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Pattern brain puzzle

  1. Apr 3, 2005 #1
    This one is probably very difficult:

    101110111110111101100011001110111?????

    What fills in the question marks?
     
  2. jcsd
  3. Apr 3, 2005 #2
    Hmm.. ill venture an odd guess...

    01111. If we split the binary in groups of four, the third-to-last quartet is a continuation of the first pattern in the 1st and 2nd quartets. The last two digits perhaps are a continuation of the first two digits of the third quartet. But this is just a guess.... i'm probably wrong.
     
  4. Apr 3, 2005 #3
    I don't understand what you mean. 01111 isn't what I had in mind though. Here's a hint: looking for repetition probably will not get you to the right answer.
     
    Last edited: Apr 3, 2005
  5. Apr 3, 2005 #4
    Ah. My first reaction was to put things in quartets (just like actual binary code) to discern patterns. So I ended up putting it in this form:

    1011
    1011
    1110
    1111
    0110
    0011
    0011
    1011
    1???
    ??

    I noticed the continuation of the "1011" 3rd from the bottom as the repetition of the 1st "1011", so I just (erroneously) styled the last five digits as a continuation of the rest of that quartet and the first two of the next.
     
  6. Apr 3, 2005 #5
    Aha, I see.
     
  7. Apr 3, 2005 #6
    i figured it out so don't read this if you don't want to know the answer:




    the answer is 11101. because he said it wasn't a simple repetition thing, i the next logical conclusion is that it's binary. because there were 5 question marks, i figured the last binary number was five digits long.

    i figured the numbers would go in increasing order (they don't have to, but i guessed, and they did). so i looked at the previous 5 digits... in binary, that's 23. so i did the previous 5, etc: 19, 17... then the previous 5 digits would have made a larger number (29), so i figured i'd decrease it to four digits, which made 13 in binary. so by this point i have 19,17,13, and it's pretty clear that it's a pattern of prime numbers. sure enough, the list goes on: 11,7,5,3,2... so the next number in the pattern would be 29, or 11101.
     
  8. Apr 4, 2005 #7
    You got it rygar!
     
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