How does the wizard in the Hobbit rescue everyone?

 Gandalf rescues the dwarves with an invisible appearance. He periodically interrupts the trolls' conversation, saying false statements in voices that resemble the trolls' voices. Bert, William and Tom each conclude that the other two are lying and/or mad and of course, they engage in more physical brutality, whacking each other in the head and arguing until dawn is suddenly upon them and they turn into rocks.