In Norway, cervical cancer prevention involves the participation of as many eligible women aged 25-69 years as possible. However, reaching and inviting every eligible women to attend cervical cancer screening and HPV vaccination is difficult. Using social nudging and gamification in modern means of communication can encourage the participation of unscreened people. Simula Research Laboratory together with the Cancer Registry of Norway have developed FightHPV, a mobile app game intended to inform adolescent and eligible women about cervical cancer screening and HPV vaccination while they play and, to facilitate their further participation to prevention campaigns. However, game design and health information transfer can be hard to reconcile, as the design of each game episode is more guided by the release of information than gameplay and playing difficulty. In this paper, we propose a constraint-based model of FightHPV to evaluate the difficulty of each episode and to help the game designer in improving the player experience. This approach is relevant to facilitate social nudging of eligible women to participate to cervical cancer screening and HPV vaccination, as shown by the initial deployment of FightHPV and tests performed in focus groups. The design of this mobile app can thus be regarded as a new application case of Artificial Intelligence techniques such as gamification and constraint programming.