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Stage: 3 and 4 Short Challenge Level: Challenge Level:1

The pages of a book are numbered $1$, $2$, $3$, $\dots$ In total, it takes $852$ digits to number all the pages of the book.

What is the number of the last page?


If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.


This problem is taken from the UKMT Mathematical Challenges.
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