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Though, if we apply your requirement, the set of problems without a unique answer must be countable as well. So, the cardinality of problems with a unique answer is still equal to the cardinality of problems without one.

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You're just using the terminology imprecisely is all. (Indeed, two things being countable does not mean they have the same cardinality; finite sets are also countable)

I think it's trivially obvious that both sets are infinite.

There are infinitely many addition problems involving two numbers, and that's a subset of the set of problems that the article claims to be smaller.

I'm not making claims about the truth or falsity of your statement, just critiquing the logic and terminology you're using (the lack of a definition for a "problem," the minor misuse of the term "countable"). Regardless, I really hope you saw the article as something besides a mathematical claim, because it clearly did not pretend to be one.

Indeed. My original comment was meant as a joke, not as a serious mathematical claim.

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