and the problem is we can't now look separately at each of those cliques and pick an assignment because at that point we might pick, say, this assignment in this clique and this assignment in that clique and now we have a conflict in regarding the value of the variable b. and it's not just a matter of saying, well, okay let's forget, for example, the fact that we picked the value b2 in this clique over here because what you, because we also picked the value c2 and intuitively we can see that c2 goes with b2 and not with b1.