# Explanation to a logical problem needed!

• Jul 6th 2008, 07:35 AM
Nupur
Explanation to a logical problem needed!
There are 3 ants at 3 corners of a triangle, they randomly start moving towards another corner.. what is the probability that they don't collide.

All three should move in the same direction - clockwise or anticlockwise. Probability is 1/4.

• Jul 6th 2008, 09:28 AM
Plato
Label the triangle $\Delta ABC$. Any bit-triple will denote the direction the ant at the vertices goes. Example: $\left( {0,1,1} \right)$ means that ant at A goes counter-clockwise while ants at B & C go clockwise. In that case ant A will collides with the ant at B. There are eight such triples. In how many will there be no collisions?
• Jul 6th 2008, 10:17 AM
Plato
Quote:

Originally Posted by janvdl

No, I think that you misread it.
That was an example in which they do collide.
Did you read the last two sentences?
There are eight such triples. In how many will there be no collisions?
Now I ask you the same question.
• Jul 6th 2008, 10:20 AM
janvdl
Quote:

Originally Posted by Plato
No, I think that you misread it.
That was an example in which they do collide.

My apologies.
• Jul 17th 2008, 02:02 AM
Twig
Quote:

Originally Posted by Plato
Label the triangle $\Delta ABC$. Any bit-triple will denote the direction the ant at the vertices goes. Example: $\left( {0,1,1} \right)$ means that ant at A goes counter-clockwise while ants at B & C go clockwise. In that case ant A will collides with the ant at B. There are eight such triples. In how many will there be no collisions?

I really liked this explanation, thanks!
• Jul 17th 2008, 07:11 AM
CaptainBlack
Quote:

Originally Posted by Nupur
There are 3 ants at 3 corners of a triangle, they randomly start moving towards another corner.. what is the probability that they don't collide.

All three should move in the same direction - clockwise or anticlockwise. Probability is 1/4.