Number of ways to split a list into consecutive parts How many ways can a list of size $n$ be split into consecutive sublists? For example, for $n=3$ the answer is 4:
$$
[[[1, 2, 3]], [[1], [2, 3]], [[1, 2], [3]], [[1], [2], [3]]]
$$
In general it is $2^{n-1}$ - why?

Write down the numbers $1$ to $n$; in between each two consecutive integers on the list, you can insert a separator or not.  Each such list with chosen insertions corresponds to one of your lists of consecutive integers.
Example (using $\mid$ as a separator):  $n=5$: The list  $1, 2 \mid 3 \mid 4, 5$ corresponds to $[1,2], [3], [4,5]$.  
Since there are two choices (seperator or not) between each pair of consecutive integers, you get your result.
