position 2 is B
- Remove B from Stack 1
- Stack 1 after: A(1), C(2), D(3) [positions renumber]
- Stack 2 after: E(1), B(2) [B placed on top]

4. Operation 3: Move top box of Stack 1 to top of Stack 2
- Top box of Stack 1 is D (position 3)
- Remove D from Stack 1
- Stack 1 after: A(1), C(2)
- Stack 2 after: E(1), B(2), D(3) [D placed on top]

5. Final Stack 2 (bottom to top): E, B, D

6. Answer: Box E is at the bottom of Stack 2

Question 4

Initially, five boxes A, B, C, D, and E are in Stack 1 (positions 1-5, bottom to top): A at position 1, B at 2, C at 3, D at 4, E at 5. A series of operations is performed: Operation 1: Move the top box of Stack 1 to a new Stack 2 Operation 2: Move the box at position 2 of Stack 1 to top of Stack 2 Operation 3: Move the top box of Stack 1 to top of Stack 2 After these operations, which box is at the bottom of Stack 2?
Step-by-step Solution:
1. Initial State:
- Stack 1 (bottom to top): A(1), B(2), C(3), D(4), E(5)
- Stack 2: Empty

2. Operation 1: Move top box of Stack 1 to Stack 2
- Remove E from Stack 1 (was at position 5)
- Stack 1 after: A(1), B(2), C(3), D(4)
- Stack 2 after: E(1)

3. Operation 2: Move box at position 2 of Stack 1 to top of Stack 2
- Box at position 2 is B
- Remove B from Stack 1
- Stack 1 after: A(1), C(2), D(3) [positions renumber]
- Stack 2 after: E(1), B(2) [B placed on top]

4. Operation 3: Move top box of Stack 1 to top of Stack 2
- Top box of Stack 1 is D (position 3)
- Remove D from Stack 1
- Stack 1 after: A(1), C(2)
- Stack 2 after: E(1), B(2), D(3) [D placed on top]

5. Final Stack 2 (bottom to top): E, B, D

6. Answer: Box E is at the bottom of Stack 2

Question 5

Initially, five boxes A, B, C, D, and E are in Stack 1 (positions 1-5, bottom to top): A at position 1, B at 2, C at 3, D at 4, E at 5. A series of operations is performed: Operation 1: Move the top box of Stack 1 to a new Stack 2 Operation 2: Move the box at position 2 of Stack 1 to top of Stack 2 Operation 3: Move the top box of Stack 1 to top of Stack 2 After these operations, which box is at the bottom of Stack 2?
Step-by-step Solution:
1. Initial State:
- Stack 1 (bottom to top): A(1), B(2), C(3), D(4), E(5)
- Stack 2: Empty

2. Operation 1: Move top box of Stack 1 to Stack 2
- Remove E from Stack 1 (was at position 5)
- Stack 1 after: A(1), B(2), C(3), D(4)
- Stack 2 after: E(1)

3. Operation 2: Move box at position 2 of Stack 1 to top of Stack 2
- Box at position 2 is B
- Remove B from Stack 1
- Stack 1 after: A(1), C(2), D(3) [positions renumber]
- Stack 2 after: E(1), B(2) [B placed on top]

4. Operation 3: Move top box of Stack 1 to top of Stack 2
- Top box of Stack 1 is D (position 3)
- Remove D from Stack 1
- Stack 1 after: A(1), C(2)
- Stack 2 after: E(1), B(2), D(3) [D placed on top]

5. Final Stack 2 (bottom to top): E, B, D

6. Answer: Box E is at the bottom of Stack 2

Question 6

Initially, five boxes A, B, C, D, and E are in Stack 1 (positions 1-5, bottom to top): A at position 1, B at 2, C at 3, D at 4, E at 5. A series of operations is performed: Operation 1: Move the top box of Stack 1 to a new Stack 2 Operation 2: Move the box at position 2 of Stack 1 to top of Stack 2 Operation 3: Move the top box of Stack 1 to top of Stack 2 After these operations, which box is at the bottom of Stack 2?
Step-by-step Solution:
1. Initial State:
- Stack 1 (bottom to top): A(1), B(2), C(3), D(4), E(5)
- Stack 2: Empty

2. Operation 1: Move top box of Stack 1 to Stack 2
- Remove E from Stack 1 (was at position 5)
- Stack 1 after: A(1), B(2), C(3), D(4)
- Stack 2 after: E(1)

