Young children's (n = 108) and adults' (n = 40) ability to compute ad-hoc quantity conversational implicatures was assessed using a new implicit task that relied on eye-tracking. The children were 2 and 5 years old. Looking times reveal that all participants interpreted simple references by relying on implicatures. However, 2-year-olds failed to derive standard ad-hoc implicatures and succeeded only on a novel type of implicature based on typicality, which was proposed with the aim of reducing the salience of non-target potential referents. These results suggest that even toddlers are able to derive conversational implicatures and that domain-general inhibitory demands, rather than domain-specific limitations in pragmatic reasoning, may play a crucial role in children's difficulties with implicatures.