The last page of the book is marked with the number 710. How many digits did everyone need for this book? to number the pages? Justify your answer.

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Answer to a math question The last page of the book is marked with the number 710. How many digits did everyone need for this book? to number the pages? Justify your answer.

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Birdie

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104 Answers

Solution:
1. Determine the number of pages with different digit counts:

- Pages 1 to 9: Single-digit pages.
* Total pages: 9
* Digits used per page: 1
* Total digits:

9 \times 1 = 9

- Pages 10 to 99: Double-digit pages.
* Total pages: 99 - 10 + 1 = 90
* Digits used per page: 2
* Total digits:

90 \times 2 = 180

- Pages 100 to 710: Triple-digit pages.
* Total pages: 710 - 100 + 1 = 611
* Digits used per page: 3
* Total digits:

611 \times 3 = 1833

2. Sum all the digits from each group:

9 + 180 + 1833 = 2022

Conclusion:
The total number of digits required to number all the pages from 1 to 710 is 2022.

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