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:

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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.


2 Answers 2



I think this is not possible.
Consider just A and F in isolation.
If both are okay, then at least B and C are broken.
If A is okay, but F is broken, then C and F are broken.
If A is broken but F is okay then A and B are broken.
If both are broken then A and F are broken so we always have at least two broken machines.


In the four scenarios considered in PROBLEM 01, the only one which produces exactly two broken machines is when A and F are both okay, in which case B and C must be the broken machines.

  • 1
    $\begingroup$ That was fast! I swear to God, one day I will post a puzzle so hard you will need an entire month to solve it, LOL! That's it. I'm just waiting to accept your answer. $\endgroup$
    – Pspl
    Nov 4, 2020 at 10:31

A compact answer:

A says C is broken. So, one of A and C is broken.
F says B is broken. So, one of B and F is broken.

It is clear from that that at least 2 machines are broken

If 2 machines are broken, they are among A, B, C, F. So E is reliable.
E tells us that between A and C, C is the broken one, and between B and F it is B.

You can check that if only B and C are broken, all other pannels are correct.


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