The page numbers in a book use 810 Digits. If the book starts with page #1 how many pages are in the book.
I think it's a trick question, because digits is underlined. Is the answer 810? What does it mean by uses 810 Digits?
yes you are correct
It there were 99 pages, the number of digits used would be 9 (with one digit) + 2x90 (with two digits) = 189. Each additional page will require 3 digits, and you need 621 more digits. That requires 207 more numbers. That would make the number of pages 306. Check my thinking.
To determine the number of pages in the book, we need to understand what is meant by "810 digits." Each page number in the book is made up of one or more digits, such as 1, 2, 10, or 100.
If the book starts with page number 1, we can assume that there are no leading zeros used for the page numbers. For example, we can exclude page numbers like 001 or 010.
Given that the page numbers use a total of 810 digits, it means that the sum of the digits used in all the page numbers equals 810. For example, if the book had only 10 pages, the sum of the digits in all the page numbers would be 1+0+2+1+0+3+1+0+4+1 = 13.
To find the number of pages, we can start by examining the simple case where each page number has only one digit. In that case, the sum of the digits is equal to the number of pages. However, since 810 is significantly larger than the sum of the digits of a small number of pages, it suggests that the book consists of more than just one-digit page numbers.
Let's consider a higher digit range. Assuming there are two-digit page numbers, we can estimate the number of pages by finding the largest two-digit number whose sum of digits is less than or equal to 810. The largest two-digit number is 99, and the sum of its digits is 9 + 9 = 18. To reach 810, we would need 810 / 18 = 45 copies of the number 99. Therefore, by considering two-digit numbers, we have accounted for 99 * 45 = 4455 pages.
To find out if there are additional page numbers with more than two digits, we can subtract the sum of the digits from the remaining 810. This would give us the number of extra digits that would be used for the three-digit page numbers, four-digit page numbers, and so on.
As there is not enough information given to precisely determine the number of pages in the book, we can conclude that it consists of at least 4455 pages, considering only two-digit page numbers.
The statement is indicating that the numbers used to represent the page numbers in the book require a total of 810 digits. This implies that the book contains at least 810 pages.
To find the exact number of pages, we need to consider that page numbers generally consist of one or more digits. Let's break down the possible scenarios:
1. If all the page numbers are single digits (i.e., from 1 to 9), then the total number of pages would be 9. However, this would result in only 9 digits being used, which is less than the given 810.
2. If all the page numbers are double digits (i.e., from 10 to 99), then the total number of pages would be 90. In this case, each page number consists of two digits, resulting in a total of 180 digits. Again, this falls short of the given 810.
3. If all the page numbers are triple digits (i.e., from 100 to 999), then we would have a maximum of 900 pages. With each page number consisting of three digits, this would sum up to 2,700 digits, which is much larger than the given 810.
Therefore, the book must have a combination of page numbers ranging from single digits to at least triple digits, in order to account for the total of 810 digits. To determine the exact number of pages, we would need more information about the specific distribution of the different page number lengths used throughout the book.