3 Ants and Triangle | Puzzles for Interview - Interview Preparation PDF Download

Introduction

Imagine there are three ants sitting on three corners of a triangle. They randomly choose a direction and start moving along the edge of the triangle. But here's the question: what is the probability that any two ants collide?

Ants' Movements

The ants move along the edges of the triangle. They can only move in one of two directions: clockwise or counterclockwise. If all three ants move in the same direction, there will be no collision. Therefore, we need to consider the cases where at least two ants move in opposite directions.

Possibilities

Each ant has two choices of edges going through the corner on which it is initially sitting. Therefore, there are a total of 2^3 = 8 possible outcomes. Out of these, there are only two ways in which no collision occurs: either all three ants move in a clockwise direction or all three ants move in a counterclockwise direction. In the remaining 6 outcomes, at least two ants move in opposite directions resulting in a collision.

Probability

The probability of collision is therefore 6/8, which can be simplified to 3/4 or 75%. This means that there is a high likelihood that two ants will collide when moving randomly along the edges of a triangle. The probability of non-collision is 2/8, which simplifies to 1/4 or 25%.

Conclusion

In conclusion, the probability of collision is high when three ants move randomly along the edges of a triangle. Only in two cases out of eight, no collision occurs. Therefore, it's safe to say that if you see three ants moving along the edges of a triangle, there's a good chance that two of them will collide.