Puzzle: There are three ants, each at a corner of an equilateral triangle. Each of them can move along any of the two sides independent of the other two ants. What is the probability that none of the ants collide with each other?

Question

Accepted Answer

Y1/X1+X2 as the time take for the trains to collide.

Bird travels to first train in (Y1/X1+a) time
Train 1 travelled (X1*Y1/X1+a) km and Train 2 travelled (X2*Y1/X1+a) km.
Remaining distance Z -(X1*Y1/X1+a) - (X2*Y1/X1+a)

We keep calculating it till we exhaust the time calculated in the first step.

We will have the time taken and we have the speed.

Accepted Answer

The ant has to move in one direction a d then come back to the same cube . This it can take one direction with the probability of 0.25 and then after reaching the next piece it can take the direction back to the initial piece with probba of 0.25. thus 0.25*0.25= 0.0625.

Now for the ant to fall off the side face.
0.25*0.25*0.25*2*4= 0.125

Accepted Answer

Every ant has the option of going left or right, that means a 0.5 probability of going left or right.

For the ants to not collide, all the ants have to move left or right in sync. 
1. The ants move left, then 0.5*0.5*0.5 = 0.125
2. The ants move right, then 0.5*0.5*0.5=0.125

This the ants won't collide if they move left or right in sync, thus 0.125+0.125= 0.25

Puzzle: There are three ants, each at a corner of an equilateral triangle. Each of them can move along any of the two sides independent of the other two ants. What is the probability that none of the ants collide with each other?

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