There are 100 students in a school, assigned numbers 1 through 100. Each student has a
Chapter 8, Problem 39(choose chapter or problem)
There are 100 students in a school, assigned numbers 1 through 100. Each student has a locker with the same number. When the school day starts, all lockers are closed. Student #1 then opens all 100 lockers. Student #2 then closes every other locker (namely those numbered 2, 4, . . . , 100). Student #3 then reverses every third locker (that is, opens a closed locker or closes an open locker beginning with the locker numbered 3). This continues with all 100 students. How many lockers are open at the end? How many lockers would be open if there are 1000 students and 1000 lockers?
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