Help me find which rooms in the mansion have the lights on.
Here's how to play:
There are 25 rooms in the mansion and each room has one person staying overnight. The person from room #1 turns on the lights in every room of the mansion. The person from room #2 turns off the lights in every room that is a multiple of 2 (that means rooms 2,4,6,8,...20,22,24 have the lights turned off). The person from room #3 changes the position of every light switch in every room that is a multiple of 3 (that means room #3, which has the lights on, is then turned off, and room #6, which now has lights off, has its lights turned on). Remember that multiples of 3 are 3,6,9,12,15,18,...  The person in room #4 changes the position of every light switch whose room numbers are multiples of 4 (remember multiples of 4 are 4,8,12,16,20,24). This pattern continues for all 25 rooms.
Which rooms in the mansion will have the lights on?