A jail consists of 100 cells in a line, all starting out closed. The warden gets drunk one night and goes along opening every single cell. He then returns to the beginning, and "toggles" every second cell -- in this case, they're all open, so he closes every other cell door. He then runs to the beginning again, and "toggles" every third cell, then again with every fourth cell, and so on until the very last run in which he only toggles the hundredth cell, then drops down from exhaustion.

How many cells are left open after this process?