MathsShare

There are 100 prisoners in 100 separate locked cells. During the night each of 100 prisoner officers visits the cells. The first officer visits every cell. The second officer visits cells 2,4,6,... etc (every 2nd cell), the third officer visits every third cell, the fourth officer visits every fourth cell and so on until the 100th officer visits the 100th cell. On a visit each officer unlocks the door if it is locked or locks the door if it is unlocked.  In the morning, how many prisoners escape and why?