We present the exact and precise (\sim 0.1\%) numerical solution of the QCD evolution equations for the parton distributions in a wide range of Q and x using Monte Carlo (MC) method, which relies on the so-called Markovian algorithm. We point out certain advantages of such a method with respect to the existing non-MC methods. We also formulate a challenge of constructing non-Markovian MC algorithm for the evolution equations for the initial state QCD radiation with tagging the type and x of the exiting parton. This seems to be within the reach of the presently available computer CPUs and the sophistication of the MC techniques.

PACS numbers: 12.38.Bx, 12.38.Cy