Consider
![9](/media/m/7/f/0/7f02ff2403dbf63ddc4395762441de88.png)
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\,](/media/m/3/2/e/32e4ed37300f0cd666553950dba3bcad.png)
such that whenever exactly
![\,n\,](/media/m/3/2/e/32e4ed37300f0cd666553950dba3bcad.png)
edges are colored, the set of colored edges necessarily contains a triangle all of whose edges have the same color.
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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.