Who is the narrator, can she or he read minds, and, more importantly, can we trust her or him?
Third Person (Omniscient)
Although we do see things from particular characters' points of view (mostly Reynie, Sticky, and Kate), this story is being told by an omniscient narrator who knows what everyone is thinking or feeling at any given moment.
The story starts out seeming like it's going to be mostly from Reynie's point of view, which makes us think it will be a third person limited voice, but we quickly realize that's not the case when we begin to hear things like, "In the end every child decided to join the team, though the decision was more difficult for some than others" (5.1), and "the children longed for more answers" (5.20). These are thoughts and feelings that a narrator whose perspective was limited to what one character at a time couldn't possibly know.
And the more we read, the more we start realizing that we're getting multiple characters' perspectives all at once. We know Sticky's anxious and Kate's outraged when Martina catches Sticky sleeping in class (15.59-60), and we know how all four members of the MBS are feeling when they're in the cafeteria trying to come up with a plan despite being preoccupied with other worries (32.75-78).
What's more, sometimes the narrator seems to know what's going to happen before it does, like when we are told, that "Reynie could not know what would happen, and this was fortunate. For if he had known, he would never have slept so easily" (28.111). When your narrator knows stuff like that? That's a sure sign you're dealing with an omniscient narrative voice.