Ant and Triangle Problem
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?
Solution
Every Ant has only Two choices (A – anticlockwise C- clockwise)
Total case – 2*2*2 = 8
Favorable Case – A1A2A3, C1C2C3 (All anticlockwise and all clockwise)
Probability = 2/8 =1/4
This Puzzle can be generalized for Squares and n-sided polygon
The probability is 1/2(n-1)
Total case – 2*2*2 = 8
Favorable Case – A1A2A3, C1C2C3 (All anticlockwise and all clockwise)
Probability = 2/8 =1/4
This Puzzle can be generalized for Squares and n-sided polygon
The probability is 1/2(n-1)