If 20 are not in any of the groups, we are left with 80 "interesting" students. Since we are told that there are more students on the fencing team, that number should be at least 71. If it is 71 then we have 80 students, among whom 71 are in the team and 70 are in the club. Therefore, the number of students who attend both = 71 + 70 - 80 = 61 (|A| + |B| - |A ∩ B|, where A is the set of the students in the team, B is the set of the students in the club). You can draw a Venn diagram if you want to see things more clearly. Finally, you need to observe that if there were more students on the fencing team (e.g. 72, 73, etc), the number of students who attend both would be larger. So 61 is the minimum.