Three Ants on Equilateral Triangle Puzzle

Ants on equilateral triangle puzzle:

• Three ants are sitting on the corners of equilateral triangle.
• Ants can pick any direction and start moving along the edge of equilateral triangle.
• What is probability that no ant should collide with each other.

Solution of ants on equilateral triangle puzzle

• Ants can move either in clockwise wise direction or anti-clockwise wise direction along the edge of equilateral triangle.
  •  To avoid collision, Ants has to move in same direction (either clockwise or anti-clockwise wise).
•  Probability of a Ant for picking the clockwise direction is 1 / 2.
  •  Probability of all three ants pick clockwise direction is 1/2 * 1/2 * 1/2 = .125
•  Probability of a Ant for picking the anti-clockwise direction is 1 / 2.
  •  Probability of all three ants pick anti-clockwise direction is 1/2 * 1/2  * 1/2 = .125
•  Probability of three ants to follow clockwise and anti-clockwise direction = Probability of clockwise direction + probability of anti-clockwise direction.
•  Probability to avoid collision = .125 + .125 = 0.25;