Can outreach inspire and lead to research and vice versa? In this work, we introduce our approach to the gamification of research in mathematics and computer science through three illustrative examples. We discuss our primary motivations and provide insights into what makes our proposed gamification effective for three research topics in discrete and computational geometry and topology: (1) DominatriX, an art gallery problem involving polyominoes with rooks and queens; (2) Cubical Sliding Puzzles, an exploration of the discrete configuration spaces of sliding puzzles on the $d$-cube with topological obstructions; and (3) The Fence Challenge, a participatory isoperimetric problem based on polyforms. Additionally, we report on the collaborative development of the game Le Carré du Diable, inspired by The Fence Challenge and created during the workshop Let's talk about outreach!, held in October 2022 in Les Diablerets, Switzerland. All of our outreach encounters and creations are designed and curated with an inclusive culture and a strong commitment to welcoming the most diverse audience possible.