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Saturday, July 26, 2008

Four Flies

Consider 4 (dimensionless) flies, 2 males and 2 females. They are situated at the corners of 1 square meter. Every fly tries to reach the male/female fly in front of her/him. Their initial situation is visualized in the picture. Since the flies are flying towards another, they will meet each other at a certain time in the center of the square.

The Question: What is the length of the path they have traveled at the moment they reach each other?

Answer: Because all flies constantly fly perpendicular to another fly, they all travel the shortest distance to each other, which is 1 meter (all flies make a kind of spiral flight to the center of the square, and during this flight, the flies constantly form a square until they meet in the center).

Conclusion: The flies all travel 1 meter.

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