How many binary strings exists that have exactly five occurrences of "00", three of "10", three of "01" and three of "11" ?
I tried to solve it using induction, or simple counting methods, I also tried to prove that there only exists 1 such binary string but couldn't.
Since there must be exactly 14 pairs of adjacent bits, a matching string needs to be 15 bits long.
There are only 32768 15-bit strings. Just test them all.