STRANGE BUT TRUE- Piece of cake: Getting the most from fewest cuts
Q. You have one round cake, seven guests, and the scholasticist of the group insisting three straight knife cuts will divide the dessert into eight equi-sized pieces. Is he crazy? –E.U.Clid
A. Got the gimmick? Make a large quadrisecting x (2 cuts) centered on the cake's midpoint then slice horizontally across half way down (3rd cut). Each quadrant is thus bisected into two equal cake eighths–eight eighths in all. Just be sure you take a piece with icing on it. Another solution– if you don't mind rearranging cake pieces– is to cut into quadrants then line those up in a row looking a little like side-by-side bow-ties. Now cut straight across the "knots," in icing egalitarianism.
Q. Why did kamikaze pilots wear helmets when they were going to die anyway? –D. MacArthur
A. 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.
Q. 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? –G. Kasparov
A. There'll be no wins at all because two perfectly foresightful players at checkers will
always play to a draw, true as well for tic-tac-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 tic-tac-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
Q. "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? –T. Gampper
A. 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.
But fairest of all is c), a modestly feminized caricature of attractive features, as when
a computer generates a face that's 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@example.com.