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Each face of a cube is given a single narrow stripe painted from the center of one edge to the center of the 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?
This problem is copyrighted by the American Mathematics Competitions.
Instructions for entering answers:
- Reduce fractions to
lowest terms and enter in the form 7/9.
- Numbers involving pi should be written as 7pi or 7pi/3
- Square roots should be written as sqrt(3),
5sqrt(5), sqrt(3)/2, or 7sqrt(2)/3 as appropriate.
- Exponents should be entered in the form 10^10.
- If the problem is multiple choice, enter the appropriate
- Enter points with parentheses, like so: (4,5)
- Complex numbers should be entered in rectangular form
unless otherwise specified, like so: 3+4i. If there is no
real component, enter only the imaginary component (i.e. 2i,
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