These sections have two main purposes: firstly they allow students who have quickly finished the previous Duo/Trio section to do something while they are waiting; secondly they provide a launch-pad for the next speaking activity.
The puzzle provides some light relief after the previous activity, while still stretching the students, and possibly introducing a little more vocabulary.
The writing allows students some time to reflect and collect their thoughts, and is closely related to the language used in the subsequent speaking activity.