#115easyBrainteasers
The Ants on a Triangle
Time Limit: 2sMemory: 256MB
Problem
Three ants are placed at the three vertices of an equilateral triangle. At a given signal, each ant independently and randomly chooses one of two directions -- clockwise or counterclockwise -- each with equal probability 1/2. Then all three ants simultaneously begin walking along the edges of the triangle at the same speed.
If two ants are ever at the same point on an edge while traveling in opposite directions, they collide.
What is the probability that no two ants collide?
Your Workspace
Think through the problem, use the hints if stuck, and reveal the solution when ready.
Hints
Hint 2 (reveal previous hint first)
Hint 3 (reveal previous hint first)