Pages in a book are numbered in typical fashion, starting with 1. The folio for page 10 will contain the tenth and eleventh digits necessary to paginate the book. On what page will the 2009th digit occur?
Please Help!!! I have no idea where to begin
To find the page on which the 2009th digit occurs, we need to determine the pattern of digit allocation in the book.
Let's break it down step by step:
1. Determine the number of digits allocated per page:
- The first nine pages will have 9 digits in total (1 digit per page starting from 1 to 9).
- From page 10 onwards, every two pages will have two digits allocated. So, for every two pages, there will be 2 additional digits.
2. Find the page range in which the 2009th digit falls:
- Subtract 9 from 2009 (2009 - 9 = 2000).
- Divide the result (2000) by 2 to determine the number of two-page groups (2000 / 2 = 1000).
- Add 10 (since we started counting from page 10) to the result to find the starting page of the range (1000 + 10 = 1010).
- Add 2000 (since we subtracted 9 previously) to get an approximation of the ending page in the range (1010 + 2000 = 3010).
3. Adjust the ending page range to make sure it is accurate:
- From the 3010th page, count backwards to allocate the remaining digits:
- 3010: Two digits allocated.
- 3008: Two digits allocated.
- 3006: Two digits allocated.
- 3004: Two digits allocated.
- 3002: Two digits allocated.
- 3000: No digits allocated.
- 2999: One digit allocated.
- 2998: One digit allocated.
- 2997: One digit allocated.
- From the 2997th page, we can see that only one digit is left to be allocated. Therefore, the 2009th digit will be on the 2997th page.
So, the answer is that the 2009th digit will occur on page number 2997.