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Answer :
Final answer:
There are 9965 pages in Jack's book.
Explanation:
To determine the number of pages in Jack's book, we need to analyze the relationship between the page numbers and the total number of digits. In a book, the page numbers start from 1 and increase sequentially. Each page number consists of one or more digits.
Based on the given information, we know that the total number of digits in the page numbers is 555. We can use this information to find a pattern or formula to calculate the number of pages.
In a book with page numbers starting from 1, the number of digits in the page numbers increases by 1 after every 9 pages. For example, the page numbers from 1 to 9 have a total of 9 digits (1 digit per page), while the page numbers from 10 to 99 have a total of 180 digits (2 digits per page).
Using this pattern, we can calculate the number of pages in Jack's book:
- For the first 9 pages, there are 9 digits.
- For the next 90 pages (10 to 99), there are 180 digits.
- For the next 900 pages (100 to 999), there are 2700 digits.
- For the next 9000 pages (1000 to 9999), there are 36000 digits.
- For the remaining pages, there are 555 - (9 + 180 + 2700 + 36000) = 366 digits.
Therefore, the number of pages in Jack's book is 9 + 90 + 900 + 9000 + 366 = 9965.
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