Your book could have **333 pages or 666 pages**.
To find the number of pages in your book, we need to consider the three given clues:
1. **More than 200 pages, but fewer than 800:** This narrows down the possible page numbers to a range between 201 and 799, inclusive.
2. **All three digits are the same:** This means the page number can be written as "nnn", where n is any digit from 0 to 9.
3. **Number is divisible by 9:** A number is divisible by 9 if the sum of its digits is divisible by 9. In this case, since all three digits are the same, the sum of digits is simply 3n. Therefore, 3n must be divisible by 9.
Now, let's find the possible page numbers that satisfy all three conditions:
- We need to check all possible values of n from 0 to 9 within the given range (201 to 799).
- For each value of n, calculate the sum of digits (3n) and check if it is divisible by 9.
- If the sum is divisible by 9, then the corresponding page number (nnn) falls within the given range.
Here are the possible page numbers that satisfy all the conditions:
* n = 3: Page number = 333 (satisfies all conditions)
* n = 6: Page number = 666 (satisfies all conditions)
Therefore, your book could have **333 pages or 666 pages**.
There are no other page numbers within the given range that satisfy all three conditions.