Open door
Number Theory
Level
2
A corridor has 1000 doors which are all closed.
- The first person to walk along the corridor changes the state of every door: they open every closed door.
- The second person only changes the state of every second door: they close every open door.
- The third person only changes the state of every third door: if it is open they close it, and if it is closed they open it.
- The fourth person only changes the state of every fourth door, and so on.
How many doors are open after the person has walked down the corridor?
30
31
32
33
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It is obvious that we are searching for perfect squares (numbers with odd number of divisors) under 1000.
here is how you can do this in Mathematica
Floor@Sqrt@1000but if you like to open and close doors, here is a much more difficult problem in ProjectEuler