100 gold coins

Relevant wiki: Truth-Tellers and Liars

• Chest A labelled 100 gold, cannot contain 100 gold. Therefore, either Chest B or Chest C contains 100 gold.
• Chest B labelled 50 gold and 50 silver, can contain either 100 gold or 100 silver. If we pick a coin from Chest B, there would be only two cases: $\begin{cases} \text {If it is gold then Chest B contains 100 gold.} \\ \text {If it is silver then it contains 100 silver and Chest C contains 100 gold.} \end{cases}$ .

Therefore, the answer is to pick a coin from $\color{gold}{\boxed{Chest \space B}}.$

Let $G$ , $GS$ , $S$ (denoting "100 gold coins", "50 gold and 50 silver coins" and "100 silver coins" respectively) be the real contents of the boxes. Then one of these has to be the case

$Chest A=GS$
$Chest B=S$
$Chest C=G$

or

$Chest A=S$
$Chest B=G$
$Chest C=GS$

Hence, poll $Chest B$ to find out which is which.

Chest B must contain entirely gold coins or entirely silver coins (since its label is incorrect). Taking a coin from Chest B will determine what its contents is. As it turns out, the information obtained is enough to determine the contents of the remaining two chests; for example, if Chest B has gold coins, then Chest C must be the mixed coins (since its label is wrong, and among its remaining two possibilities, one is discarded for being Chest B), and Chest A is the silver coins. Thus the answer is Chest B .

To show that Chest A and Chest C are not the answer, just see that if we get a silver coin from Chest A or a gold coin from Chest C, we don't gain any information; all possibilities still remain.

Chest A labelled 100 gold, cannot contains 100 gold. Therefore, either Chest B or Chest C contains 100 gold. Chest B labelled 50 gold and 50 silver, can contain either 100 gold or 100 silver. If we pick a coin from Chest B, there would be only two cases: . Therefore, the answer is to pick a coin from CHEST B

My "plain English" solution.

So we only get one shot at getting information that lets us figure out which box has what coins. With the goal of getting useful information, we can solve this pretty easily.

Checking box A is risky. There's no possibility of it being the gold box, so if I draw a gold coin, I know I've got the 50/50 box. But if I draw a silver, I have no way of telling whether A is the 50/50 or silver box., so I literally have no new information. If you check from box C, you get a similar result, but with silver.

However, since I know that the signs are all wrong, I know that box B is either all gold or all silver. So lets draw from that:

If I get a silver coin, I know that Box B is all silver. Since Box A can't be gold (because the sign is wrong), and since I just figured out box B is all silver, Box A logically has to be the 50/50 box. That leaves us with box C as the gold box. If I draw gold from Box B, then I can use the same logic to conclude that Box C is the 50/50 box, and box A is all silver.

Long story short, check box B.

If every chest is labled wrong, than chest a couldnt contain 100 cold, and with that said, chest b couldnt contain 50 gold and 50 silver, and cheat c couldnt contain 100 silver. Now, go back to chest b. If it cannot contain 50/50 of each gold and silver, than it can only contain of 100 silver or gold. Therefore, chest b is the chest u should choose, because it is the chest with 2 possible outcomes. The other two chests have an outcome of either 50/gold and 50/silver, or 100 gold or 100 silver, making it impossible to know

If incorrectly labeled, chest b will either be 100 gold coins or 100 silver coins.

choosing B there are just 2 possibilities: you pick a silver coin, so this chest contains 100 silver coins for sure, the chest labeled 100 silver coins must contain 100 gold coins and the other one, labeled 100 gold coins, contains 100 silver coins. If you pick up a gold coin... the same chest contains 100 gold coins, the chest labeled 100 silver coins contains 50-50 and the last one, labeled 100 gold coins contains 100 silver coins.

There are no other possibilities, considering that ALL the chests must be wrongly labeled.

As all chests are labelled wrong, chest B will contain either 100 Gold coins or 100 Silver coins. Pick a coin from chest B, if it comes gold then chest B contains 100 Gold otherwise chest C will contain 100 Gold.

1. Chest A = 50+50 or 100S [Discard chest A]
2. Chest B = 100G or 100S

3. Chest C = 50+50 or 100G

4. Attempt : Pick from chest B. Possible outcomes = 1G coin or 1S coin

If 1G coin implies all coins are gold (from step 2) - implies chest B has 100G coins

If 1S coin implies all the coins are silver (from step 2) - implies chest C has 100G coins

I read it as one chest having x, another having y, and the third having half x plus half y. Since x and y are equally infinite variables, it had to have been chest B.

Because the labels are wrong, the chest labeled 50/50 must contain either pure gold or pure silver, while the other two are uncertain, therefore making B the best choice.

Since the label is incorrect, you know that box b DOES NOT have 50 gold plus 50 silver; therefore it must have either all gold or all silver. So, picking one coin out of that box will tell you which box has the gold coins.

There can be only one

You have to choose B since from thr wrong label you know B contains either all gold or all silver. So if you pick a gold coin from B that means B is the chest with all gold. If you pick a silver from B tbat means B is all silver. So the chest with all gold is C since A has the wrong label.

It doesn't make sense to me. I would assume that 50 gold coins and 50 silver coins are better in value than 100 silver coins. If that is the case, then it is best to choose Chest C because you know that Chest C cannot have 100 silver coins since the chests are incorrectly labelled.

Everything is mislabeled, so we immediately know that Chest A is not all gold. Thus the all-gold chest is either Chest B or Chest C.

