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Some people always carry a pen with them, so that if an idea comes to mind, they will always be able to write it down. Pens sometimes run out of ink. So, just in case, people carry two pens. The problem is that often, when one carries two identical pens, they seem to run out of ink at about the same time – which defeats the whole purpose of carrying two pens. In this paper, we provide a simple statistics-based explanation of this phenomenon, and show that a seemingly natural idea of carrying three pens will not help. The only way to avoid the situation when all the pens stop working at about the same time is to carry pens of different types. Mathematics Subject Classification: 97K50, 97K80, 60F05, 62N05

Two pens in a pocket must be different: a nerd-oriented lesson from statistics