Final answer:
The full-stem curl allows for the greatest mobility in pin curls.
Step-by-step explanation:
The type of pin curl that allows for the greatest mobility is the full-stem curl. In a full-stem curl, the entire strand of hair is wrapped around the curling pin, which allows for more movement and flexibility. The other types of curls mentioned, such as the no-stem curl, half-stem curl, and closed-center curl, restrict movement to some extent.