Question 40
There are $N$ closed segments on a line. It is known that for every $d$, $0 \lt d \le 1$, there exist two points, in one segment or in two different segments, at distance $d$.
a) Prove that the sum of the lengths of the segments is greater than or equal to $\frac{1}{N}$.
b) Prove, for each $N$, that $\frac{1}{N}$ cannot be replaced by a larger number.
a) Prove that the sum of the lengths of the segments is greater than or equal to $\frac{1}{N}$.
b) Prove, for each $N$, that $\frac{1}{N}$ cannot be replaced by a larger number.