Got my oxford university entrance test tomorrow and hate this question on an old paper. Getting really stressed now haha and would reallly appreciate an answer. Got to be without calculators too.
There are 1000 doors in a line. All are initially closed.
There are also 1000 students.
The first changes the state of every door, ie, opens them all.
The second person changes the state of every second door, ie, will close all the even numbers.
The third person changes the state of every third door, ie, if the third is open, they will close it, if the 6th is closed they will open it.
So on and every student changes the state of every door their number is a factor of.
You have to find how many doors are open after the 1000th person has been.
Does anyone know a way to do this without writing everything out incase something similar comes up tomorrow?
I think the second part said what if there were 2000 people and 2000 doors or something so there must be a formula of some sort for it.
I'm back off to revise :'(