This puzzle is a favorite in interviews and is designed to test logical thinking and problem-solving skills. It’s deceptively simple yet requires a keen understanding of probability and spatial reasoning. Let’s dive into the popular “3 Ants and Triangle Puzzle,” a classic that challenges your logical acumen.
The Puzzle:
Imagine a triangle with three ants placed at its corners. These ants can move in any direction along the triangle’s edges. The question is:What is the probability that any two ants will collide while moving?
Take a moment to pause and think about this puzzle. Try solving it before reading further.
Analyzing the Puzzle:
Understanding the Movements:
- Each ant has two choices: to move clockwise or anticlockwise.
- This gives us 2×2×2=82 \times 2 \times 2 = 82×2×2=8 total movement possibilities.
When Collisions Occur:
- A collision happens if two ants move towards the same edge.
- For example, if Ant 1 moves clockwise and Ant 2 moves anticlockwise along the same edge, they’ll collide.
- So, there are 6 chances for a collision to occur totally.
When Collisions Don’t Occur:
- No collision will occur if all three ants move in the same direction (clockwise or all anticlockwise).
- So, there are 2 chances for a collision to occur.
Calculating Probabilities:
Final Probability:
That’s only 2 out of 8 cases where no collision happens. So, the probability of no collision is 1 in 4.
Conclusion:
The “3 Ants and Triangle Puzzle” is a great example of how simple problems can make us think deeply.
