Assignment:
Students at an elementary school tried an experiment. When recess was over, each student walked into the school one at a time. The first student opened all the first 100 locker doors. The second students closed all the locker doors with even numbers. The third student changed all the locker doors with numbers that were multiples of three (change means close the open doors and open the closed doors). The fourth student changed all dors numbered with multiples of four; the fifth student changed all doors that were multiples of five, and so on. After 100 sutdents had entered the school, which locker doors were open?
Provide complete and step by step solution for the question and show calculations and use formulas.