We also immediately know that Chest B must be either all gold or all silver, but not a mix. So take a coin from Chest B.

If it is gold, then you know Chest B is all gold. You're done.

If it is silver, then you know that Chest A is not all gold and that Chest B is not all gold. Therefore Chest C must be all gold.

Chest B is incorrectly labeled essentially as the only "mixed" chest. This means that Chest B Must be either all gold or it is all silver. Thus drawing one coin out of Chest B lets us know what EVERY coin in Chest B is. This gives two cases.

Case 1: We drew a gold coin out of Chest B Congratulations, you know for sure that Chest B is the 100 gold piece chest.

Case 2: We drew a silver coin out of Chest B We know that Chest B is the 100 silver coin chest. Since we know that each chest is incorrectly labeled, Chest A cannot be the 100 gold chest. Chest A cannot be the 100 silver coin chest, because that's Chest B. Thus, Chest A must be the 50/50 chest. With 2 of the chests determined, we know what Chest C is; the gold chest.

Thus, drawing one coin from Chest B informs us either way.

From the condition givens, we know chest b wont have 50gold coins+50silvercoins. That means it can only contains 100gold or 100silver. So just check chest b since you can know which chest will have the 100gold since : if you get 1gold coin that means it is the right chest. And if you get 1 silver. It means it contains 100silver coins. So theright must be chest c because chest a wont contain 100gold coins

The label is known to be wrong. The chest which is labelled "in doubt" is chest B: "50 gold and 50 silver". Therefore, the content of chest B could not be "50 gold and 50 silver" actually. The possibility is 100 gold, or 100 silver. That should be our major point break in finishing the problem.

Must be B. If all are false, then it must either have all gold or all silver. If piece is gold, then B has all the gold. If silver, then as A can't be correct due to it's false description saying it is, the chest with all gold would be C.

• A either has 50 silver/50 gold or 100 silver. B either has 100 silver or 100 gold. C either has 50 silver/50 gold or 100 gold.

• If you picked A, and a silver coin comes up, it tells you nothing about that chest or the others, as a silver coin could mean it is either 50 silver/50 gold OR 100 silver, and we already knew it had to be one of those two. If a gold coin comes up, it must have 50 silver/50 gold, which means C is the one with 100 gold. However this only gives you a 25% chance of knowing.

• If you picked C, and a gold coin comes up, it tells you nothing about that chest or the others, as a gold coin could mean it is either 50 silver/50 gold OR 100 gold, and we already knew it had to be one of those two. If a silver coin comes up, it must have 50 silver/50 gold, which means B is the one with 100 gold. However, this only gives you 25% chance of knowing.

• If you picked B, and a silver coin comes up, it means, that means it has 100 silver and C has 100 gold. If a gold coin comes up, that means it has 100 gold coins.

• You should pick B to determine which has 100 gold coins (which would have to be either B itself or C)

• The reasoning is actually quite simple:

_ 1. We know A can't have 100 gold coins because it says it does and we know that is a lie. It has to have one of the other two things. As such, if we picked A, we will have a 50% chance of getting gold if it has 50 silver/50 gold, and only then would we know that C has the 100 gold. We would know this because we would know A has the 50 silver/50 gold, which would mean C can't have that, and 100 gold is the only other choice for C. However, we only know this if we get a gold coin, which only has a 50% chance of happening and only if it has the 50 silver/50 gold, which is only 50% likely, so getting any significant knowledge from chest A is only 25% likely to happen. If we got a silver coin, it would mean that chest A could either have 50 silver/50 gold OR 100 silver. Since we couldn't tell which it has with a silver coin, and it having 100 silver would mean that chest B would be the one with the 100 gold, we would have to guess which has 100 gold if we picked chest A.

__ 2. We know C can't have 100 silver coins because it says it does and we know that is a lie. It has to have one of the other two things. As such, if we picked C, we will have a 50% chance of getting silver if it has 50 silver/50 gold, and only then would we know that B has the 100 gold. We would know this because we know C has the 50 silver/50 gold, which would mean A can't have that, and only 100 silver is left for chest A, meaning chest B can't have that, meaning only 100 gold is left for chest B. However, we only know this if we get a silver coin, which only has a 50% chance of happening and only if it has the 50 silver/50 gold, which is only 50% likely, so getting any significant knowledge from chest C is only 25% likely to happen. If we got a gold coin, it would mean that chest C could either have 50 silver/50 gold OR 100 gold. It would have the possibility of having 100 gold, and we would have to guess which has 100 gold if we picked chest C.

__ 3. We know chest B can't have 50 silver/50 gold coins because it says it does and we know it is a lie. It has to have one of the others. Since it can't have 50 silver/50 gold, no matter what kind of coin we get tells us something.

__ -----A. If we get a silver coin, it means that chest C has to have the 100 gold. Since chest B can't have 50 silver/50 gold, when a silver coin is picked, it has to mean that it has 100 silver. This means that chest A has to have 50 silver/50 gold, since its other option is the 100 silver that we just ruled that chest B must have. As such, the only thing left for chest C, of the 50 silver/50 gold or 100 gold, is the 100 gold.

_ -----B. If we get a gold coin, it gets really easy. As we mentioned, chest B can only have either 100 silver or a 100 gold. If a gold coin is picked up, we know chest B has 100 gold, doesn't matter what the other chests have. No matter what coin you sample if you pick chest B, significant knowledge is gained, and you can know which chest has the 100 gold (it is either chest B or chest C, by the way).