How did the children discover Mr. Curtain's plan for world domination?

The children discovered Mr. Curtain's plan for world domination by reading classified press releases in the Institute Control Building. This method of discovery is significant because it demonstrates the children's resourcefulness and their adventurous spirit. They were determined to unveil the truth behind the mysterious activities at the Institute and did so by accessing official documents that were meant to be confidential. This moment is pivotal in the story as it not only reveals the extent of Mr. Curtain’s ambitions but also emphasizes the theme of the importance of knowledge and information in overcoming challenges.

In contrast, the other choices reflect less direct ways of discovering Mr. Curtain's intentions. Rumors among the Executives might suggest a level of speculation but lack concrete evidence. Mr. Benedict's secret meetings with the children focused more on their education and preparedness rather than revealing critical information about Mr. Curtain's plans. Hacking into the Institute's systems would imply a more technical approach and risk, which was not the method the children used. Thus, accessing the classified press releases stands out as the most accurate depiction of how they uncovered Mr. Curtain's true motivations.