Do young children appreciate the importance of access to premises when judging what another person knows? In Experiment 1, 5-year-olds (N=31) were sensitive to another person's access to premises when predicting that person's ability to point to a target after eliminating alternatives in a set of 3 cartoon characters. Experiment 2 replicated the finding when 5- to 6-year-olds (N=102) judged who the other person thought the target was, and whether the other person knew who the target was. Experiment 3 demonstrated that children aged 57 years (N=107) more successfully imputed inference by elimination than syllogistical inferential knowledge. Findings suggest that an early understanding of inference by elimination offers a route into understanding that people can sometimes gain knowledge without direct perceptual access.