You divide the cards stack in two and put the top part at the bottom of the other part (which was the bottom part and will be now the top). The relative order of the cards is maintained: you don’t shuffle them. But if you cut them in this way several times, it obfuscates the original location of the cards (as it’s in practice impossible to follow their position changes) so you can’t tell who put which card where. Therefore the final arrangement, when revealed, is anonymized.

Okay gotcha, what was confusing me was how we could randomize it and preserve the relationships of the cards at the same time, but I see now this shuffle is more like "secure by magic trick" than "secure by cryptography", that makes sense. Or equivalently, we put it into a black box, that flips a secure coin, and either does or doesn't swap the cards. Thank you.

No, it is not magic. It really is cryptography.

Yeah sorry, my original wording was confusing, I've tried to clarify that the _shuffle_ is the magic trick, the overall cryptosystem is real.

The only thing that makes sense is keeping the middle red card in place and swapping the top two for the bottom two repeatedly? Anything else could change the answers?

I dont get the exercise

No, the order of the cards is preserved. The "cutting" of the deck is just a rotation.