The paper presents the Olimpiadi di Problem Solving, a mild and inclusive competition aimed to promote computational thinking and general problem-solving in Italian schools. We describe motivation, teaching strategies behind the initiative, as well as its structure, organization and give some sample of the problems proposed to students. We also present some data that show the broad participation of Italian schools to the initiative, and a preliminary analysis of the results obtained by the students in the last 5 editions, which suggests that the competition fosters deep learning of computational thinking knowledge and skills.