Pattern Brain Puzzle: Solve the 101110111110111101100011001110111 Mystery

[BicycleTree]

This one is probably very difficult:

101110111110111101100011001110111?

What fills in the question marks?

 

[motai]

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.

 

[BicycleTree]

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.

 

[motai]

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.

 

[BicycleTree]

Aha, I see.

 

[rygar]

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.

 

[BicycleTree]

You got it rygar!