Lemma 4 plays a central role in our analysis. It gives a bound on the number of terms which are almost satissed by an assignment a, in terms of k and j. It is natural to ask how good is this bound. The following example, due to Galia Givaty (private communication), shows that it is essentially optimal (up to constants). More precisely, for any values of k and j we give a function F k;j with k j...