  In 1955, Greenwood and Gleason showed that the Ramsey number R(3, 3, 3) = 17
by constructing an edge-chromatic graph on 16 vertices in three colors with no
triangles. Their technique employed finite fields. This same result was
obtained later by using another technique. In this article, we examine the
complete graph on 17 vertices, K17, which can be represented as a regular
polygon of 17 sides with all its diagonals. We color each edge of K17 with one
of the three colors, blue, red or yellow. The graph thus obtained is called
complete trichromatic graph K17^(3) (the superscript determines the number of
colors). A triangle contained in graph K17^(3) with edges colored with one and
only one color is called monochromatic. It has been shown that for any coloring
of the K17^(3) edges, K17^(3) contains at least one monochromatic triangle.
This article examines the problem of determining the minimum number of
monochromatic triangles with the same color contained in K17^(3).
