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Saving the RAF's bullet-ridden planes

The Puzzler


RAY: It was a dark and stormy night at a secret airfield somewhere in England during WW II. The Royal Air Force had summoned one of England's most noted mathematicians to help them solve a problem. German anti-aircraft fire based on the ground was inflicting heavy losses on the Brits. Their planes were being shot down right and left. The RAF had to do something to diminish their losses.


Clearly, they could put armor plating on the bottoms of the fuselages and the wings, but there were several problems with that idea. Their range and their ability to carry bombs would be considerably reduced because of the additional weight.


TOM: They had to be very selective!


RAY: A nameless mathematician crawled underneath the planes and looked at where the bullet holes were on the underside. They were all over the place as you might expect -- in the wings and the fuselage, and seemingly distributed randomly on the undersides. He studied hundreds of planes, took pictures, drew a number of sketches -- and then he made his recommendation.


The question is, what armor plating, if any, did he recommend putting on these planes -- and why?


His recommendation very simply was to armor plate the unhit areas that the returning planes had in common. When he surveyed the undersides of these planes, he noticed that there were a few spots that all of them had in common that had no bullet holes. And he had to assume that the ones that hadn't returned had bullet holes in those locations. They were in the English Channel someplace.


TOM: Did they ever return? No, they never returned.


RAY: And their fate is still unlearned. Do we have a winner?


TOM: The winner that we chose through our random method is John Robertson from Chilocoth, Ohio. And for having his answer selected from among the thousands of correct answers that we received, John Robertson will get his choice of T-shirts.

[ Car Talk Puzzler ]

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