I was recently doing a combinatorics problem, where we had to select 4 books from a set of 10 ,where the selected books are not adjacent to each other. The author put forward the idea of using a 10-digit binary number and the books to be selected were 1's and the others were 0's. While playing with the idea I eventually found that(Image above)
and so on, and thus followed the Fibonacci Sequence! Does anyone know why it is? Please share you opinions!