I understand how the recursion works, but I do not know how to retrieve the secret number from each of the games.

At a glance, I would need a reference to each game.

Is there another approach I should be looking at?

The game structure you created contains attributes, one of which is the secret number. In order to access it, you would simply call structure-attribute, as shown in the link that CSLUONG4 posted where in order to get the student id# you call student-id#. Hope that helps!