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# 852 digits are used to number the pages of a book consecutively from page 1. How many pages are there in the book?

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852 digits are used to number the pages of a book consecutively from page 1. How many pages are there in the book?

Jun 23, 2023

#1
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The first 9 pages use 1 digit each, so they use 9 digits.

The next 90 pages use 2 digits each, so they use 180 digits.

The remaining pages use 3 digits each. Let n be the number of these pages. Then 3n is the number of digits used to number these pages, so 3n=852−9−180=663. Therefore, n=221​.

Jun 23, 2023
#2
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You had the right idea but didn't implement it correctly:

1- There are 9 single digits from 1 to 9 ==9 pages

2 - You have 180 digits from 10 to 99 ==180 / 2 ==90 pages

3 - You have: 852 - 9 - 180 ==662 digits / 3 ==221 pages.

4 - Total pages in the book==9 + 90 + 221 ==320 pages

Jun 23, 2023
#3
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If the book uses sequential page numbering using 852 digits, then the total number of pages can be determined by dividing this figure by 2. Since each page has two sides - front and back. I just really love math. I don't like literature, so when asked of mice and men, I used supremestudy.com/essay-examples/of-mice-and-men for that. Therefore, this book should have approximately 426 pages. If I'm not mistaken.

Jun 29, 2023