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Vernonia High School has 85 seniors, each of whom plays on at least one of the school’s three varsity sports teams: football, baseball, and lacrosse. It so happens that

74

are on the football team;

26

are on the baseball team;

17

are on both the football and lacrosse teams;

18

are on both the baseball and football teams; and

13

are on both the baseball and lacrosse teams. Compute the number of seniors playing all three sports, given that twice this number are members of the lacrosse team.

Problem Statement