Mick gets some (the odds are on his side) (satisfiability)
Vašek Chvátal, Bruce A. Reed · 1992
Consider a randomly generated boolean formula F (in the conjunctive normal form) with m clauses of size k over n variables; k is fixed at any value greater than 1, but n tends to infinity and m = (1 + o(1))cn for some c depending only on k. It is easy to see that F is unsatisfiable with probability 1-o(1) whenever c>(ln 2)2/sup k/; the authors complement this observation by proving that F is satisfiable with probability 1-o(1) whenever c1.>