3. Operation 2: Move box at position 2 of Stack 1 to top of Stack 2
- Box at position 2 is B
- Remove B from Stack 1
- Stack 1 after: A(1), C(2), D(3) [positions renumber]
- Stack 2 after: E(1), B(2) [B placed on top]

4. Operation 3: Move top box of Stack 1 to top of Stack 2
- Top box of Stack 1 is D (position 3)
- Remove D from Stack 1
- Stack 1 after: A(1), C(2)
- Stack 2 after: E(1), B(2), D(3) [D placed on top]

5. Final Stack 2 (bottom to top): E, B, D

6. Answer: Box E is at the bottom of Stack 2

Question 7

Initially, five boxes A, B, C, D, and E are in Stack 1 (positions 1-5, bottom to top): A at position 1, B at 2, C at 3, D at 4, E at 5. A series of operations is performed: Operation 1: Move the top box of Stack 1 to a new Stack 2 Operation 2: Move the box at position 2 of Stack 1 to top of Stack 2 Operation 3: Move the top box of Stack 1 to top of Stack 2 After these operations, which box is at the bottom of Stack 2?
Step-by-step Solution:
1. Initial State:
- Stack 1 (bottom to top): A(1), B(2), C(3), D(4), E(5)
- Stack 2: Empty

2. Operation 1: Move top box of Stack 1 to Stack 2
- Remove E from Stack 1 (was at position 5)
- Stack 1 after: A(1), B(2), C(3), D(4)
- Stack 2 after: E(1)

3. Operation 2: Move box at position 2 of Stack 1 to top of Stack 2
- Box at position 2 is B
- Remove B from Stack 1
- Stack 1 after: A(1), C(2), D(3) [positions renumber]
- Stack 2 after: E(1), B(2) [B placed on top]

4. Operation 3: Move top box of Stack 1 to top of Stack 2
- Top box of Stack 1 is D (position 3)
- Remove D from Stack 1
- Stack 1 after: A(1), C(2)
- Stack 2 after: E(1), B(2), D(3) [D placed on top]

5. Final Stack 2 (bottom to top): E, B, D

6. Answer: Box E is at the bottom of Stack 2

Question 8

Initially, five boxes A, B, C, D, and E are in Stack 1 (positions 1-5, bottom to top): A at position 1, B at 2, C at 3, D at 4, E at 5. A series of operations is performed: Operation 1: Move the top box of Stack 1 to a new Stack 2 Operation 2: Move the box at position 2 of Stack 1 to top of Stack 2 Operation 3: Move the top box of Stack 1 to top of Stack 2 After these operations, which box is at the bottom of Stack 2?
Step-by-step Solution:
1. Initial State:
- Stack 1 (bottom to top): A(1), B(2), C(3), D(4), E(5)
- Stack 2: Empty

2. Operation 1: Move top box of Stack 1 to Stack 2
- Remove E from Stack 1 (was at position 5)
- Stack 1 after: A(1), B(2), C(3), D(4)
- Stack 2 after: E(1)

3. Operation 2: Move box at position 2 of Stack 1 to top of Stack 2
- Box at position 2 is B
- Remove B from Stack 1
- Stack 1 after: A(1), C(2), D(3) [positions renumber]
- Stack 2 after: E(1), B(2) [B placed on top]

4. Operation 3: Move top box of Stack 1 to top of Stack 2
- Top box of Stack 1 is D (position 3)
- Remove D from Stack 1
- Stack 1 after: A(1), C(2)
- Stack 2 after: E(1), B(2), D(3) [D placed on top]

5. Final Stack 2 (bottom to top): E, B, D

6. Answer: Box E is at the bottom of Stack 2

Question 9

Initially, five boxes A, B, C, D, and E are in Stack 1 (positions 1-5, bottom to top): A at position 1, B at 2, C at 3, D at 4, E at 5. A series of operations is performed: Operation 1: Move the top box of Stack 1 to a new Stack 2 Operation 2: Move the box at position 2 of Stack 1 to top of Stack 2 Operation 3: Move the top box of Stack 1 to top of Stack 2 After these operations, which box is at the bottom of Stack 2?
Step-by-step Solution:
1. Initial State:
- Stack 1 (bottom to top): A(1), B(2), C(3), D(4), E(5)
- Stack 2: Empty

