How many times can you divide a list of n elements in 1/2
You haven't explained what "divide in half" means, but let's assume that it means to divide the list into two halves of as equal size as possible (equal if the number of elements is even, almost equal if it's odd).

You can draw recursive "division in half" as a tree. The root is labelled by the original number of vertices, $n$. A node labelled $1$ is a leaf. Any other node labelled $m &gt; 2$ has two children labelled $\lfloor m/2 \rfloor$ and $\lceil m/2 \rceil$ (this is the "division in half"). As yemelitc shows in their answer, the number of leaves is $n-1$; this is irrespective of the division being "in half". On the other hand, the depth of the tree (number of edges in longest path from root to leaf) is $\lceil \log_2 n \rceil$. You can try to prove this in the case where $n = 2^k$ (you can use induction on $k$).