In this paper I wish to discuss what is widely thought to be a critical problem for utilitarians, or at least for act-utilitarians. The problem is presented by situations in which the relevant utilities available are a function of group actions in a special way, viz., where the consequences of the group's acts are clearly crucial, but the way in which these co,nsequences distribute to the particular individuals who compose the group is loose or indeterminate. Popular examples are cases in which most of the group is required in order to get the thing done, but it doesn't matter which of many possible appropriate-sized subsets does it, and there is some reason for not performing in each individual case; cases in which what matters is that everybody does the same thing but it doesn't matter which thing everybody does; and cases in which both factors are at work. It is alleged that in these various situations, the individual who adheres to the act-utilitarian principle will correctly conclude that he ought to do the wrong thing; and yet everybody could, would, or should reason the same way, and hence the utility-maximizing action(s) can not be done even though everyone knows what they are. Everyone knows that a certain group action is the optimific action, but because of the peculiar problem about group consequences and looseness, it is impossible for this action to be performed. It is then inferred that utilitarianism, or act-utilitarianism as the case may be, is logically unsatisfactory, self-defeating, or even inconsistent. Sometimes this is held to be a reason why there must be a difference in principle between act and rule utilitarianism,