Three ants are sitting at the three corners of an equilateral triangle. Each ant starts randomly picks a direction and starts to move along the edge of the triangle. What is the probability that none of the ants collide?
Imagine a box with two cogwheels, one big with 24 teeth and one small with 8 teeth. The big one is firmly attached to the center of the box which means it does not turn or move while the small one rotates around the big one.
How many times do you think that the smaller wheel will turn compared to the box when it turns once around the big one?
In 2007, a puzzle was released and $2 million prizes were offered for the first complete solution. The competition ended at noon on 31 December 2010, with no solution being found. Wiki