Pages of a book from digits

Calculus Level 2

A book has been numbered starting from 1 and using 489 digits in total.

How many pages are there in this book?

199 200 239 300

Helith Dulina by Helith Dulina , 19, Sri Lanka

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2 solutions

Michael Mendrin
May 5, 2018

Solve for n n

9 + 2 ( 99 − 9 ) + 3 ( n − 99 ) = 489 9 + 2(99-9) + 3(n-99)=489

to get n = 199 n=199

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Zico Quintina
May 5, 2018

The first 9 pages need one digit, the next 90 need two, for a total of 189 digits. There are another 300 digits remaining, and three digits per page means another 100 pages, for a grand total of 199 pages.

Though, the math notwithstanding, shouldn't a book always have an even number of pages?

1 Helpful 0 Interesting 0 Brilliant 0 Confused

The problem should not be listed as Calculus. Thank you.

Marta Reece - 3 years, 1 month ago

Maybe it does have an even number, but the last page is blank and not numbered..

Marta Reece - 3 years, 1 month ago

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