# Ten binary passwords (The **** and *** sequence)

Your agent has retrieved an encoded hard disk from the enemy. It has ten files. Each file has been encrypted using a different password. The encryption algorithm used in uncrackable. Hence you used brute-force to crack the first seven passwords. After this, it is taking too long to do so. However, the contents of the files are genuine and you need to crack the remaining three.

Here are the first seven passwords:

10
1110
11110
100110
1110010110
111100111010110
100110011110111010110


Find the remaining three. I hope my hints aren't too revealing. I will give the eighth code after a week, and one or two more hints (if this remains unsolved).

Hint 1:

It does not involve addition, subtraction, multiplication or division.

Hint 2:

Don't convert them into decimal numbers.

Hint 3:

Every code is longer than the previous, and every code contains only 0s and 1s. All these rules are true for any more numbers in the series.

Hint 4:

A similar pattern is more popular and even has a wikipedia page on it.

P.S. This is my first number sequence puzzle.

• Digits of code 3, 6 and 7 aren't even. Intentional or error? – The Dark Truth Oct 13 '15 at 10:38
• Reminds me of the Look and Say sequence, but I can't put my finger on why. – Tryth Oct 13 '15 at 10:44
• @TheDarkTruth Error. I knew it was true for the decimal sequence, I didn't realise that it was not true for the binary sequence. – ghosts_in_the_code Oct 13 '15 at 15:15