Stolen!

Logic Level 2

A museum called worldwide museum, there are three historical objects, these are, Gun of Robert Clive, shield of Mughal emperor Akbar and the sword of Genghis Khan. At night all three objects were stolen by thieves. The security guard noticed that and called the cops. Cops arrested three suspicious peoples , they are Albert, Bob and Cod. They make three statements,

Albert: Cod stole the gun.

Bob: Cod stole the sword.

Cod: Both are lying.

• One who has the shield always lies.

• One who has the gun always tells truth.

Who stole the shield?

Bob Albert Cod

2 solutions

Maximos Stratis
Jun 11, 2017

We will prove this by contradiction.

Assume Bob stole the shield
Then, Bob is lying which means that Cod did not steal the sword. By that we conclude that Cod has the gun and Albert has the sword. Cod, who has the gun and says the truth, says that Albert is lying which means that Cod did not steal the gun. Contradiction

Assume Cod stole the shield
Then, Cod is lying which means that at least one of them is telling the truth. But if either of them tells the truth that means that Cod stole the gun or the sword, according to which one tells the truth. Contradiction

Thus, it was $\boxed{Albert}$ who stole the shield.

Assuming that all three of them are guilty of stealing one thing each, and they they each knew what the others stole.

Siva Budaraju - 3 years, 12 months ago

Of course! Is there any way to do it without using these?

maximos stratis - 3 years, 12 months ago

There is. There are only 2 implied assumptions :
1) all the suspects knew who stole what, no matter their guilty or innocent status, and
2) the guilty party / parties are none other than the 3 suspects.

Saya Suka - 4 months ago

Assume Bob stole the shield

Your explanation : "Then, Bob is lying which means that Cod did not steal the sword. By that we conclude that Cod has the gun and Albert has the sword. Cod, who has the gun and says the truth, says that Albert is lying which means that Cod did not steal the gun. Contradiction"

B stole the shield. B lied. The sword wasn't stolen by C, so possibly by A or B himself. The gun can't be stolen by C who denied doing it or by A who falsely accused C. So B must also stole the gun, but B can't be both always lying (as shield thief) AND always tells the truth (as gun thief). ==> Contradiction

Assume Cod stole the shield

Your explanation : "Then, Cod is lying which means that at least one of them is telling the truth. But if either of them tells the truth that means that Cod stole the gun or the sword, according to which one tells the truth. Contradiction"

C stole the shield. C lied. The denials are both false. Both the other 2 statements are true, and thus C stole them all. Again, this time instead of B, it's C as the sole thief of the 3 artefacts who can't be both always lying (as shield thief) AND always tells the truth (as gun thief). ==> Contradiction

Saya Suka - 4 months ago

Saya Suka
Feb 4, 2021

Albert : Cod stole the gun.
Bob : Cod stole the sword.
Cod : Both are lying.

• One who has the shield always lies.
• One who has the gun always tells truth.

At least two of the three gave statements that are contradictory to each other, with A accusing C with gun, B accusing C with sword and C denying both accusations.

Since we are told that the gun thief always tell the truth, that means if a gun thief was rightly accused by another truth-teller, then the truthful defendant would have to fess up to that crime. But the scenario at hand didn't happen this way, thus the one accused to be gun thief, C, must be innocent of gun stealing AND that his accuser, A, must be totally lying.

Now that we know that both of C and A can't be the gun thief (C by his truthful denial whilst A by his false accusation that amount to lying, as both should be impossible actions for a truthful gun thief), and considering that the gun is somehow still missing, then it could only be B who stole it.

Since B as a gun thief must be truthful, then C must have truly stole the sword and his denial is a lie in regards to B's true accusation, but on the other hand his denial is true regarding A's false accusation.

Since B is completely truthful and C is partially truthful, then we're only left with a completely lying A ==> A must be the shield thief.

Notes

No other assumptions are made other than that the thief or thieves are amongst the suspects caught. Even this is implied within the 2 bulleted claims of the actual stealer(s) credibility (if any of the artefacts was stolen by anyone other than the suspects, then there won't be any meaningful point made because the 'actual' thief or thieves could not have said anything completely true nor anything completely false since their statement(s) aren't being taken by the detectives in the investigations that resulted in the 2 bulleted conclusions).

You don't have to assume they ONLY stole ONE article EACH, but you can be sure that those who is / are guilty must be amongst the 3 (with an open mind of possible innocent suspect(s) from the earliest beginning of your deductions, plus the possibility of a thief having stolen multiple items all by himself). We also have to consider that by the 2 conclusions we're given, then it is implied that the suspects all knew who stole what and not ignorant to these facts to be able to tell either the truths or even lies, both meaningfully and successfully.

Stolen!

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