Two lovely brothers, Greg and Grey, like to annoy each other. They bought one hundred Christmas lights which can be switched on and off independently.
Greg switched on all the lights and went to the kitchen to get some gingerbread. Meanwhile, Grey flipped the switch of every second light (lights 2, 4, 6 etc.). When Greg returned after his snack, he flipped the switch of every third light (lights 3, 6, 9 etc.).
Siblings kept flipping switches until Grey changed the state of the 100th light. Afterwards, was the light number 48 on or off?
We can look at this little sibling fight as a game with 100 rounds. This 48th light was affected only in rounds whose number is a divisor of 48, i.e. rounds number 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48. After counting these divisors we understand that the 48th light was affected an even number of times (exactly 10), which means it’s off now.
What about the light number 50?
Certain about Uncertainty 