These q×q pieces will be presented to you in disorder, result of a (hidden) affine transformation of the plane. And your goal is to recover the image by finding the inverse affine transformation. You have the right to multiple tries in order to do it.
Recall that an affine transformation is a linear transformation followed by a translation. All are operations over Fq.
You may play this game even without understanding the mathematics behind. In this case don't go further than q=5; the game risks to be very frustrating. We also recommend another online jigsaw Shifting puzzle which requires much less mathematical background.