2. Operation 1: Move top box of Stack 1 to Stack 2
- Remove E from Stack 1 (was at position 5)
- Stack 1 after: A(1), B(2), C(3), D(4)
- Stack 2 after: E(1)

3. Operation 2: Move box at position 2 of Stack 1 to top of Stack 2
- Box at position 2 is B
- Remove B from Stack 1
- Stack 1 after: A(1), C(2), D(3) [positions renumber]
- Stack 2 after: E(1), B(2) [B placed on top]

4. Operation 3: Move top box of Stack 1 to top of Stack 2
- Top box of Stack 1 is D (position 3)
- Remove D from Stack 1
- Stack 1 after: A(1), C(2)
- Stack 2 after: E(1), B(2), D(3) [D placed on top]

5. Final Stack 2 (bottom to top): E, B, D

6. Answer: Box E is at the bottom of Stack 2

Question 10

Initially, five boxes A, B, C, D, and E are in Stack 1 (positions 1-5, bottom to top): A at position 1, B at 2, C at 3, D at 4, E at 5. A series of operations is performed: Operation 1: Move the top box of Stack 1 to a new Stack 2 Operation 2: Move the box at position 2 of Stack 1 to top of Stack 2 Operation 3: Move the top box of Stack 1 to top of Stack 2 After these operations, which box is at the bottom of Stack 2?
Step-by-step Solution:
1. Initial State:
- Stack 1 (bottom to top): A(1), B(2), C(3), D(4), E(5)
- Stack 2: Empty

2. Operation 1: Move top box of Stack 1 to Stack 2
- Remove E from Stack 1 (was at position 5)
- Stack 1 after: A(1), B(2), C(3), D(4)
- Stack 2 after: E(1)

3. Operation 2: Move box at position 2 of Stack 1 to top of Stack 2
- Box at position 2 is B
- Remove B from Stack 1
- Stack 1 after: A(1), C(2), D(3) [positions renumber]
- Stack 2 after: E(1), B(2) [B placed on top]

4. Operation 3: Move top box of Stack 1 to top of Stack 2
- Top box of Stack 1 is D (position 3)
- Remove D from Stack 1
- Stack 1 after: A(1), C(2)
- Stack 2 after: E(1), B(2), D(3) [D placed on top]

5. Final Stack 2 (bottom to top): E, B, D

6. Answer: Box E is at the bottom of Stack 2

Question 11

Initially, five boxes A, B, C, D, and E are in Stack 1 (positions 1-5, bottom to top): A at position 1, B at 2, C at 3, D at 4, E at 5. A series of operations is performed: Operation 1: Move the top box of Stack 1 to a new Stack 2 Operation 2: Move the box at position 2 of Stack 1 to top of Stack 2 Operation 3: Move the top box of Stack 1 to top of Stack 2 After these operations, which box is at the bottom of Stack 2?
Step-by-step Solution:
1. Initial State:
- Stack 1 (bottom to top): A(1), B(2), C(3), D(4), E(5)
- Stack 2: Empty

2. Operation 1: Move top box of Stack 1 to Stack 2
- Remove E from Stack 1 (was at position 5)
- Stack 1 after: A(1), B(2), C(3), D(4)
- Stack 2 after: E(1)

3. Operation 2: Move box at position 2 of Stack 1 to top of Stack 2
- Box at position 2 is B
- Remove B from Stack 1
- Stack 1 after: A(1), C(2), D(3) [positions renumber]
- Stack 2 after: E(1), B(2) [B placed on top]

4. Operation 3: Move top box of Stack 1 to top of Stack 2
- Top box of Stack 1 is D (position 3)
- Remove D from Stack 1
- Stack 1 after: A(1), C(2)
- Stack 2 after: E(1), B(2), D(3) [D placed on top]

5. Final Stack 2 (bottom to top): E, B, D

6. Answer: Box E is at the bottom of Stack 2

Question 12

Initially, five boxes A, B, C, D, and E are in Stack 1 (positions 1-5, bottom to top): A at position 1, B at 2, C at 3, D at 4, E at 5. A series of operations is performed: Operation 1: Move the top box of Stack 1 to a new Stack 2 Operation 2: Move the box at position 2 of Stack 1 to top of Stack 2 Operation 3: Move the top box of Stack 1 to top of Stack 2 After these operations, which box is at the bottom of Stack 2?
Step-by-step Solution:
1. Initial State:
- Stack 1 (bottom to top): A(1), B(2), C(3), D(4), E(5)
- Stack 2: Empty

