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There are three books on table A which h...

There are three books on table A which has to be moved to table B. The order of the book on Table A was 1, 2, 3, with book 1 at the bottom. The order of the book on table B should be with book 2 on top and book 1 on bottom. Note that you can pick up the books in the order they have been arranged. You can’t remove the books from the middle of the stack. In how many minimum steps can we place the books on table B in the required order?

A

1

B

2

C

3

D

4

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem of moving the books from Table A to Table B in the required order, we can follow these steps: ### Step-by-Step Solution: 1. **Initial Setup**: - Table A has books arranged as follows from bottom to top: - Book 1 (bottom) - Book 2 - Book 3 (top) - Table B is empty. - The required order on Table B is: - Book 2 (top) - Book 1 (bottom) 2. **Step 1**: - Pick up Book 3 from Table A and place it on Table B. - Current state: - Table A: 1 (bottom), 2 (middle) - Table B: 3 (top) 3. **Step 2**: - Pick up Book 2 from Table A and place it on Table B. - Current state: - Table A: 1 (bottom) - Table B: 2 (middle), 3 (top) 4. **Step 3**: - Now, we need to place Book 1 on Table B. However, we cannot place it directly on top of Book 2 since it is below Book 3. - To do this, we first need to remove Book 3 from Table B and place it back on Table A. - Current state: - Table A: 1 (bottom), 3 (top) - Table B: 2 (middle) 5. **Step 4**: - Now, pick up Book 1 from Table A and place it on Table B. - Current state: - Table A: 3 (top) - Table B: 1 (bottom), 2 (top) 6. **Step 5**: - Finally, pick up Book 3 from Table A and place it on Table B. - Current state: - Table A: empty - Table B: 3 (top), 2 (middle), 1 (bottom) ### Final Arrangement on Table B: - The books are now arranged in the required order: - Book 2 (top) - Book 1 (bottom) ### Total Steps Taken: - In total, we have taken 5 steps to arrange the books in the required order. ### Answer: The minimum number of steps required to place the books on Table B in the required order is **5**.
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