Question 59
Let $n$ be a positive integer. On the segment $[0, n]$ of the real line there are marked $m$ pairwise distinct segments with integer endpoints. It is known that it's impossible to choose a set of these segments such that the sum of their lengths is $n$ and their union is $[0, n]$. (We say that the two segments are distinct if their endpoints doesn't coincide. The union of the segments is considered as the union of the sets of real numbers.)
Find the maximal possible value of $m$.
Find the maximal possible value of $m$.