Hint for Puzzle #46: Three Ants on The Corners of a Triangle

cartoon ant on a triangle46. Three ants are sitting at the three corners of an equilateral triangle. Each ant randomly picks a direction and starts to move along the edge of the triangle. What is the probability that none of the ants collide?

How about other shapes, Square? N sides?
diagram of a triangle with 3 ants sat at each vertex Easier than it looks this. As with most of these types of question we need to think what possible configurations there are and which of them meet our requirements.

Each of the three ants can move in 2 directions. Meaning there are 2x2x2 configurations. But how many of these meet the criteria of there being no collisions?

Where next?
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