Question: A swan is in the center of a circular lake but he cannot take flight from the water, only on land. On the parameter of the lake there is a hunting dog that desperately wants the swan but cannot swim. So the swan must make it to the land before taking off and must do so before the dog makes it to him. The dog is almost 4 times faster than the swan and always runs to the point around the lake closest to the swan.
How can the swan get out of the lake and take flight before the dog gets him?
Answer: The swan can travel 1/4 of the way to land then swim in a circular path around the center of the lake (the swan will be moving slightly faster around than the dog in their circles). Once the swan is as far as he can get away from the dog in his circle he can swim the remaining 3/4 of the way to shore. The dog must travel the radius of the lake time pi (radius * π) while the swan only has to travel 3/4 the radius four times slower (3/4 * radius * 4). So the swan will make it to the shore and fly before the dog reaches it.
Question: You have a glass of water that looks about half full. How can you tell, only using the glass of water itself, if the glass is half full or not?
The glass is a right cylinder.
Answer: Tip the glass of water until the water reaches the rim of the glass and if the water lines up perfectly with the bottom rim of the glass, it is half full.