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The huntsman and his dog

A huntsman is walking at constant speed to his hunting lodge which is 2km away. His dog is very excited and is running ahead of the huntsman but at constant speed, too. When the dog has reached the hunting lodge, he turns around and runs back to his master, turns around again and runs again to the hunting lodge. The game goes on until the dog and the huntsman reach the hunting lodge at the same time. For the dog is completey exhausted now, the huntsman asks himself:

How many kilometres did my dog run?


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