35 are the books of Tanach as they would appear in a scroll.

While we usually count 24 (counting the [Twelve][1] as one), Yoreh Deah 283:1 specifies that when writing one giant Tanach scroll, the same multi-space break between books is also used between sub-books of the Twelve.  So 35 blocks of text altogether.  

(Poor Nechemiah, no book for him, YD 283 doesn't even mention his name.)


  [1]: http://en.wikipedia.org/wiki/Twelve_minor_prophets