The current study looks at preschoolers ability to discover higher-order patterns spontaneously, without being explicitly taught to do so. The higher-order pattern of interest was the degree of transitivity among the relations of three arbitrary dimensions. Preschoolers and adults were taught two relations (i.e., A = B; B = C), and they were asked to guess the third relation (i.e., between A and C). In each case, a relation was a perfect correlation between two arbitrary relations (e.g., heavy = large). The crucial manipulation pertained to how difficult it was to learn the two relations. The two relations either matched in direction (which was conceived as low learning difficulty), or they had opposite directions (which was conceived as high learning difficulty). Our prediction was that the higher-order pattern of transitivity becomes apparent when learning difficulty is high. The argument is that a local mismatch makes it difficult for children to focus merely on the isolated relations, and thus sets the stage for higher-order insights. Results confirm our hypothesis, both for preschoolers and adults. Participants were more likely to engage in higher-order transitive reasoning in the case of a local mismatch between the to-be-learned relations than in the case of a local match.