[FaceKicker]

I like the spirit of the question, but it kind of bothers me. The fact is, no matter what finite number of hypotheses you test before making your one guess about the rule, there will always be an infinite number of possible "rules" that could fit all the information you have so far (where a "rule" is a function mapping triplets to booleans).

So in the example he gave, let's say I decide to try his "falsification" technique as well. I ask about all the same 6 triplets he gives as examples, and then decide that the rule is "ascending numbers". So I guess that. Nope, that's wrong in this particular case - the rule was actually "ascending numbers where the second one is at least as close to the first number as it is to the third". As you can imagine, you could play that game forever. I don't think his guess of "even increasing numbers" is any less reasonable than the correct answer of "increasing numbers". Maybe the rule is "ascending integers" - he didn't try falsifying that by guessing 3.14 in one of his triplets. There are unlimited "patterns" he'd have to try falsifying.

I think the ideas behind the problem are good but you'd need to constrain it in some way for it to be reasonable.