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Page numbering (inverse problem)
A printer numbers the pages of a book starting with 1 and uses 3069 digits in all. How many pages does the book have?
1143
1066
1044
1064
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Explanation
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No. of digits in 1-digit page nos. = 1 x 9 = 9.
No. of digits in 2-digit page nos. = 90 x 2 = 180
.No. of digits in 3-digit page nos. = 900 x 900 = 2700
.No. of digits in 4-digit page nos. = 3069 - ( 9 + 180 + 2700) = 180.
∴ No. of pages with 4-digit page nos. = (180 / 4) = 45.
Hence, total number of pages = (9 + 90 + 900 +45) = 1044.
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