FRIDAY'S NASTY QUESTION: You are tasked with deciding where to apply armour to bomber planes

On alternate Friday afternoons we are posting cryptic questions from 7city Learning. Add your answers in the comments box at the bottom of the page. Reverence will be accorded to the person who provides the correct answer first. We'll add the official answer to the bottom of this article on Monday afternoon.

You are working for the Royal Airforce and have been asked to research the application of armour to bombers. You can't put it everywhere because it will make the aircraft too heavy.

Fortunately, you have data for every hit on planes returning from their missions. How should you use this information in deciding where to place the armour reinforcement?

Answer:

The trick here is that we only have data for aircraft that survived. Since hits on aircraft are going to be fairly uniformly distributed over all places that are accessible by gunfire one should place the reinforcements at precisely those places which appeared to be unharmed in the returning aircraft. They are the places where hits would be 'fatal'. This is a true 2nd World War story about the statistician Abraham Wald who was asked precisely this.