The problem with so-called "analytical problems" is that so very many of them aren't analytical at all, they are based on trivia.

For example, the lamps one. Because it's been used by MS for years, it's all over the web. "Solving" it may or may not show any ability other than the l33t skillz of terminal Google abuse and trivia memorizing.

Seriously, would you hire someone who knows how to do the "split groups of steel balls" problem (look it up if you don't know it), but who doesn't know how to write an outer join, over someone who goes, "Steel balls? Er... um ... well ... heck, I'll have to think about that", but who has published multiple excellent books on the subject of SQL, and has been an MVP for two or three centuries, etc., etc., etc?

Even as a tie-breaker, with candidates who are otherwise indistinguishably skilled (or incompetent, your call), it's generally better to pick the one who you think will get along with the rest of the team better, or who wants a slightly lower paycheck, or any number of other, more direct, criteria. Heck, even though it may get me in trouble, given a choice of two equally skilled people, I'll pick the pretty girl over the ugly girl/whatever guy.

Anything is better than, "how can use a bulldozer to separate two stacks of firewood, without turning the buldozer on, if your hands have been burned off and you've got a terminal case of dandruff?" or comparably silly problems. (For anyone curious, the answer to ALL such trivia/logic questions, is, of course, "42". Or, any number between 40 and 45, if it's a government job.)