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The 3 Ants Puzzle
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The famous 3 Ants puzzle : Explained and generalized!

Sanghamesh S Vastrad
University of Toronto

Unacademy user
i want to prepared IT offiicer
Sehaj Risham
a year ago
u can refer online lectures provided
people answering 6 instead of 8 are the ones who left Permutations combinations in class 11, leave aside Pand C this is basic MAT knowledge..
what of square has diagonal?
Good explanation, Thank you
how topossible become 8?
Mohit Neniwal
3 months ago
every ant has 2 possibilities. so 3 ants having 2*2*2=8
if every ant has 2 directions soo we have only 6 possibilities noo
  1. Frequently Asked Puzzles in Job Interviews INTRODUCTION SANGHAMESH S VASTRAD

  2. Overview Explanation of logic and code snippets, if necessary Each chapter will be of a particular puzzle Total of 6-7 chapters Pre-requisites : None

  3. The 3 ants Problem

  4. Problem statement 3 ants sitting on three There are corners of a triangle. All ants randomly pick a direction and start moving along edge of the triangle. What is the probability that any two ants don't collide?

  5. Logic Every ant has two choices Hence, total number of possibilities = 2^3 8

  6. Solution All ants move in clockwise or anti-clockwise direction

  7. Answer Therefore, probability they won't collide = 2/8 or Variation Circle or any other shape with only 3 ants

  8. Generalization What if the number of ants is n on a n-sided polygon? Always only 2 solutions possible, i.e, clockwise or anti-clockwise

  9. Generalized solution Probability of not colliding-2/2 Please provide your feedback and rate this course Up Next: 5 Horses Puzzle