Let A be an m x n matrix with entries drawn from a normal distribution with zero mean. The probability that the set of linear inequalities A.x > 0 has a solution (for the n-component vector x) is a fun calculation (try it!) and, I'm told, was first worked out by Ludwig Schlaefli. For large m and n the probability switches abruptly from 1 to 0 as the ratio m/n passes through 2. There is a similar phenomenon for the much harder problem of random 3-SAT formulas, where they abruptly become unsatisfiable when the ratio of clauses to variables crosses a threshold. In that problem it is hardest, computationally, to determine satisfiability right at the transition. Does the easier linear programming problem have a similar complexity peak at the transition? -Veit