From the article: > To distill the essence of the halting problem into a simpler form, Radó imagined sorting Turing machines into groups based on how many rule

From the article: > To distill the essence of the halting problem into a simpler form, Radó imagined sorting Turing machines into groups based on how many rules they had — one group for all one-rule Turing machines, another for all two-rule machines, and so on. Sure, that leaves infinitely many such groups, since a Turing machine can have any number of rules. But the number of distinct machines in every group is finite, since there are only so many possible combinations of rules. > With two rules, there are already over 6,000 distinct Turing machines to consider; that number swells to millions with three rules, and to billions with four. I'm pretty sure the standard terminology is "states", not "rules". This deviation made it harder to understand. Each state produces 2 transition rules, depending on the symbol at the tape head.