# The Lucky Chest [duplicate]

This question already has an answer here:

There are three Chests containing 100 coins each, The labels on the three chests are :

Label 1 : "100 gold coins"

Label 2 : "50 gold and 50 silver coins"

Label 3 : "100 silver coins"

You are informed that all three of the labels are incorrectly placed. You have the chance to pick a random coin from any chest and then choose a chest to keep.

Which chest would you choose that you get the "100 gold coins"?

## marked as duplicate by Tryth, Deusovi♦, CodeNewbie, Raystafarian, AJLOct 1 '15 at 10:31

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

• @Tryth It's not a exact duplicate as in "First day of school" one gets additional information through the student leaving one of these doors. – Aron_dc Oct 1 '15 at 10:19
• Agree, it's not a duplicate, given you have less information. However, I fear this also implies there's no 100% answer on the question either. – Tim Couwelier Oct 1 '15 at 10:41
• The principle are same.... there is also given that you could get a random coin from any of the heap .. i forgot to add that... thanks for directing me Tryth ;) – prakhar londhe Oct 1 '15 at 10:43
• The accepted answer is that there is no answer? The question says which chest would you pick to get 100 gold coins and not which chest would you pick to maximize how many gold coins you get. – Engineer Toast Oct 1 '15 at 13:16
• @prakharlondhe I added the text and it improves the odds but it still doesn't get 100% chance of picking the all gold chest. What if you the coin you pick is gold? You still don't know if that chest is all gold or half gold. All you know is that it's not all silver but you already knew that because it's labeled all silver and you know that's wrong. – Engineer Toast Oct 1 '15 at 20:46

## 1 Answer

There are two possible scenarios:

 chest 1: 100 silver coins - chest 2: 100 gold coins - chest 3: 50 of both
chest 1: 50 of both - chest 2: 100 silver coins - chest 3: 100 gold coins

In both scenarios chest 3 contains at least 50 gold coins, so it is the safest to pick. Yet it is not guaranteed that it contains the 100 coins.

Because I am allowed to pick a coin from one of the chests, it is certain that I'll get the 100 gold coins. I will pick a coin from the second chest. If it is gold I know that the coins are placed as in scenario 1 and I should choose the chest 2. Au contraire, if the coin is silver I know the 100 gold coins are in chest 3.

• I don't understand why there are only 2 scenarios. Don't you have ABC, ACB, BAC, BCA, CAB, CBA ? That's 6 scenarios. – Spacemonkey Oct 1 '15 at 21:27
• The riddle says that all labels are incorrectly placed. Let's name the chests G for the golden one, S for the silver one and B for the 50/50 one. GSB and GBS are not possible, since (at least) the first label would be initially true. SBG is not possible, since the second label would be initially true. Same reasoning for BGS and the third label. That leaves the two scenarios that I mentioned: SGB and BSG. – Christoph Oct 1 '15 at 21:34
• Ah, I didn't take it literally, in which case I would indeed stand corrected : ) – Spacemonkey Oct 1 '15 at 21:35