We report on the design process and the design rationales of a physical mini-game, to be played by seniors and youngsters. First, we explain that we seek enactive interaction, rather than physical action. Next, we elaborate on how competition correlates with social interaction, relying on FIRO theory. Then, we analyze how the sensor technology within the WiiMote affords acceleration. Via an evaluation of existing physical mini-games, seniors and youngsters empirically verify these three design rationales on enactive interaction, competition and acceleration. We conclude that these rationales result in ease-of-use, equality-in-ease-of-use and visibility-of-player-action, which in turn stimulate competition and consequently intergenerational play. Finally, we present the design and user evaluation of our physical mini-game, designed in accordance with these rationales.