# 1000 Prisoners in a cell

**Number Theory**Level 3

There are 1000 cells in a prison.Each cell has a prisoner. When i divide all the cell by a number (starting with 1 to 1000) and if the remainder is 0, then the door will be inverted (i.e. if it's close then it will open or vice versa). When i keep those cells on dividing till 1000, at last how many cells will be opened? Initially all doors are closed..... Let's take an example:- if i divide all the cells(1 to 1000) by 1,then remainder will be 0 for all cells. Therefore every cell will open.Now, if i divide again by 2 then only even number's cell will close.I continue this process till 1000...How many cells are open????