Friday Puzzle... and Cicada Math

Another Friday puzzle to rev up your brains before the weekend:

 A book requires 552 digits to be numbered from its first page (page 1) to its last page (???).  How many pages are there in the book? (answer below)

(I've adapted the problem from this site:

http://www.numericana.com/answer/recreational.htm#pages )

...and to additionally stretch your mind, especially if you're a computer scientist or programmer, an interesting piece (that's making its way around the Web) here applying the "cicada principle" to the world of web design:

http://tinyurl.com/3j4r2oj
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book answer: 220