IMO 1992

Let $\,{\mathbb{R}}\,$ denote the set of all real numbers. Find all functions $f: {\mathbb{R}}\rightarrow {\mathbb{R}}\,$ such that $$f\left( x^{2}+f(y)\right) =y+\left( f(x)\right) ^{2}\hspace{0.2in}\text{for all} x,y\in \mathbb{R}.$$

Consider $9$ points in space, no four of which are coplanar. Each pair of points is joined by an edge (that is, a line segment) and each edge is either colored blue or red or left uncolored. Find the smallest value of $n\,$ such that whenever exactly $n\,$ edges are colored, the set of colored edges necessarily contains a triangle all of whose edges have the same color.