The Locker Problem

Hannah Van Arsdale
Penguinz
9/27/09

The Locker Problem
In total, 31lockers were opened and 961 were closed. The ones that were left open were perfect squares. This happened because the amount of their factors were uneven. As an example, locker 16 was left open because it is a perfect square. Students 1,2,4,8, and 16 touched it because these are all factors of 16. Ex: 1x1=16, 8x2=16, and 4x4=16. However, because 4x4=16, you only show one 4, making the number of factors odd. So if you used the locker 18 as an example, the students 1,2,3,6,9, and 18 would touch this locker. This would make an even amount of factors, having the locker stay closed.