2020 SWMC 6 Problems

Problem 1

Give the only positive value of in .

Problem 2

An AoPS user is lining up the 5 names of his helpers in his Mock Contest. However, he does not want aops-g5-gethsemanea2 to be first, second, or third in line. How many ways can he arrange the names to still keep himself happy?

Problem 3

30 students lined up to get food from one of the cafeteria booths in their school. How many terminating zeros (zeros at the end) are in the number of arrangements of these 30 students?