As the name implies, the page number problem is closely related to the page number of books. The page number problem is actually an application problem based on the page number of books.

How many digits does it take to page a book? On the other hand, knowing how many digits are needed to compile the page number of a book and finding the page number of this book are two basic contents in the page number problem.

In order to solve the page number problem smoothly, let's first look at the relationship between "number" and "the number of digits that make it up". A number has 9 numbers, and 9 numbers are needed to form all the numbers; There are 90 * * * in two digits, and it takes 2× 90 = 180 (digits) to form all two digits; There are 900 three-digit numbers * * *, and it takes 3× 900 = 2700 (digits) to form all three digits ... For the sake of clarity, we list the relationships among the number of n digits, the number of digits needed to form all n digits and the number of digits needed to form all numbers not greater than n digits as follows:

As can be seen from the above table, if a book is less than 100 pages, the number of digits required to arrange the page numbers of this book will not exceed189; If the page number of a book is 10000, because

2889< 10000