WWII Planes

During World War II, the mathematician Abraham Wald was asked to help with determining which parts of the allied forces’ planes must be armored better. After examining the surviving American planes, he noticed that there were many holes in the fuselage, and very few in the engines. After careful thinking, he suggested that the armor on the engines must be improved. Why?

Abraham Wald realized that the holes should have been distributed more evenly across the planes. Therefore the planes which had more holes in the fuselage survived, while the planes which had more holes in the engines got destroyed.

Roll a Pencil

You roll a 5 sided pencil on the table. On one of its sides, it is written “HB Pencil”, the others are blank. What is the chance that the side with text on it ends up straight on top?

The chance is 0%. Since the pencil has an odd number of sides, it is impossible that any of them ends up straight on top.

Cut the Paper

You have a sheet of paper and a rectangular piece cut from it, as shown in the picture. What is the easiest way to cut the paper into two pieces with equal areas?

Make a cut through the centers of the small and the big rectangle. The cut will split both the area of the big and the small (absent) rectangle by half, and therefore will do the same to their difference – the given sheet of paper.