  We study EC3, a variant of Exact Cover which is equivalent to Positive 1-in-3
SAT. Random instances of EC3 were recently used as benchmarks for simulations
of an adiabatic quantum algorithm. Empirical results suggest that EC3 has a
phase transition from satisfiability to unsatisfiability when the number of
clauses per variable r exceeds some threshold r* ~= 0.62 +- 0.01. Using the
method of differential equations, we show that if r <= 0.546 w.h.p. a random
instance of EC3 is satisfiable. Combined with previous results this limits the
location of the threshold, if it exists, to the range 0.546 < r* < 0.644.
