probability in geometry

[demoskopico]

Two objects are placed on opposite corners of a cube. The objects are designed only to move along the edges of the cube and are equipped with a power device which allows them to do so at the same constant speed of S inches per minute. If both objects begin moving at the same time, each taking one of the shortest paths towards the initial position of the other, what is the probability that the two objects will collide?

please, someone who gives me a plain and clear explanation...

[kevin]

How many paths of shortest distance will take the first object to its destination?

[demoskopico]

How many paths of shortest distance will take the first object to its destination?

i think six paths

[kevin]

Would the answer not be 1/6 then?

Assume that one object is at (0,0,0) and the other at (1,1,1). Also assume that the first object moves right, then up, then out to (1,1,1). The meeting point would be at (1,0.5,0) so In order to meet, the second would have to move in, then down, then left, 1 of the 6 paths it could choose