There are 100 closed doors in a row, numbered 1 to 100. A person walks by each door, opening every door. A second person walks by each door, closing every second door (doors 2, 4, 6, …). A third person walks by, toggling every third door (closing open doors, opening closed doors). This continues for 100 people. After all 100 people have walked by, which doors are open?
Answer
Doors whose numbers are perfect squares (1, 4, 9, 16, 25, 36, 49, 64, 81, 100)