Let d equals d(n) be the minimum d such that for every sequence of n subsets F//1, F//2,. . . , F//N of left brace 1, 2,. . . , n right brace there exist n points P//1 P//2,. . . , P//N and n hyperplanes H//1 H//2,. . . , H//N in R**D such that P//J lies in the positive side of H//I if and only if j epsilon F//I. Then n/32 less than equivalent to d(n) less than equivalent to (1/2 plus o(1))n. This implies that the probabilistic unbounded-error 2-way complexity of almost all the Boolean functions of 2p variables is between p - 5 and p, thus solving some open problems.