  Finally, it seems plausible to assume that probabilities vary continuously as we change directions in R3, so small imperfections of selection of observables that block the argument (but only for measured values!) in the single case will wash out in the long run (see Mermin 1999, in Other Internet Resources). This in itself does not constitute an argument, since in the colourable sets of observables in MKC’s constructions probabilities also vary (in a sense)  continuously.[17]  We might, however, exploit Mermin’s reasoning in the following way. Reconsider Clifton’s set of eight directions (in Figure 3) leading to a colouring constraint for the outermost points which statistically contradicts the QM statistics by a fraction of 1/17. Using Clifton and Kent’s colourable set of directions DCK we are unable to derive the constraint for the eight points, since these eight points do not lie in DCK; namely, as we move, in the colourable subset, from one mutually orthogonal triple of rays to the next, we never hit upon exactly the same ray again, but only on one approximating it arbitrarily closely.  Assume a set S of systems wherein observables, corresponding to members of DCK and approximating the eight directions in Fig. 3 arbitrarily closely, all have values — in accordance with the HV premise. Then we can derive Clifton’s constraint for the outermost points in the following sense. Consider the subset S′ ⊂ S of systems where any direction approximating point (1, 1, 1) gets value 1 (or colour white). In order to meet the predictions of QM, in S′ all directions approximating (1, 0, −1) and (1, −1, 0) must receive values such that the probability of value 0 (or colour black) is extremely close to 1. Analogously, in another subset S″ ⊂ S of systems with directions approximating (−1, 1, 1) as having value 1 (colour white) all directions approximating (1, 0, 1) and (1, 1, 0) must receive values such that the probability of value 0 (colour black) is extremely close to 1. Consider now members of S′ ∩ S″. In any of them there will be, for any approximation to (1, 0, −1) with value 0 (colour black), an exactly orthogonal point that approximates (1, 0, 1) and also has value 0 (colour black) such that there is a third orthogonal point approximating (0, 1, 0) and having value 1 (colour white). Likewise for (0, 0, 1). But (0, 1, 0) and (0, 0, 1) are orthogonal, and for all members of S′ ∩ S″ the directions approximating them both have value 1 (colour white), while QM predicts that the probability for values 1 for the approximated directions values is 0. In order to ensure that this prediction is met, S′ ∩ S″ must be an extremely small subset of S, which is to say that the probability for both (1, 1, 1) and (−1, 1, 1) (the leftmost and rightmost points in fig. 3) must be close to 0 and approximate 0 better and better as S grows. QM, on the contrary, predicts a probability of 1/17. (Recall also that this number can be pushed up to 1/3 by choosing a set of 13 directions!)