He can learn the algorithms and apply them to the cards in order to check his understanding. He just needs to make sure that he acts like a computer would - only ever comparing two cards at once.
He can simulate this by having all cards placed face down apart from the two that he's currently doing the comparisons with. At the end he can flip all the cards over to make sure he got the intended result.
I'm sure by doing this he could learn all sorts of algorithms this way, and learn to code in the same way.
He may not have a computer, but don't they say that the greatest computers are the ones in our heads?! He just needs to dumb it down a bit for the sake of the exercise.