Question

This is extension to the Locker problem.“One hundred students are assigned lockers 1 through 100. The student assigned to locker number 1 opens all 100 lockers. The student assigned to locker number 2 then closes all lockers whose numbers are multiples of 2. The student assigned to locker number 3 changes the status of all lockers whose numbers are multiples of 3 (e.g. locker number 3, which is open gets closed, locker number 6, which is closed, gets opened). The student assigned to locker number 4 changes the status of all locker whose numbers are multiples of 4, and so on for all 100 lockers. Which lockers would stay open at the end of all 100 runs?”

Now Suppose one day, few students are absent. Regardless, those present complete the procedure and skip the students who are absent. For example, if student #3 is absent, then nobody changes the status of all lockers whose numbers are multiples of 3. At the end of the process, only locker number 1 is open and all the other 99 lockers are closed. How many students were absent that day?

Answer 1