Light Switch Problem

[P4 Maths and Up: Factors]

Kept you waiting, huh?

The light switch problem is easily addressed if you consider the factors of the numbers being pressed. For example, (5x5 = 25), and number 25 only has three factors: 1, 5 and 25. As the number of factors are odd, the light switch will be touched precisely 3 times. If the light switches were switched off from the start, they will stay switched on; if they were switched on from the start, they will switch off.

This property is available only to perfect squares. Most other numbers won't have an odd number of positive factors to make the problem work.