Genius

Kadin was working on a math problem for his homework and asked for my help. He actually didn't bring the problem home but said he remembered it. He tried to explain it to me and it was something like this:
A jail has 100 cells. The guard comes in the first day and unlocks all the cells. On the second day he locks all the cells that are multiples of two. On the third day he unlocks all the cells that are multiples of 3 (or something like that, Kadin wasn't exactly sure) and so on. The question was, on the 100th day, which cells would be unlocked?

So we agreed there must be a pattern. Kadin had gone through and figured out