What did Reynie discover about the supposed freedom of the children at the Institute?

Reynie’s discovery about the supposed freedom at the Institute reveals that, in fact, there were many rules governing the children's behavior and actions. While the outward appearance was one of independence and a lack of restrictions, Reynie came to understand that these rules were often subtle and enforced in ways that maintained control over the children. This realization highlights the manipulation and underlying structure of authority present at the Institute, contradicting the facade of freedom that the adults conveyed to the children. Recognizing the existence of these many rules was crucial for Reynie and his friends as it underscored the nature of their circumstances and the need for them to think critically about their environment and the intentions behind it.