3.1. Alina and Masha wanted to create an interesting version of the school tour olympiad. Masha proposed several problems and rejected every second problem of Alina's (exactly half), Alina also proposed several problems and did not reject only every third problem of Masha's (exactly a third). In the end, there were 10 problems, and initially, 27 were proposed. How many more problems did Masha propose than Alina?
Answer: 15

Solution. In total, 17 tasks were rejected. Note that among the tasks proposed by Alina, an equal number were included and rejected, and among the tasks proposed by Masha, the number of rejected tasks is twice the number of tasks that remained in the variant. Since the number of rejected tasks is 7 more than those included, exactly 7 of Masha's tasks were included in the variant, meaning she proposed 21. Since 3 of Alina's tasks were included, she proposed 6. The difference in the number of proposed tasks is $21-6=15$.