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 maybe solution
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