Algorithms, puzzles

Logic puzzle. The three chests puzzle.


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Ok ok, this has nothing to do with coding, so why is it here? Well it’s a nice puzzle! And I felt good figuring it out. And this is my blog, and I post whatever I want mmmmmkay? Just kidding, I think it’s a fun puzzle and I would love to share the solution.



The puzzle challenges you with a very confusing starting condition. There are three chests in front of you, they are enumerated as A, B and C, each one of them has a label supposedly describing what’s inside the chest:

  • The label on chest A reads “100 gold coins”
  • The label on chest B reads “50 gold coins and 50 silver coins”
  • The label on chest C reads “100 silver coins”

I’m saying supposedly because, at this point, the puzzle kindly informs you that these labels are lying, each of them actually describes the content of a different chest.

Dammit.

Your goal is to figure out which chest contains the 100 gold coins. There is one thing you can do though. While blindfolded, you can pick one coin from a chest of your choice. You can check which coin you picked up, silver or gold, and use that information to figure out which chest holds the 100 gold coins treasure.
So from which chest should you pick up the coin?

Wanna give it a try? What follows is the solution so you should pause reading now if you feel like trying.

Solution

Like most problems, this one as well unravels it’s secret if looked at from a different point of view. Can we maybe read the labels in a different way? We know that a label does not describe the content of its chest. So let’s rewrite the labels as follows:

  • The label on chest A now reads “A does not contain 100 gold coins”
  • The label on chest B now reads “B does not contain 50 gold coins and 50 silver coins”
  • The label on chest C now reads “C does not contain 100 silver coins”

That helps a bit, at least we are not stuck, we are moving. However this does not provide any clue yet on where we should pick the coin from. The only eye catching information we have at this point is that the 100 gold coins are not in chest A. But this is not really useful yet.
Maybe we can do some more juggling with the labels to squeeze more informations out, for instance the sentence on chest A’s label after the first step says:

“A does not contain 100 gold coins”

We reverse this sentence and it becomes:

“Chest A contains either 50 gold + 50 silver coins or 100 silver coins”

Straightforward right? There are three possibilities for the content of chest A and the label already told us that the 100 gold coins are not inside chest A. So it must be one of the other twos. When we apply this to all three labels we get the following:

  • “Chest A contains either 50 gold + 50 silver coins or 100 silver coins”
  • “Chest B contains either 100 gold coins or 100 silver coins”
  • “Chest C contains either 100 gold coins or 50 gold coins + 50 silver coins”

Look at that! That’s our solution! We should pick a coin from chest B. By picking the coin from this chest we have two possible outcomes:

  • If we get a gold coin then we found our treasure chest. There are two possibilities for chest B, 100 gold or 100 silver coins.
  • If we get a silver coin then we know for sure that chest C contains our 100 gold coins treasure. Since they are not in chest B nor in chest A they must be in chest C.

The solution was there since the beginning, that’s what I liked about this puzzle, it seems really confusing at the beginning but the solution is actually hidden in the meaning of each label, all you have to do is go deeper when reading them. I hope you enjoyed this post, remember to always look at things using different eyes!

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