We present BrainNet which, to our knowledge, is the first multi-person non-invasive direct brain-to-brain interface for collaborative problem solving. The interface combines electroencephalography (EEG) to record brain signals and transcranial magnetic stimulation (TMS) to deliver information noninvasively to the brain. The interface allows three human subjects to collaborate and solve a task using direct brain-to-brain communication. Two of the three subjects are "Senders" whose brain signals are decoded using real-time EEG data analysis to extract decisions about whether to rotate a block in a Tetris-like game before it is dropped to fill a line. The Senders' decisions are transmitted via the Internet to the brain of a third subject, the "Receiver," who cannot see the game screen. The decisions are delivered to the Receiver's brain via magnetic stimulation of the occipital cortex. The Receiver integrates the information received and makes a decision using an EEG interface about either turning the block or keeping it in the same position. A second round of the game gives the Senders one more chance to validate and provide feedback to the Receiver's action. We evaluated the performance of BrainNet in terms of (1) Group-level performance during the game; (2) True/False positive rates of subjects' decisions; (3) Mutual information between subjects. Five groups of three subjects successfully used BrainNet to perform the Tetris task, with an average accuracy of 0.813. Furthermore, by varying the information reliability of the Senders by artificially injecting noise into one Sender's signal, we found that Receivers are able to learn which Sender is more reliable based solely on the information transmitted to their brains. Our results raise the possibility of future brain-to-brain interfaces that enable cooperative problem solving by humans using a "social network" of connected brains.