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A Printer Numbers the Pages of a Book Starting with 1 and Uses 3189 Digits in All. How Many Pages does the Book have?

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Explanation

  • A printer numbers the pages of a book starting with 1 and uses 3189 digits in all.

This question is divided into four steps.

  • In the first step; we will find-out the digits used in the 1-digit page number.
  • In the second step; we will determine the digits used in the 2-digit page number.
  • In the third step; we will evaluate the digits used in the 3-digit page number.
  • In the fourth step; we will determine the digits used in the 4-digit page number.

Now; we will consider the page numbers through simple process of calculation.

After calculating the required values in first, second, third  and four steps; we will add them up to get our required answer (9 + 90 + 900 + 75 = 1074)

To Find

Number of pages = ?

Solution

Number of digits in the 1-digit page number = (9 – 0) x 1 = 9 x 1 = 9

Number of digits in the 2-digit page number = (99 – 9) x 2 = 90 x 2 = 180

Number of digits in the 3-digit page number = (999 – 99) x 3 = 900 x 3 = 2700

Number of digits in the 4-digit page number = 3189 – (9 + 180 + 2700) = 3189 – 2889 = 300

Number of pages with 4-digit page number = 300/4 = 75

Total number of pages = 9 + 90 + 900 + 75 = 1074 answer

Conclusion

A printer numbers the pages of a book starting with 1 and uses 3189 digits in all. There will be 1074 pages in the book.

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