In this note we solve the Muntz problem for the space C(K) whenever K (0,1) is a countable compact set which satisfies certain additional as- sumptions and we propose the general case as an open question. Every introductory course in Approximation Theory should contain at least one proof of the following classical result, which is a nice generalization of the Weierstrass approximation theorem: Theorem 1 (Muntz, 1914). Let