The first math problem I created was spawned from a visualization on a rare occasion smoking marijuana. I started imagining cubes falling from the sky, and just observing this process. I got curious about the chance of one cube landing on top of another. This led to the problem:
Given a square boundary of size B, place squares of side length S one at a time completely inside of the boundary at random locations. How many squares on average will you place before a pair of squares overlaps?
The first math problem I created was spawned from a visualization on a rare occasion smoking marijuana. I started imagining cubes falling from the sky, and just observing this process. I got curious about the chance of one cube landing on top of another. This led to the problem:
Given a square boundary of size B, place squares of side length S one at a time completely inside of the boundary at random locations. How many squares on average will you place before a pair of squares overlaps?