|Animal Riddles|

Let's test your physicist's mind!

Riddles


The Wolf, The Goat, and The Cabbage

A man once had to travel with a wolf, a goat and a cabbage. He had to take good care of them, since the wolf would like to taste a piece of goat if he would get the chance, while the goat appeared to long for a tasty cabbage.
After some traveling, he suddenly stood for a river. This river could only be crossed using the small boat laying nearby at a shore. The boat was only good enough to take himself and one of his loads across the river. The other two subjects/objects he had to leave on their own. How must the man row across the river back and forth, to take himself as well as his luggage safe to the other side of the river, without having one eating another?


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The Hare and The Turtle

A turtle crawled slowly along a road. A hare came running from behind. One would expect the hare to overhaul the turtle easily. Imagine the turtle to be at a certain spot, at a certain time. However, when the hare arrives at that spot, the turtle has moved a little distance forward, thus being still ahead of the hare. Now the hare runs to that spot he sees the turtle has moved to. But when he arrives at that second spot, again the turtle (not waiting for the hare to arrive) has moved forward a little. And everytime the hare runs to the spot where he has seen the turtle last, he finds the turtle has moved forward and stays (slightly) ahead of the hare.
How can it be, that the fast running hare does not seem to be able to overhaul the slowly crawling turtle?


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Answer: The man first takes the goat to the other side, since leaving the wolf and the cabbage together will not give any trouble. After rowing back alone, he takes one of the others (let's say the wolf) to the other side. Now he must take the goat back again, since otherwise the wolf would have goat for dinner. The man leaves the goat on the first shore, while taking the cabbage to the second (where the wolf is already). Then he rows for the last time back to pick up the goat.
It takes a lot of rowing, but that will keep him in form...

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Answer: Indeed everytime the hare arrives at the place he spotted the turtle before, he must admit that the turtle is still ahead since he moved forward in the meantime.
However, since the hare runs much faster than the turtle, the distance covered by the turtle is much shorter than the distance the hare has moved between the previous two spots. In fact, the hare is getting closer all the time, and the time steps from spot to spot are getting shorter rapidly. This spot-to-spot-running of the hare is continuing countless times, while the time steps get infinitely small.
In fact the distance (or time) the hare needs to come alongside of the turtle is the infinite sum of continuously decreasing (time) steps. Mathematically, it can be proven easily that this infinite sum is finite itself!

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