In numbering the pages of a book, a printer used 3289 digits. How many pages were in the book, assuming that the first page in the book was number 1.

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- Sep 3rd 2010, 08:15 PMMATNTRNGDifficult Word Problem
In numbering the pages of a book, a printer used 3289 digits. How many pages were in the book, assuming that the first page in the book was number 1.

- Sep 4th 2010, 05:53 AMSoroban
Hello, MATNTRNG!

There's no formula for this problem.

I had to baby-talk my way through it.

Quote:

In numbering the pages of a book, a printer used 3289 digits.

How many pages were in the book, assuming

that the first page in the book was number 1?

. .

Hence: . digits were used

. . in the first 100 four-digit numbers.

. . . .

Therefore, the book had 1099 pages.

- Sep 4th 2010, 06:22 AMundefined
I think you basically found a formula.

Being lazy to derive, I looked up on OEIS (id:A033713 - OEIS Search Results)

So if the number of digits used is d, then we find the n such that

and the number of pages is

But in fact the are easily recognisable

Using not-exactly-standard notation, where the number of 8's is n-1.

In other words,

So there's no need to solve for n, we can tell just by looking. - Sep 5th 2010, 09:05 AMMATNTRNG
Wow this is amazing. Thank you for looking at this