  We study a class of random 3-SAT instances having exactly one solution. The
properties of this ensemble considerably differ from those of a random 3-SAT
ensemble. It is numerically shown that the running time of several complete and
stochastic local search algorithms monotonically increases as the clause
density is decreased. Therefore, there is no easy-hard-easy pattern of hardness
as for standard random 3-SAT ensemble. Furthermore, the running time for short
single-solution formulas increases with the problem size much faster than for
random 3-SAT formulas from the phase transition region.
