Dodge the bullets – Aeroplane safety Puzzle

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. They had to be very selective!

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?

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