Multi-Treasure Logic

Logic Level 1

You are in a room with three chests. You know at least one has treasure, and if a chest has no treasure, it contains deadly poison.

Each chest has a message on it, but all the messages are lying .

  • Left chest: "The middle chest has treasure."
  • Middle chest: "All these chests have treasure."
  • Right chest: "Only one of these chests has treasure."

Which chests have treasure?

Only A has treasure A and C have treasure Only B has treasure B and C have treasure Only C has treasure All of the chests have treasure A and B have treasure

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Jason Dyer by Jason Dyer

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4 solutions

Peter Macgregor
Nov 30, 2016

Taking B and C's false statements together shows that TWO of the chests contain treasure.

A's false statement shows that B does not contain treasure.

And so the treasure must be in chests A and C.

9 Helpful 1 Interesting 3 Brilliant 0 Confused

This is how i work mine out ( it may not be a correct technique, sorry) : A: The middle chest have treasure. B: All these have treasure. C: Only one of these chests has treasure.

Now, the key phrase is that all the messages on all the chests are lying. And look at Chests A's message, as it says that B have treasure. So, since it is lying, it should be that B does not have any treasure. Now look at B's message, "All of these chests have treasure," but you know that's a lie, and you already figured out that B does not have treasure, thanks to A's message. Now look at C's message, "only one of these chests have treasure," but it's a lie. Not one, but two. So, since it is two chests that have treasure, it should be A and C.

Janice Tan - 1 year, 10 months ago
Siva Budaraju
Nov 23, 2016

For the solution, I assuming left chest = A; middle chest = B; right chest= C.

First, the A says the B has treasure. So B must not have treasure. Then, B says all contain treasure. So, either 1 or 2 of them can contain treasure. But, C says only one contains treasure. So, 2 chests contain treasure. We already know B can't have treasure. So chests A & C contain treasure!

6 Helpful 0 Interesting 0 Brilliant 0 Confused

Doesn't the picture say a, b and c on the chest or was that picture added later?

Peter van der Linden - 4 years, 6 months ago

Picture was added later.

Jason Dyer Staff - 4 years, 6 months ago
Charity Aghahowa
Dec 11, 2016

Left chest: "The middle chest has treasure."

Middle chest: "All these chests have treasure."

Right chest: "Only one of these chests has treasure."

From looking at all of the statements, which are lies we are able to work out...

B does not have the treasure, not all of the chests contain treasure and more than one has treasure.

Therefore 2 chests have treasure and it is not B

Leaving us with the answer of A and C containing treasure.

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Leonardo DiPierro
Nov 28, 2020

Since all the statements are false, we should use logical negation towards them. Let's analyze these claims:

  • 'A' chest, the first one, says, 'the middle chest has treasure'. We know that it's a lie then the middle doesn't have any treasure.
  • 'B' claims that all chests have treasure. Okay, there're two true interpretations:
    1. 'All these chests don't have treasure';
    2. 'Not all these chests have treasure'; So, which one is correct? Let's continue thinking.
  • 'C' says, 'Only one of these chests have treasure'. Since the statement lies, we also have only two possible interpretations.
    1. 'Only one of these chests doesn't have treasure'
    2. 'Not only one of these has treasure' These two statements are not mutually exclusive. They are not contradictory and both are correct. Indeed, the first one says that there are two chests without treasure(and we know it's 'B'), and the second one claims that at least one has.

The 'B' chest also has two statements, but one of them isn't proper. 'Not all these chests have treasure' — this statement perfectly fits in(it is correct, because this chest is 'B') but not the 'All these chests don't have treasure' — we know that at least one has. So, the second B's statement logically invalid(it's contrary to the facts) therefore we use the first one.

Based on these reasonings, we can conclude that only 'A' and 'C' have treasure.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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