Self-Referential Sentences

Discussion in 'Games and Contests' started by Meagain, May 12, 2015.

  1. MeAgain

    MeAgain Dazed & Confused Lifetime Supporter Super Moderator

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    I just ran across this little gem in a book I'm reading.
    Supposedly there are two possible answers, of course the answers are not given.

    I've worked out one possible, but I did it last night while half asleep so I might be wrong as I haven't double checked it.

    What you need to do is complete the following sentence by filling in the blanks:

    It looks simple, the number of occurrences of 0 is 1,
    The number of occurrences of 0 is 1, of 1 is 1,......

    No wait, the number of occurrences of 0 is 1, of 1 is 2,......

    ...and so on. The sequence sets up feedback loops that oscillate and eventually stabilize. There is a branch at one point, which I followed but I haven't checked out the other route yet.
     
  2. MeAgain

    MeAgain Dazed & Confused Lifetime Supporter Super Moderator

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    But neat....

    By the 33th generation (I think) I get a split, showing the 33rd generation below as the 34th generation it could either be:

    The number of occurrences of 0 is 1, of 1 is 4, of 2 is 2, of 3 is 2, 4 is 2, of 5 is 1, of 6 is 1, of 7 is .........dam, I screwed up.....gotta start over!
     
  3. MeAgain

    MeAgain Dazed & Confused Lifetime Supporter Super Moderator

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    Okay, I have it!

    The answer is either:

    The number of occurrences of 0 is 1, of 1 is 7, of 2 is 4, of 3 is 1, 4 is 1, of 5 is 1, of 6 is 1, of 7 is 1, of 8 is 2, of 9 is 1.

    or:

    The number of occurrences of 0 is 1, of 1 is 8, of 2 is 2, of 3 is 1, 4 is 2, of 5 is 1, of 6 is 1, of 7 is 2, of 8 is 1, of 9 is 1.

    Both of which add to 65 as does the previous 4 generations, that is 6 generations that add to 65 and the first adding to 57 for a total of 7 generations total before repetition sets in.

    If I did it right.
     
  4. BeachBall

    BeachBall Nosey old moo

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    No ... you haven't it!

    In your first answer you say the number of occurrences of 1 is 7 ... but I count 8; and you say the number of occurrences of 2 is 4 ... but I count 2; and you say the number of occurrences of 4 is 1 ... but I count 2; and you say the number of occurrences of 8 is 2 ... but I count 1

    And in your second answer you say the number of occurrences of 1 is 8 ... but I count 7; and you say the number of occurrences of 2 is 2 ... but I count 4; and you say the number of occurrences of 8 is 1 ... but I count 2

    So all in all, you're still a long way off getting it!
     
  5. puggybear

    puggybear stars may twinkle-but I shine!

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    Yep.....what SHE said.

    [like I'm daft enough to disagree with the freestyle pencil-chewing champ of 1982...]

    But,in truth,Little Miss grumpy IS correct. I counted 7,4 & 2 respectively,as well.
     
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  6. rollingalong

    rollingalong Banned

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    nope...tried and failed....don't see how it can be solved if the question evolves with every answer.....i think steam was coming out my ears :)
    ....


    just the first run through ends up with 1 going up to 10....making zeros original answer incorrect


    or some shit like that
     
  7. puggybear

    puggybear stars may twinkle-but I shine!

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    That's close enough for jazz,rollypoly....it's just a subjugated-integer version of Fibonacci sequencing,bruv.
    Just don't fall into the trap of using factorial sequentials and it becomes obvious....




    meh-I DEFFO need espresso-NOW!
     
  8. rollingalong

    rollingalong Banned

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    is that a real thing?...seriously i only have basic high school math....nothing fancy taught by priests

    i did email this to 3 sisters and a daughter..and a stoner friend lol.....plus the grand kids...they are probably all cursing me right now haha
     
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  9. GLENGLEN

    GLENGLEN Banned

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    WOW......I Can't Even Pronounce Those Words Let Alone Understand What They Mean......[​IMG]



    Cheers Glen.
     
  10. BeachBall

    BeachBall Nosey old moo

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    HERE is the correct answer:

    In this sentence, the number of occurrences of 0 is 1, of 1 is 7, of 2 is 3, of 3 is 2, of 4 is 1, of 5 is 1, of 6 is 1, of 7 is 2, of 8 is 1, of 9 is 1

    :daisy: :daisy: :daisy: :daisy: :daisy: :daisy:


    (and I DIDN'T do it by iteration ... )



    I have not quite completed the maths to prove it, but I do not believe there IS a second correct solution. It's kinda complicated, however, so you might not all understand it ... best content yourself with the fact that I have provided you with the solution!
     
  11. puggybear

    puggybear stars may twinkle-but I shine!

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    Oi,BeachBum,psst!
    Babe-nobody likes a smartarse.....even if that arse is pert,tight and shapely. Coz so was Red Rum's!

    [just a word t'the wise,Toots...m'kay?]
     
  12. themnax

    themnax Senior Member

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    in order to understand recursion, you must furst understand recursion
     
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  13. rollingalong

    rollingalong Banned

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    In this sentence, the number of occurrences of 0 is one, of 1 is one, of 2 is one, of 3 is one, of 4 is one, of 5 is one, of 6 is one, of 7 is one, of 8 is one, of 9 is one.
     
  14. The Walking Dickhead

    The Walking Dickhead orbiter of helion

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    If you write the numbers in the spaces using only letters it's easier to solve this.
     
  15. The Walking Dickhead

    The Walking Dickhead orbiter of helion

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  16. rollingalong

    rollingalong Banned

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    not easier...its the answer to the question.....which I solved....other wise it isn't a proper sentence..



    improper use of the comma.....ten yard penalty....loss of a down
     
  17. The Walking Dickhead

    The Walking Dickhead orbiter of helion

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    It wasn't specified that the sentence had to be truthful in the original exercise, nor even grammatically correct therefore there are thousands of millions if not perhaps an infinite number of possible solutions, all of which are correct.
     
  18. rollingalong

    rollingalong Banned

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    there can only be one answer...the correct one
     
  19. pensfan13

    pensfan13 Senior Member

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    No need to overthink it. Put the best answer. If no answer is given then you aren't wrong.
     
  20. morrow

    morrow Visitor

    I'm going with beachball :)
     

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