math riddle

here's the question

their is a jail with 100 jail keepers and 100 cells in a row numbered,the first jail keeper goes down the row of cells and unlocks all the multiples of 1.The second locks all the multiples of 2 or unlocks.the thrid unlocks or locks all the multiples of 3 and so on until the 100 jailkeeper locks or unlocks the last one.which jail cells are unlocked  

i dun know

the answer is all the

square numbers

because they have a odd number of multiples

i know this one; its 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100