In the "Your own adventure" books, the reader starts at page 1, and every page either (1) ends the story, or (2) sends him to another page, or (3) offers a choice among two possible pages.
each page can be reached from only one other page -- except for the 1st page, that cannot be reached from any page;
that all pages can eventually be reached by picking an appropriate path from page 1;
that if a book can be converted into another just by reordering choices and renumbering pages, they are considered to be the same;and that these books are always 100 pages long...
How many essentially different books can be published?
(In reply to Solution
Instead of working with 100 pages, let's keep to 3. Page 1 could offer a choice, and both pages 2 and 3 be endings, so your conclusion "only one page in the book can end the story" is wrong.
Just for the sake of it, with a 100 pages long book, page 1 could lead to page 2 that could lead to page 3... up to page 98, which could offer two options: one leading to page 99 (an end) and other leading to page 100 (a different end).