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Students then look for patterns and write the answer algebraically.
There are 1000 lockers, all shut and unlocked, and 1000 students. Suppose the first student goes along the row and opens every other locker. The second student then goes along and shuts every other locker beginning with number 2. The third student changes the state of every third locker beginning with number 3. The fourth student changes the state of every fourth locker beginning with number 4.