Question: Why did kamikaze pilots wear helmets when they were going to die anyway?

Answer: In the wake of military setbacks in 1944, the Japanese military launched a campaign of kamikaze attacks where pilots attempted to crash their planes into U.S. warships, says Cornell's Robert Frank in "The Economic Naturalist: In Search of Explanations for Everyday Enigmas."

The aviator helmet had become emblematic of what it meant to be a pilot: Kamikaze pilots were pilots, and all pilots wear helmets. Also, planes commonly experienced severe turbulence before reaching their targets, and here the Japanese commanders had clear reasons for wanting the pilots adequately protected.

But the most compelling explanation is that the pilots' charge was to destroy their targets by any means necessary, and while this often meant flying directly into the target, it didn't always. The express intent of the pilots was to complete their mission, not to commit suicide. The hope was that the pilots would return safely, even though the expectation was that they would not.

Question: Top checkers players challenge each other to a round robin of games, after which Brainiac-the-Well-Programmed-Computer will join in. Can you guess the winner?

Answer: There'll be no wins at all because two perfectly foresightful players at checkers will always play to a draw, true as well for tick-tack-toe, says Adrian Cho in "Science" magazine.

It takes a "mistake" for a championship-caliber player to lose at these games. While this has been known about tick-tack-toe for some time, only recently did computer scientist Jonathan Schaeffer show that well-played checkers too ends in a standoff, "the most complex game ever solved." Given that there are some 500 billion billion possible arrangements of checkers on the board, better and better computers were needed to pull off the proof. Then some clever simplifying ideas were introduced, along with hundreds of computers laboring for nearly two decades before the old game of reds and blacks, diagonals, jumps and kings finally succumbed to analysis.

One final caveat: Though in theory a person can play a computer to a standoff, eventually the worn-down human would make a mistake, allowing the computer to prevail.

Question: "Mirror, mirror on the wall, who's the fairest of them all?"

a) a perfectly average female face b) half a face merged with its mirror image to look like a whole face c) a computer-generated "hyperfemale" face

Answer: They're fair, fairer, fairest, in the proper progression: Start with b), because combining half a face with its mirror image forms a perfectly symmetrical new version of the face, which would boost its looks a tad, says David G. Myers in "Social Psychology." Next go for a), or the averaging effect: In a revealing study by Judith Langlois and Lorri Roggman, when they digitized 16 female faces and then computer-averaged them into a single composite face, viewers found the composite more attractive than almost all the actual faces. So in some respects perfectly average is quite attractive, because idiosyncrasies or imperfections are smoothed out and glossed over. (This even holds true for dogs, birds and wristwatches — Jamin Halberstadt et al.)

But fairest of all is c), a modestly feminized caricature of attractive features, as when a computer generates a face that is close to average but incorporates a slightly smaller-than-average lower jaw, somewhat fuller lips, and larger-than-average eyes.

Send STRANGE questions to brothers Bill and Rich at [email protected], coauthors of "Can a Guy Get Pregnant? Scientific Answers to Everyday (and Not-So- Everyday) Questions," from Pi Press.