Two points are selected at random (independentlyand uniformly) along a 1-meterlong stick, and the stick is broken at the two selected points. What is the probability that the three pieces so obtained can be assembled into a triangle (i.e., that the length of the longest of the three pieces is less than the sum of the lengths of the other two, i.e., that none of the pieces is more than 0.5 meter in length)?