  We call the minimum order of any complete graph so that for any coloring of
the edges by $k$ colors it is impossible to avoid a monochromatic or rainbow
triangle, a Mixed Ramsey number. For any graph $H$ with edges colored from the
above set of $k$ colors, if we consider the condition of excluding $H$ in the
above definition, we produce a \emph{Mixed Pattern Ramsey number}, denoted
$M_k(H)$. We determine this function in terms of $k$ for all colored $4$-cycles
and all colored $4$-cliques. We also find bounds for $M_k(H)$ when $H$ is a
monochromatic odd cycles, or a star for sufficiently large $k$. We state
several open questions.
