A colored space is the pair (X,r) of a set X and a function r whose domain is (X2). Let (X,r) be a finite colored space and Y,Z⊆X. We shall write Y?rZ if there exists a bijection f:Y→Z such that r(U)=r(f(U)) for each U∈(Y2). We denote the numbers of equivalence classes with respect to ?r contained in (X2) and (X3) by a2(r) and a3(r), respectively. In this talk we prove that a2(r)≤a3(r) when 5≤|X|, and show what happens when the equality holds. This is joint work with Masashi Shinohara.