# Ant and Triangle Puzzle

## Solve the Ant and Triangle Puzzle

Solve the Ant and Triangle Puzzle. 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?

## Detailed Explanation

The ants can only avoid a collision if they all decide to move in the same direction (either clockwise or anti-clockwise). If the ants do not pick the same direction, there will be a collision. Each ant has the option to either move clockwise or anti-clockwise. There is a one-in-two chance that an ant decides to pick a particular direction. Using simple probability calculations, we can determine the probability of no collision.

N(No collision) = N(All ants go in a clockwise direction) + N( All ants go in an anti-clockwise direction) = $0.5 \times 0.5 \times 0.5 + 0.5 \times 0.5 \times 0.5 = 0.25$

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