Explanations:To solve this problem, we need to determine the number of books between the Ancient history book and the Medieval history book in a row of 64 books. The Ancient history book is positioned 25th from the left, and the Medieval history book is positioned 30th from the right.
First, let's determine the position of the Medieval history book from the left. Since the Medieval history book is 30th from the right, we can find its position from the left by subtracting its position from the right from the total number of books and adding 1 (to account for the book itself):
\[ \text{Position from left} = 64 - 30 + 1 = 35 \]
So, the Medieval history book is 35th from the left.
Next, we need to find the number of books between the 25th and 35th positions. The number of books between two positions can be calculated by subtracting the smaller position from the larger position and then subtracting 1 (to exclude the books at the positions themselves):
\[ \text{Number of books between} = 35 - 25 - 1 = 9 \]
Thus, there are 9 books between the Ancient history book and the Medieval history book.
This problem tests the ability to understand and manipulate positions in a sequence, a fundamental skill in logical reasoning and problem-solving. It is important to carefully consider the positions and the total number of items in the sequence to avoid common mistakes such as miscounting or forgetting to exclude the books at the positions themselves.