AoPS Wiki talk:Problem of the Day/August 23, 2011

Twenty bored students take turns walking down a hall that contains a row of closed lockers, numbered $1$ to $20$ . The first student opens all the lockers; the second student closes all the lockers numbered $2$ , $4$ , $6$ , $8$ , $10$ , $12$ , $14$ , $16$ , $18$ , $20$ ; the third student operates on the lockers numbered $3$ , $6$ , $9$ , $12$ , $15$ , $18$ : if a locker was closed, he opens it, and if a locker was open, he closes it; and so on. For the $i^{\text{th}}$ student, he works on the lockers numbered by multiples of $i$ : if a locker was closed, he opens it, and if a locker was open, he closes it. What is the number of the lockers that remain open after all the students finish their walks?

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AoPS Wiki talk:Problem of the Day/August 23, 2011