I think I've counted the cases correctly.
Please check my reasoning.
Each face of a cube is given a single narrow stripe painted from the center of one edge to the center of its opposite edge.
The choice of the edge pairing is made at random and independently for each face.
What is the probability that there is a continuous stripe encircling the cube?
I know the total possiblities would be 2 to the 6th power, but not sure from here.
There are 3 orientations for the continuous stripe.
The other two faces can have their stripes in ways.Code:*-------* *---o---* *-------* / /| / o /| / /| / / o / o / | o o o o o | / / o| / o / | / /o | *-------* o * *---o---* * *-------* o * | |o / | o | / | | o/ o o o o o / | o | / | | o | |/ | o |/ | |/ *-------* *---o---* *-------*
Hence, there are: . ways to have a continuous stripe.