48. Each pair of six computers is connected by a wire. Can all these wires be colored with one of five colors so that from each computer five wires of different colors come out?
$\triangle$ To solve this, let's draw a convex hexagon and draw all its diagonals (Fig. 13). Let each vertex of the hexagon represent one of the computers, and each segment represent a wire connecting two computers. We will number the different colors with natural numbers from 1 to 5 to distinguish them from each other.

Let's start, for example, from vertex $A$; draw segments of all five colors from it. Move to vertex $B$ and draw four segments of all colors from № 2 to № 5, taking into account that the segment $B A$ coming out of this vertex is already colored in color № 1. Then we will deal with vertex $C$. And so on. In the end, we get a positive answer to the question of the problem.

Answer: it is possible.

In Figure 13, every two vertices of the graph are connected by their own edge. Such a graph is called complete.