Problem 46. Which doors are open?

There are n doors in an alley. Initially they are all shut. You have been tasked to go down the alley n times, and open/shut these doors in a particular manner:

  • Toggle the state of each door you visit. That is, if the door is shut, open it, and if the door is open, shut it.
  • On the i-th trip down the alley, start with door i and visit every i-th door.

Given n doors, return the list of open doors.

Example:

Let's say n = 3.

  • On your first trip, you start from the first door and toggle every door. Now all three doors are open.
  • On your second trip, you start from the second door and toggle every other door. Since there are only three doors, this means you shut the second door. Now doors 1 and 3 are open.
  • On your third trip, you start from the third door and toggle every third door. Now only door 1 is open.

So:

 Input  n = 3
 Output y is 1

Solution Stats

59.84% Correct | 40.16% Incorrect
Last Solution submitted on Apr 22, 2024

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