Christmas is coming and Santa is working hard to wrap all the presents until the 24th of December.
He has six wrapping machines: A, B, C, D, E and F, that work $24/7$ all at the same time. But the harsh weather of the North Pole keeps breaking the machines. Each machine has a panel that indicates the state of one or two other machines. However, if that machine is broken itself, the displayed information on its panel may not be true. However, if a machine is working properly, its panel displays valid information.
The elves made a Main Control Panel so Santa can track all the six individual panels at once. On a certain day, Santa sees the this display on the Main Control:
PROBLEM 01: Given this display, is there any way of having just one broken machine?
PROBLEM 02: If Santa has two broken machines, which ones are they?
This is an old puzzle from a book I had when I was a kid.