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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(2): Program needed . . . | Comment 8 of 9 |
    (In reply to re: Program needed . . . by Charlie)

    An objection... when we have 2n nodes, and we add 1, if we add F(n)*F(n) to the sum, we will have repeated some combinations.

    Call the F(n) different books A,  B, C, ...Z. We could have A with any of A to Z, but B only with B to Z (A with B has been done), and C only with C to Z... and so on, so in this case we should add F(n)*(F(n)+1)/2.

      Posted by Federico Kereki on 2006-11-20 14:51:24

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