We propose a novel social robot called partially disembodied robot. This system has the advantages of real-world robots and virtual agents, guaranteeing a high social presence without sacrificing space efficiency. The robot consists of body parts that mimic human hands and eyes in order to give the user visual feedback, and is able to react to human contact through 3D detection, thus allowing the possibility for the user to interact through touching the robot. We evaluated how our system regulates users' behaviors during the solving process of the Tower of Hanoi problem. First, the users solve a Tower of Hanoi problem while being helped by the robot, but without having defined its body. In the second phase, the users were asked to define the robot's body and to play with it using the different interactions implemented. Finally, they were asked to solve the Tower of Hanoi problem once again, this time with the robot's body they defined. We could observe that the presence of the robot was perceived much more clearly by the user after they defined the robot's body, and when they were able to physically interact with it. Users' social response to the robot also seemed to be mediated by their feelings about its social presence. Finally, we found that the shyness of the users can impact the size of the robot's body that they define.