Mobile interactions with public displays are often indirect and not very convenient for multiple users at the same time. In this paper we use the physical, touch-based interaction with Near Field Communication (NFC) to investigate direct mobile interactions with public displays for multiple users. For that purpose, we adopt the Whack-a-Mole game for dynamic NFC-displays, which combine the physical interaction with NFC-tagged objects and the visual output capabilities of public displays. We show that a grid of NFC-tags can be used to implement direct mobile interaction with public displays in general and a highly interactive multiplayer game in particular. Our study shows that users appreciate this physical, NFC-based mobile interaction, although technical advances are still necessary in order to improve its recognition rate of about 70%. The study also indicates that users are willing to interact with large displays in public, but prefer private or semi-public places, where their interactions attract less attention.