the pages in jacks book are numbered from 1 there are 555 didgits that these numbers add up to, how many pages in the book?
To find the number of pages in Jack's book, we need to determine the sum of the digits in the page numbers.
Let's break down the problem step by step:
1. Determine the number of digits in the page numbers:
- The last page number is 555, which means there are three digits (5, 5, and 5).
- The first page number is 1, so there is one digit.
- Therefore, the total number of digits is 3 - 1 + 1 = 3.
2. Find the sum of the digits:
- Since there are three digits in total, we need to find a number whose digits sum up to 555.
- One way to approach this is by finding the largest possible number with three digits that has a digit sum of 555. In this case, it is 999.
- However, this requires every page to have a three-digit number, which is not realistic considering the first page is number 1.
- So, we proceed by subtracting 1 from 555, resulting in 554, which we will distribute among the two remaining digits.
3. Distribute the remaining sum among the remaining digits:
- Starting with the leftmost digit, we subtract 9 (the largest possible single-digit number) from 554. This leaves us with 545.
- Now, we can assign the value 9 to the first digit (hundreds place).
- For the second (tens place) and third (ones place) digits, we distribute the remaining 545.
- Since we need to preserve the order of the digits and maximize the number of pages, we assign 98 and 97 to the second and third digits, respectively.
4. Calculate the number of pages:
- The first digit (hundreds place) is 9, indicating nine hundred pages.
- The second digit (tens place) is 8, indicating an additional 80 pages.
- The third digit (ones place) is 7, indicating seven more pages.
- Adding these together, we have 900 + 80 + 7 = 987 pages.
Therefore, Jack's book has 987 pages.