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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.)
    Solution re: Program needed . . . | Comment 7 of 9 |
    (In reply to Program needed . . . by Leming)

    2       1
    3       2
    4       3
    5       6
    6       11
    7       24
    8       47
    9       103
    10      214
    11      481
    12      1030
    13      2337
    14      5131
    15      11813
    16      26329
    17      60958
    18      137821
    19      321690
    20      734428
    21      1721998
    22      3966556
    23      9352353
    24      21683445
    25      51296030
    26      119663812
    27      284198136
    28      666132304
    29      1586230523
    30      3734594241
    31      8919845275
    32      21075282588
    33      50441436842
    34      119586625008
    35      286881743651
    36      682038158682
    37      1638972182530
    38      3906927413303
    39      9406152137879
    40      22472056451247
    41      54179250293408
    42      129717291829971
    43      313221456747456
    44      751296610669843
    45      1816290103898606
    46      4364276162884639
    47      10564366228522933
    48      25423289186419875
    49      61603562059151316
    50      148469252145358808
    51      360148324479758398
    52      869106865433804787
    53      2110095700233524285
    54      5098455346557047973
    55      12390057717097408538
    56      29970227726060634017
    57      72888562557661326864
    58      176499842031226901381
    59      429600857419170466984
    60      1041278357437152358167
    61      2536196542286478666139
    62      6153056349381741585301
    63      14997398318018924847928
    64      36415646728341951903548
    65      88812597580192574525063
    66      215825550418242438223860
    67      526698364894729912571199
    68      1280889862705293577927296
    69      3127554316181503287301649
    70      7611480898206798369956079
    71      18595392659190014140264908
    72      45285076599371342669883879
    73      110688203671795668277235660
    74      269731061685359096419812596
    75      659621468982340192204331003
    76      1608347489785603397241511596
    77      3934899947331339053124909760
    78      9599957125050059282635482771
    79      23497383827105781742164365797
    80      57356780899998599652248264948
    81      140445346913283003802613003390
    82      343003250570726221462813158332
    83      840230790925103153705975373025
    84      2053039366403003049949666409068
    85      5031007658238870403920117152710
    86      12298660818108757545415589434116
    87      30149320261600708547986929592390
    88      73734219258619332834890575674726
    89      180814310616014862689768523024832
    90      442394836724735448917277216463620
    91      1085229905277955181235904456588703
    92      2656264327240487951606370531218366
    93      6518016487344095077522813166239962
    94      15960060530428381780150591272215609
    95      39175508765992561988656569988484369
    96      95960278101215884134653913840825280
    97      235610003979934719849295201203681289
    98      577332543305844394680393171492662521
    99      1417925471818225717475443872638589060
    100     3475608424184069405814897461789989796

    making the answer 3,475,608,424,184,069,405,814,897,461,789,989,796.

     10   dim F(100)
     20   F(1)=1
     30   for I=2 to 100
     40     T=F(I-1)
     50     J=I-2:K=1
     60     while J>=K
     70        T=T+F(J)*F(K)
     75        J=J-1:K=K+1
     80     wend
     85     F(I)=T
     90     print I,T
    100   next

     


      Posted by Charlie on 2006-11-20 14:39:01
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