Can You Solve the Simple Math Problem That Fooled Einstein?

Philip Ellis
Photo credit: YouTube/MindYourDecisions

From Popular Mechanics

In 1934, psychologist Max Wertheimer sent a letter to his friend, the physicist Albert Einstein, with the following puzzle enclosed:

There's an old car that needs to go up and down a hill. The hill is 1 mile going up, and 1 mile going down. Because the car is old, it can only average a speed of 15 mph during the ascent, but may be able to go faster during the descent.

The question is: How fast must the car be going downhill, in order for its speed to reach an average of 30 mph for the entire 2-mile journey?

At the time Einstein received the letter, he had already been honored with the Nobel Prize for Physics, and come up with his famous E = mc2 equation. So this should have been super simple for him to figure out, right? Apparently not. According to German psychologist Gerd Gigerenzer's book Risk Savvy: How to Make Good Decisions, Einstein wrote that he didn't see the "trick" until he had already calculated the answer.

YouTuber Presh Talwalkar breaks down the solution to the puzzle in the video above, starting by working backward, and calculating what is the necessary time for a car to average 30 mph on a 2-mile journey. By dividing the journey length, 2, by the speed, 30, you get the time: 1/15 of an hour, or 4 minutes.

Next, Talwalkar figures out how long the car takes going up the hill by dividing the length of that portion of the journey, 1, by its average speed, 15, which simplifies again to 1/15 of an hour, or 4 minutes.

So the car takes 4 minutes to climb the hill, but it must also take 4 minutes for the entirety of the trip, meaning there is no time to get down the other side. The conclusion, then, is that there is no right answer: Wertheimer sent Einstein a trick question.

It might have been the only possible way to stump the smartest man on the planet.

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