2. Operation 1: Move top box of Stack 1 to Stack 2
- Remove E from Stack 1 (was at position 5)
- Stack 1 after: A(1), B(2), C(3), D(4)
- Stack 2 after: E(1)

3. Operation 2: Move box at position 2 of Stack 1 to top of Stack 2
- Box at position 2 is B
- Remove B from Stack 1
- Stack 1 after: A(1), C(2), D(3) [positions renumber]
- Stack 2 after: E(1), B(2) [B placed on top]

4. Operation 3: Move top box of Stack 1 to top of Stack 2
- Top box of Stack 1 is D (position 3)
- Remove D from Stack 1
- Stack 1 after: A(1), C(2)
- Stack 2 after: E(1), B(2), D(3) [D placed on top]

5. Final Stack 2 (bottom to top): E, B, D

6. Answer: Box E is at the bottom of Stack 2

Question 13

Initially, five boxes A, B, C, D, and E are in Stack 1 (positions 1-5, bottom to top): A at position 1, B at 2, C at 3, D at 4, E at 5. A series of operations is performed: Operation 1: Move the top box of Stack 1 to a new Stack 2 Operation 2: Move the box at position 2 of Stack 1 to top of Stack 2 Operation 3: Move the top box of Stack 1 to top of Stack 2 After these operations, which box is at the bottom of Stack 2?
Step-by-step Solution:
1. Initial State:
- Stack 1 (bottom to top): A(1), B(2), C(3), D(4), E(5)
- Stack 2: Empty

2. Operation 1: Move top box of Stack 1 to Stack 2
- Remove E from Stack 1 (was at position 5)
- Stack 1 after: A(1), B(2), C(3), D(4)
- Stack 2 after: E(1)

3. Operation 2: Move box at position 2 of Stack 1 to top of Stack 2
- Box at position 2 is B
- Remove B from Stack 1
- Stack 1 after: A(1), C(2), D(3) [positions renumber]
- Stack 2 after: E(1), B(2) [B placed on top]

4. Operation 3: Move top box of Stack 1 to top of Stack 2
- Top box of Stack 1 is D (position 3)
- Remove D from Stack 1
- Stack 1 after: A(1), C(2)
- Stack 2 after: E(1), B(2), D(3) [D placed on top]

5. Final Stack 2 (bottom to top): E, B, D

6. Answer: Box E is at the bottom of Stack 2

Question 14

Initially, five boxes A, B, C, D, and E are in Stack 1 (positions 1-5, bottom to top): A at position 1, B at 2, C at 3, D at 4, E at 5. A series of operations is performed: Operation 1: Move the top box of Stack 1 to a new Stack 2 Operation 2: Move the box at position 2 of Stack 1 to top of Stack 2 Operation 3: Move the top box of Stack 1 to top of Stack 2 After these operations, which box is at the bottom of Stack 2?
Step-by-step Solution:
1. Initial State:
- Stack 1 (bottom to top): A(1), B(2), C(3), D(4), E(5)
- Stack 2: Empty

2. Operation 1: Move top box of Stack 1 to Stack 2
- Remove E from Stack 1 (was at position 5)
- Stack 1 after: A(1), B(2), C(3), D(4)
- Stack 2 after: E(1)

3. Operation 2: Move box at position 2 of Stack 1 to top of Stack 2
- Box at position 2 is B
- Remove B from Stack 1
- Stack 1 after: A(1), C(2), D(3) [positions renumber]
- Stack 2 after: E(1), B(2) [B placed on top]

4. Operation 3: Move top box of Stack 1 to top of Stack 2
- Top box of Stack 1 is D (position 3)
- Remove D from Stack 1
- Stack 1 after: A(1), C(2)
- Stack 2 after: E(1), B(2), D(3) [D placed on top]

5. Final Stack 2 (bottom to top): E, B, D

6. Answer: Box E is at the bottom of Stack 2

Question 15

Initially, five boxes A, B, C, D, and E are in Stack 1 (positions 1-5, bottom to top): A at position 1, B at 2, C at 3, D at 4, E at 5. A series of operations is performed: Operation 1: Move the top box of Stack 1 to a new Stack 2 Operation 2: Move the box at position 2 of Stack 1 to top of Stack 2 Operation 3: Move the top box of Stack 1 to top of Stack 2 After these operations, which box is at the bottom of Stack 2?
Step-by-step Solution:
1. Initial State:
- Stack 1 (bottom to top): A(1), B(2), C(3), D(4), E(5)
- Stack 2: Empty

