A simple, yet abstract problem of this type? How about the following (answer on page 4): It's very dark and four mountain climbers stand before a very rickety rope bridge that spans a wide chasm. They know the bridge can only safely hold two people and that they possess only one flashlight, which is needed to avoid the holes in the bridge. For various reasons one of the hikers can cross the bridge in 1 minute, another in 2 minutes, a third in 5 minutes and the fourth, who's been injured, in 10 minutes. Alas, when two people walk across the bridge, they can only go as fast as the slower of the two hikers. How can they all cross the bridge in 17 minutes?
4. Calculation. Being able to solve a problem using a bit of algebra, it should go without saying (except to Washington Post columnist Richard Cohen -- link on page 4), can be useful to a politician, whether the issue is taxes, health policy or stock broker commissions.
A simple, yet abstract problem of this type? How about the following, which is not irrelevant to broker commissions (answer below): A 100-pound sack of potatoes is 99 percent water by weight. After staying outdoors for a while, it is found to be only 98 percent water. How much does it weigh now?
5. Deduction, Again, it should go without saying that the ability to make simple deductions is a prerequisite for good decision-making.
A simple, yet abstract problem of this type? How about the following (answer on page 4): Imagine there are three closed boxes, each full of marbles on a table before you. They're labeled "all blue marbles," "all red marbles," and "blue and red marbles." You're told that the labels do describe the contents of the boxes, but all three labels are pasted on the wrong boxes. You may reach into only one box blindfolded and remove only one marble. Which box should you select from to enable you to correctly label the boxes?
Although these problems are much easier than those employers use when hiring entry-level programmers, it would be nice to know that the various candidates, who often are more given to bombast than to logic or evidence, could solve them with ease (although being able to solve them wouldn't be a guarantee of anything). The venue for their solution would be a quiet study with no aides, no pundits, no hot lights, and no intense scrutiny.
What's your guess about how the various candidates would fare with such puzzles? Mine is that a few would find most of the problems trivial, some would have difficulty with them, and the rest wouldn't be sufficiently patient to even try them.
Answers to 1.) 90 inches, 3,600 square inches, 108,000 pounds. (the area increases by a factor of 30^2 (900), and the volume or weight increases by a factor of 30^3 (27,000).
Hint and answer to 2.) Estimate the population of New York City, the number of households in the city, the percentage of them (and other organizations) that have pianos, how frequently each piano will be tuned on average, how many pianos the average tuner tunes, and put these together for a rough estimate. (Such problems are called Fermi problems in honor of the Italian physicist Enrico Fermi.) The annual highway toll is approximately 14 times the number of deaths in the 9/11 attacks.