(FORTUNE Magazine) – So you're up for a great job, and after the usual chitchat the interviewer asks you a question from far left field. The phrase "just for fun" is sometimes invoked here, but clearly fun isn't the point. For instance, your interlocutor may say, "Let's suppose you have a gold chain with seven links. You need to hire an assistant and pay him one gold link per day for seven days. Each day the assistant needs to be paid for his services without underpayment or overpayment. What is the fewest number of cuts you can make to the chain for this to work out?" Or the interviewer may brandish a wine bottle, a coin, and a cork, and say, "I'm going to put this coin in this bottle and then stop the opening with the cork. How would you get the coin out without breaking the bottle or pulling the cork?" (Answers are below.)

Welcome to the wacky world of the puzzle question, an increasingly popular device for making you even more nervous than you already were--and at least theoretically, gauging your ability to analyze problems and work out creative solutions. John Kador, author of a new book called How to Ace the Brainteaser Interview (McGraw-Hill, $14.95), estimates that brainteasers make up only about 10% of the interview process at companies that use them, but that 10% could make or break you. "Interviewers believe that puzzles help them separate the outstanding candidates from the merely great ones," he says. "It's easy to distinguish between an average performer and a superstar. But how do you select among superstars?" For this as for so much else, we have Microsoft to thank. The software behemoth is notorious for bedeviling candidates with queries like "Why are manhole covers round?" (A couple of answers: (1) So they won't fall through the manhole, and (2) They roll, so they're easier to move.)

Happily, Kador's book not only reveals more than 200 puzzle questions that might pop up in an interview but also tells how to approach answering them ("The more obvious an answer is, the more incorrect it is likely to be")--and, crucially, what to do if you are stumped. "Don't let interviewers see you panic, but do let them see you think out loud," Kador says. He quotes former Microsoft developer Adam Barr: "You have to show them that your mind is cycling. Even if you never get to the right answer, they might be impressed by your strategy." Don't bother objecting that the puzzles are irrelevant to your job skills. If you do, explains Kador, "interviewers will respect your position. They won't hire you, but they will respect your position." Swell.

The answers to the two questions above: For the chain, assume that your assistant is willing to give change. You'll make two cuts--after the first and third links. This gives you a single link, a piece with two links, and a strand with four links. On Day 1, you give your assistant one link. Day 2: two links (getting the first one back as change). Day 3: Give him the single link again. Day 4: Exchange the four-link strand for the other three links. And so on. You get the idea. As for the wine bottle, just push the cork in and extract the coin. But you already figured that out, didn't you?