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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.)
    re: maybe solution -- on second thought | Comment 4 of 9 |
    (In reply to maybe solution by Charlie)

    For 5 pages, I think there would be 6 possibilities rather than the 5 predicted by the Fibonacci series:

    Straight through, 1,2,3,4,5.

    One branch of 1 page off a mainline of 4, with the branch being off the first, second or third page. This is 3 more.

    A branch from the first page that leads to two sets of two pages each without branch.

    A brance from the first page leading on the one hand to an ending and on the other to a 2-branch.

    With 1,1,2,3,6, it starts to look like Sloan A003214, Number of binary forests with n nodes.

      Posted by Charlie on 2006-11-20 12:25:05
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