The paper presents a collection of problems from the Chernorizec Hrabar math tournament that takes place in Bulgaria during the last 28 years. The formulation of a question as a probability problem is used for different math ideas to be linked in a complex test unit. The complexity of the problem requires searching for the correct answer by applying not only advanced math knowledge and skills, but also a synthetic-type thinking, including some sense of mathematics. The multiple-choice format of the tournament problems allows students to skip a lot of routine work and to focus on the purified mathematical ideas. On one hand, the expected reasoning for the answer choice appears as an extract of the comprehensive problem solution. On the other hand, the reasoning forms the carcass of a sophisticated math task that challenges student�s synthetic competence.