[variety]

Conversely, we can think of this as a rather poor filtering technique, because it grants an a nearly automatic pass to anyone who happens to have read any of the popular programming books (or blogs) where the "problem" is presented in easily digestible form, is presented as an "interesting" problem, and it's known that a tractable and optimal solution exists.

A much more important (and deeper) skill is to be able to solve (or reasonably approach) problems they have never seen. And an even more important and deeper skill than that is the ability to recognize algorithmic problems embedded "in the wild" (in naturally occurring business contexts), and to tell the interesting ones from the non-interesting ones (and the trivial from the hard... and among the hard, the plausibly solvable ones from the intractable rabbit holes) without the imprimatur of having someone from a place like Google or MIT telling you that they're "interesting" problems (let alone tractably solvable).

Of course, this kind of skill is much, much harder to test for -- if it can be tested for in the awkward setting of a tech interview at all.