2. Operation 1: Move top box of Stack 1 to Stack 2
- Remove E from Stack 1 (was at position 5)
- Stack 1 after: A(1), B(2), C(3), D(4)
- Stack 2 after: E(1)

3. Operation 2: Move box at position 2 of Stack 1 to top of Stack 2
- Box at position 2 is B
- Remove B from Stack 1
- Stack 1 after: A(1), C(2), D(3) [positions renumber]
- Stack 2 after: E(1), B(2) [B placed on top]

4. Operation 3: Move top box of Stack 1 to top of Stack 2
- Top box of Stack 1 is D (position 3)
- Remove D from Stack 1
- Stack 1 after: A(1), C(2)
- Stack 2 after: E(1), B(2), D(3) [D placed on top]

5. Final Stack 2 (bottom to top): E, B, D

6. Answer: Box E is at the bottom of Stack 2

Question 16

Initially, five boxes A, B, C, D, and E are in Stack 1 (positions 1-5, bottom to top): A at position 1, B at 2, C at 3, D at 4, E at 5. A series of operations is performed: Operation 1: Move the top box of Stack 1 to a new Stack 2 Operation 2: Move the box at position 2 of Stack 1 to top of Stack 2 Operation 3: Move the top box of Stack 1 to top of Stack 2 After these operations, which box is at the bottom of Stack 2?
Step-by-step Solution:
1. Initial State:
- Stack 1 (bottom to top): A(1), B(2), C(3), D(4), E(5)
- Stack 2: Empty

2. Operation 1: Move top box of Stack 1 to Stack 2
- Remove E from Stack 1 (was at position 5)
- Stack 1 after: A(1), B(2), C(3), D(4)
- Stack 2 after: E(1)

3. Operation 2: Move box at position 2 of Stack 1 to top of Stack 2
- Box at position 2 is B
- Remove B from Stack 1
- Stack 1 after: A(1), C(2), D(3) [positions renumber]
- Stack 2 after: E(1), B(2) [B placed on top]

4. Operation 3: Move top box of Stack 1 to top of Stack 2
- Top box of Stack 1 is D (position 3)
- Remove D from Stack 1
- Stack 1 after: A(1), C(2)
- Stack 2 after: E(1), B(2), D(3) [D placed on top]

5. Final Stack 2 (bottom to top): E, B, D

6. Answer: Box E is at the bottom of Stack 2

Question 17

Initially, five boxes A, B, C, D, and E are in Stack 1 (positions 1-5, bottom to top): A at position 1, B at 2, C at 3, D at 4, E at 5. A series of operations is performed: Operation 1: Move the top box of Stack 1 to a new Stack 2 Operation 2: Move the box at position 2 of Stack 1 to top of Stack 2 Operation 3: Move the top box of Stack 1 to top of Stack 2 After these operations, which box is at the bottom of Stack 2?
Step-by-step Solution:
1. Initial State:
- Stack 1 (bottom to top): A(1), B(2), C(3), D(4), E(5)
- Stack 2: Empty

2. Operation 1: Move top box of Stack 1 to Stack 2
- Remove E from Stack 1 (was at position 5)
- Stack 1 after: A(1), B(2), C(3), D(4)
- Stack 2 after: E(1)

3. Operation 2: Move box at position 2 of Stack 1 to top of Stack 2
- Box at position 2 is B
- Remove B from Stack 1
- Stack 1 after: A(1), C(2), D(3) [positions renumber]
- Stack 2 after: E(1), B(2) [B placed on top]

4. Operation 3: Move top box of Stack 1 to top of Stack 2
- Top box of Stack 1 is D (position 3)
- Remove D from Stack 1
- Stack 1 after: A(1), C(2)
- Stack 2 after: E(1), B(2), D(3) [D placed on top]

