  We present the exact and precise (~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.
