What device do the children utilize to signal Mr. Benedict?

The children utilize a flashlight to signal Mr. Benedict, which is an effective method of communication, especially in situations where they need to remain discreet or avoid drawing attention. Flashlights can produce distinct visual signals, such as Morse code or simple on-and-off patterns, which allows for a covert way of signaling at a distance. This method is particularly suitable in the context of their adventures, where stealth and secrecy are often paramount, reflecting the clever and resourceful nature of the main characters.

The other options, while potentially useful in different contexts, do not align as closely with the skills and situations presented in the story. A horn or bell would make noise and could attract unwanted attention, while a mirror, while possibly useful for signaling via reflected light, may not have been practical or effective in the specific scenarios the children encountered. Therefore, the flashlight not only serves its purpose well but also complements the overall theme of ingenuity and subtlety present in "The Mysterious Benedict Society."