Radio Astronomy Systems Research Group

In the forest, there is a meadow. A fox and a rabbit each take 10 seconds to cross this meadow. One day, they both cross this meadow. Their arrival time is uniformly distributed from 4:00 to 4:01 pm. If the fox and the rabbit happen to be in the meadow at the same time, the fox will eat the rabbit. What is the probability that the rabbit survives?¹⁾

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One day, you are swimming in the middle of a perfectly circular lake. While you are swimming, a wolf wanders up to the edge of the lake. You know this wolf can run 4 times faster than you can swim, and he always runs toward the point on the edge of the lake closest to your current position. If you can get to a point on the shore before the wolf you will get away. If the wolf beats you there, he's gonna eat you. How do you get away? ²⁾

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In a box, there are 3 black hats and 2 white hats. Tom, Bob and Bill each take a hat from the box and place it on their head without looking. They are lined up with Tom at the back, and Bill at the front (so Tom can see Bob and Bill, Bob can see Bill, but Bill can't see anyone). They cannot see their own hat. They are each asked if they know what color hat they are wearing. Tom says he doesn't know, Bob also says he doesn't know, but Bill says that he does know what color his hat is. How does he know, and what color is his hat? ³⁾

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Two trains are traveling toward each other. Both are traveling at 50 km/h. When they are exactly 200 km apart, a fly starts traveling from one train to the front of the other. Once he gets there, he turns around and travels back to the first train. He continues until the trains meet. How far is the fly's total travel distance? ⁴⁾

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What is the missing number in this sequence? ⁵⁾

4 6 12 18 30 42 60 x 102

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You have two eggs and a 100 story building. You are to discover the breaking limit of the eggs by throwing them out the window on any floor. What is the minimum number of throws to discover the breaking limit?

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