  We study constraint satisfaction problems on the so-called 'planted' random
ensemble. We show that for a certain class of problems, e.g. graph coloring,
many of the properties of the usual random ensemble are quantitatively
identical in the planted random ensemble. We study the structural phase
transitions, and the easy/hard/easy pattern in the average computational
complexity. We also discuss the finite temperature phase diagram, finding a
close connection with the liquid/glass/solid phenomenology.
