<p>We build upon a recent definition of a common explanation for the label shared by a group of observations. The motivation stems from explaining how a specific action, when playing a card game, leads to an acceptable reward at the end of the game. Since there are various ways to achieve this goal, groups of acceptable trajectories are first extracted from a rule-based ILP model. Subsequently, common explanations are enumerated for each group of trajectories. A significant contribution of this article is the introduction of a new definition of preferred common explanations: they must be both subset-minimal and maximally instantiated. These so-called leq-minimal common explanations (<i>leq-MCE</i>s for short) happen to be subsets of the least general generalisation of the observations in the group. We propose efficient algorithms to enumerate <i>leq-MCE</i>s and a scheme to extract a diverse subset of these leq-MCEs to be presented to human interlocutors. Experiments are conducted on a card game.</p>