A disc is spinning on a spindle, and you don't know which way. You are given a set of pins. Describe how you would use them to determine which way the disc is spinning.
You have a bag of with "N" number of strings. At random, you pull out a string's end. You pull out another string end and you tie the two together. You repeat this until there are no loose ends left to pull out of the bag. What is the expected number of loops?
Think of a product or service that no one has ever thought of before, one that you think would be revolutionary for your university. How would you market it?
A dwarf-killing giant lines up 10 dwarfs from shortest to tallest. Each dwarf can see all the shortest dwarfs in front of him, but cannot see the dwarfs behind himself. The giant randomly puts a white or black hat on each dwarf. No dwarf can see their own hat. The giant tells all the dwarfs that he will ask each dwarf, starting with the tallest, for the color of his hat. If the dwarf answers incorrectly, the giant will kill the dwarf. Each dwarf can hear the previous answers, but cannot hear when a dwarf is killed. The dwarves are given an opportunity to collude before the hats are distributed. What strategy should be used to kill the fewest dwarfs, and what is the minimum number of dwarfs that can be saved with this strategy?
How do you compute the collision of two moving spheres? Give me both the mathematical equations for the solution as well as an algorithmic implementation.
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