3 Ants and Triangle Puzzle

3 Ants and Triangle Puzzle: Test Your Logical Thinking

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.
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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.
created using capcut

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.

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