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.

Knowing that:

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?

The essentially different ways that the book can be published is  F(100)=    2494155217372585318678938493802359939

Posted by K Sengupta on 2023-04-25 22:24:23