Question 19
Several segments have been chosen on a line (with possible overlaps). If the left two-thirds of each segment is colored blue, the set of blue points is a segment of length $31$. If the right two-thirds of each segment is colored red, the set of red points is a segment of length $23$. Let $M$ and $m$ be the maximum and minimum length of a segment of the collection, respectively.
What is the minimum value that $M - m$ can have?
What is the minimum value that $M - m$ can have?