Human computation is a paradigm that relies on human beings to support resolution of computational problems. However, differently than machines, human beings need sorts of motivation to execute tasks. Games with a purpose are human computation systems that use entertainment as a motivational factor. To accomplish this, problems are modeled in a way that they can be solved through actions executed in those games. In these models, each player is considered a processing unit that composes a hybrid human-machine distributed system, in which each player executes tasks in exchange for fun. In the last years, many games to resolve computational problems have been created, such as text translation and image labeling. Nevertheless, in most of those games, the necessary task to solve the real problem, e.g., text digitalization, is directly assigned to players in a competition whose the winner is the one who types faster. Given this, in this work we adapt and formalize a model for elaboration of games with a purpose that isolates the problem that is being solved. The main goal of this model is to make players play without knowing the problem being solved. In addition, we also propose a method to estimate pairwise similarities based on this formalization, following an algorithm that finds clusters based on the estimated similarities. Finally, some games are implemented to evaluate the proposed method.