A group of 21 students participates in a discrete mathematics competition. There are Q questions that have to be answered. For each question exactly 4 students are assigned to work together, while the others take a short break. The questions are distributed to ensure that every pair of students only works together on exactly one exercise. This works out exactly! How many exercises does the competition have? (Hint: Consider how many pairs occur in a group of 4 students.)
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Answer:Q=35 - number of questions