You are spending the summer polishing your thesis in the university library. Every day you take the escalator into the subway, turn right and catch a train going up North to the university. One day you realize that the trains on your left going in the opposite direction can bring you to the beach. It is summer and nothing is wrong with some leisure. You carefully calculate that even if you spend half of the remaining summer vacation in the library it should be enough to finish the thesis. You decide to spice up your summer by allowing some chance to guide your life: every day you catch the first train that comes to the platform. It may be train on the left going to the beach or train on the right heading to the university.
You think that because you wake up and come to the platform randomly in-between 9 and 10am, and the trains go on a regular schedule, with the same frequency in both directions, you should end up spending about the same amount of time in the library and at the beach. On the first week of this experiment you are surprised that chance brought you to the library only once a week. “I know, it will correct itself on a long run, like heads-and-tails game” you say and continue with the same strategy. But even after two months you find yourself at the library only 1/5th of the time. How could this happen if you do not cheat?
(Puzzle answer is below. Please try to solve it before checking out the answer!)
– (aka TheMathMom) illuminates and demystifies mathematics for adults, describing its fun use in everyday life. TheMathMom has been featured in the Boston Globe, The Jewish Advocate, and Redbook Magazine. Her weekly newsletter contains stories and puzzles for the whole family, and tips on perceiving math and presenting it to kids as a toy, a tool, and a friend. Learn more at TheMathMom.com.
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