You stop applying the hammer when each sub-problem (rock fragment) is small enough.

Recursion on the Rocks

Here (again) are the two parts to recursion:

If the problem is easy, solve it immediately.
If the problem can't be solved immediately, divide it into smaller problems, then:
- Solve the smaller problems.

Here are how this applies to the rock-destruction problem:

When a piece is small, don't pound it any further.
To destroy a large rock, hit it with a hammer. The rock shatters into smaller pieces.
- Apply this procedure to each of the pieces.

Say that you wish to divide a line into 16 equal pieces.

What is the first thing that you do?