90. On a plane, there are 4 points $A_{1}, A_{2}, A_{3}, A_{4}$, the distance between any two of which is not less than 1. What is the maximum possible number of line segments $A_{i} A_{j}$ of length 1 connecting these points pairwise?
90. The number $v_{2}(4)<6$, otherwise the number of diameters of a system of four points on a plane could equal the "complete" number of six segments connecting our points, and by the result of problem 87 a) this is not the case. However, the number of segments equal to 1, connecting the points of our system of four points on a plane, can equal 5:

$$
v_{2}(4)=5
$$

(Fig. 159).

Note. It is also obvious that $v_{2}(3)=3$ and generally

$v_{k}(n)=C_{n}^{2}\left(=\frac{n(n-1)}{2}\right) \quad$ for $\quad n \leqslant k+1$.