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Arbitrary Adventures Analysis (Posted on 2006-11-20) Difficulty: 3 of 5
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?

    No Solution Yet Submitted by Old Original Oskar!    
    Rating: 4.0000 (1 votes)

    Comments: ( Back to comment list | You must be logged in to post comments.)
    Some Thoughts re: Solution -- disagree | Comment 2 of 9 |
    (In reply to Solution by Paul)

    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).

      Posted by Federico Kereki on 2006-11-20 10:55:07

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