Do you like the card game Set? This is ProSet. Dots cancel each other out between cards. Create a set of cards by clicking on them. If one card has a purple dot, add a card with a purple dot to the set to cancel that dot out. Add a third card with a purple dot to the set and the purple dot comes back. Create a set where every dot is cancelled out.
The neat thing about this is that to construct the deck, we just make an array of the integers 0 to 63 and write them out in binary. We then use the binary number as an indication that a dot is "on" or "off". Each time we add a card to the deck, we do an xor.
The other neat thing I've been told about this is if we have a hand of 7 cards, it's supposed to be mathematically impossible for there not to be a set. I have played this enough to think the number might be 8, so now you get 8 cards to choose from.