5. Final Stack 2 (bottom to top): E, B, D

6. Answer: Box E is at the bottom of Stack 2

Question 18

Initially, five boxes A, B, C, D, and E are in Stack 1 (positions 1-5, bottom to top): A at position 1, B at 2, C at 3, D at 4, E at 5. A series of operations is performed: Operation 1: Move the top box of Stack 1 to a new Stack 2 Operation 2: Move the box at position 2 of Stack 1 to top of Stack 2 Operation 3: Move the top box of Stack 1 to top of Stack 2 After these operations, which box is at the bottom of Stack 2?
Step-by-step Solution:
1. Initial State:
- Stack 1 (bottom to top): A(1), B(2), C(3), D(4), E(5)
- Stack 2: Empty

2. Operation 1: Move top box of Stack 1 to Stack 2
- Remove E from Stack 1 (was at position 5)
- Stack 1 after: A(1), B(2), C(3), D(4)
- Stack 2 after: E(1)

3. Operation 2: Move box at position 2 of Stack 1 to top of Stack 2
- Box at position 2 is B
- Remove B from Stack 1
- Stack 1 after: A(1), C(2), D(3) [positions renumber]
- Stack 2 after: E(1), B(2) [B placed on top]

4. Operation 3: Move top box of Stack 1 to top of Stack 2
- Top box of Stack 1 is D (position 3)
- Remove D from Stack 1
- Stack 1 after: A(1), C(2)
- Stack 2 after: E(1), B(2), D(3) [D placed on top]

5. Final Stack 2 (bottom to top): E, B, D

6. Answer: Box E is at the bottom of Stack 2

Question 19

Initially, five boxes A, B, C, D, and E are in Stack 1 (positions 1-5, bottom to top): A at position 1, B at 2, C at 3, D at 4, E at 5. A series of operations is performed: Operation 1: Move the top box of Stack 1 to a new Stack 2 Operation 2: Move the box at position 2 of Stack 1 to top of Stack 2 Operation 3: Move the top box of Stack 1 to top of Stack 2 After these operations, which box is at the bottom of Stack 2?
Step-by-step Solution:
1. Initial State:
- Stack 1 (bottom to top): A(1), B(2), C(3), D(4), E(5)
- Stack 2: Empty

2. Operation 1: Move top box of Stack 1 to Stack 2
- Remove E from Stack 1 (was at position 5)
- Stack 1 after: A(1), B(2), C(3), D(4)
- Stack 2 after: E(1)

3. Operation 2: Move box at position 2 of Stack 1 to top of Stack 2
- Box at position 2 is B
- Remove B from Stack 1
- Stack 1 after: A(1), C(2), D(3) [positions renumber]
- Stack 2 after: E(1), B(2) [B placed on top]

4. Operation 3: Move top box of Stack 1 to top of Stack 2
- Top box of Stack 1 is D (position 3)
- Remove D from Stack 1
- Stack 1 after: A(1), C(2)
- Stack 2 after: E(1), B(2), D(3) [D placed on top]

5. Final Stack 2 (bottom to top): E, B, D

6. Answer: Box E is at the bottom of Stack 2

Question 20

Initially, five boxes A, B, C, D, and E are in Stack 1 (positions 1-5, bottom to top): A at position 1, B at 2, C at 3, D at 4, E at 5. A series of operations is performed: Operation 1: Move the top box of Stack 1 to a new Stack 2 Operation 2: Move the box at position 2 of Stack 1 to top of Stack 2 Operation 3: Move the top box of Stack 1 to top of Stack 2 After these operations, which box is at the bottom of Stack 2?
Step-by-step Solution:
1. Initial State:
- Stack 1 (bottom to top): A(1), B(2), C(3), D(4), E(5)
- Stack 2: Empty

2. Operation 1: Move top box of Stack 1 to Stack 2
- Remove E from Stack 1 (was at position 5)
- Stack 1 after: A(1), B(2), C(3), D(4)
- Stack 2 after: E(1)

3. Operation 2: Move box at position 2 of Stack 1 to top of Stack 2
- Box at position 2 is B
- Remove B from Stack 1
- Stack 1 after: A(1), C(2), D(3) [positions renumber]
- Stack 2 after: E(1), B(2) [B placed on top]

4. Operation 3: Move top box of Stack 1 to top of Stack 2
- Top box of Stack 1 is D (position 3)
- Remove D from Stack 1
- Stack 1 after: A(1), C(2)
- Stack 2 after: E(1), B(2), D(3) [D placed on top]

5. Final Stack 2 (bottom to top): E, B, D

6. Answer: Box E is at the bottom of Stack 2
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