Bob has a bookshelf containing 25 textbooks, 11 picture books, and 6 foreign-language books. There is at least one book in each of the seven combinations of categories. If there are more foreign-language textbooks than picture textbooks and more picture textbooks than foreign-language picture books, how many books are on the bookshelf?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. **The deadline is Wednesday, February 25, 2015 at noon Pacific Time.** I will post the answer shortly after.