The problem asks how many digits are used to number a book with 2024 pages.

1. Problem Description

The problem asks how many digits are used to number a book with 2024 pages.

2. Solution Steps

First, we consider the number of digits used for single-digit page numbers (1 to 9).

There are 9 such page numbers, so we use $9 \times 1 = 9$ digits.

Next, we consider the number of digits used for double-digit page numbers (10 to 99).

There are $99 - 10 + 1 = 90$ such page numbers, so we use $90 \times 2 = 180$ digits.

Next, we consider the number of digits used for triple-digit page numbers (100 to 999).

There are $999 - 100 + 1 = 900$ such page numbers, so we use $900 \times 3 = 2700$ digits.

Finally, we consider the number of digits used for four-digit page numbers (1000 to 2024).

There are $2024 - 1000 + 1 = 1025$ such page numbers, so we use $1025 \times 4 = 4100$ digits.

The total number of digits used is $9 + 180 + 2700 + 4100 = 6989$.

3. Final Answer

6989