P4+Math

This is the problem of the week. If you have comments or questions, or want to answer someone else’s question, please click on the discussion tab above. If you need help on how to solve the problem – look there for help. A School has a hall with 100 lockers, all of which are closed. One hundred students start down the hall. The first student opens every locker. The second student closes all the lockers that are multiples of 2. The third student changes (closes an open locker or opens a closed one) all multiples of 3. The fourth student changes all multiples of 4. And so on. After all students have finished with the lockers, how many lockers are closed and which ones?