1 of 100: Can you find the gold?

Relevant wiki: Logical Puzzles

If statement A is true, then statement B must be true. But there is only one true statement. The same situation on B and D, either of them is true, there will be two true statements.

So statement C must be true, the gold must be in chest A, B, or D.

And the gold can't be in chest A or D, or the statement A or D will be true, that causes two-true-statement.

Finally, the gold could only be in chest B.

Assume statement A is TRUE. Then, it follows statement B is TRUE, which leads to a contradiction as only one is TRUE. So, statement A is FALSE, and box A can't have the treasure.

Assume statement B is TRUE. This would lead to box D having the gold, as A doesn't from the previous information. But, this would lead to statement C being TRUE, which is a contradiction, as only one is TRUE. Hence, statement B is FALSE.

Assume statement D is TRUE. But, this would lead to statement C being TRUE, and only one is TRUE so statement D is FALSE. So, the one TRUE statement must be C

Hence, the treasure must be in box B or D. But, as statement D is FALSE, it can't be in box D.

Hence, the treasure is in BOX B

Chest A cannot be true because then Chest B would be true too and only one chest can have a true statement, the same reasoning goes for Chest D because if the gold is in Chest D, then that means that Chest B has a true statement as well. Chest B cannot be true without Chest A or Chest D being true, so Chest C must be true. Chest C says that the gold is NOT in Chest C, so it can only be Chest A, B, or D. Because both A and D untruthfully state that the gold is in there, the gold cannot be in Chest A or D, meaning that it must be in Chest B. Overall, Chest C has the true statement but the gold is in Chest B.

if statement A is true.then B must be true.but there is a bit of confusion with A & D.so, C is that one which is true.

so,A,B or D can be the answer.but A & D cannot be true cz there is only one true which is C.

at last there only remains B. so,B is the answer.

If Statement B is true that would also make statements A or D true as well. And if either statements A or D are true then that would also make Statement B true. The issue is that the problem states that only ONE of the statements are true. Therefore, The only true statement is Statement C :"The gold is not here." This also means that Statements, A,B and D are all false, meaning that the gold is in neither Chest A or D. So the only chest that is left is Chest B.

If statement A or statement D is true, then statement C must be false. And this can never happen because the gold is only in one chest. If statement B is true, then statement D and statement A are both false. And this can never happen because according to B , the gold must be in one of the two boxes A or D . Then C must be the only correct statement which implies that the gold is in B .

If either of A or D have gold then their corresponding statements would be true which will mandate for the statement B to be true. Similarly if statement B is true it will mandate for either of statement A or statement B to be true. So till now it is clear that A and B don't have gold and statements A, B and D are false.

Thus, We come up to the conclusion that statement C is True and B has gold.

Using the Set Theory We assumed that each chest is an independent set Therefore, we have Sets A, B, C, D, respectively. From the question, it can be deduced that Set A and D are the Subset of B. Therefore the gold can be found in Chest B.

If the gold is in Box B, then Box A and Box D which says "The gold is in here" would be false. Then, the statement on Box B would also be false. Only the statement on Box C would be correct. Therefore, the gold is in Box B

Two part: True statement + Where the gold is.

A can't be true because of B.

B can't be true because of A and D.

D can't be true because of B.

So, by elimination C is true.

C can't contain treasure.

A can't contain it (see above).

D can't contain it.

So, again by elimination B must contain the coins.

If $C$ was true, then both $A$ and $D$ are false, which means the gold must be in B.

This problem is very interesting. Firstly, you need to narrow your options down. When analyzing this, you can see that both A and D are saying "The Gold is here". This is contradicting of each other and we no at least one of those statements are false. From here, we test out the 'what if' for the other statements. For statement C, it says " The Gold is not in here." If we assume this is true, then the rest of the statements are a lie. That means that the gold is neither in A or D, and the gold is in chest C. If D's statement is correct, then B's statement is a lie, so that means it isnt in D, which doesn't make sense. Same with A. Therefore, the gold is in B

Basically, my basis was C since it was stated that the gold is not here. Then, since A and D are contradicting because both chest proclaims that the gold is in there and then B supports both A and D and no statement was given to support B. So for me, it must be in B which is correct.

If C is false, then the gold is in C. That would make A and D false automatically. Thus, the only remaining chest, B, would have to be true to satisfy the requirement of 1 true statement. However, if the gold is in C, then B is false. Therefore, we know C cannot be false.

Since C is true, everything else must be false. This immediately eliminates A and D, leaving us only with chest B.

If statement A is correct, then statement B is also correct but only one statement must be correct. So, statement A is false. Same is with statement D.

If statement C is correct, then gold is in any of the other 3 chests and it is certainly not in chest C.

Statement A = Wrong (mentioned above)

Statement B = Wrong (If stmnt. B is true, that would make either A or D true, which is a contradiction to 'only one true statement')

Statement C = Correct (Now, any one of the other three chests (A, B or D) has gold)

Statement D = Wrong (mentioned above)

Now, gold cannot be in A or D, as that would make two more statements true. Upon statement C and denying A and D, (thus gold is not in A, C or D) gold is in B.

A : $G_A$

B : $G_A \lor G_D$

C : $\lnot G_C$

D : $G_D$

Suppose A's statement is true. Then, B's is also true, but there are not 2 true statements. Hence, A is false. The same reasoning applies to D's statement. As A and B are false, $(\lnot G_A\land\lnot G_D$ ) is true. So, B is false. So, as there is only one statement left, it is the true one: C.

From this: the gold is not on A, nor on D , nor on C . Therefore, it is on B.

Assume C is correct then A, B and D are lies. A and D are obvious lies and therefore B must be a lie and thus B has the Gold.

Only one state is true, therefore, AB can't both be true, nor can AD. Furthermore, CA can't both be true, nor can CD. Therefore C must be true and B must is the only option that will allowed since it must be false.

Well, if we pick either A,C, or D you will notice that these statements imply that in some way one of the other statements have to be true. If A or D is true, then B must be true. If C is true, then A or D could be true which then implies B is true. So B must hold the gold.

If Statement B is true that would also make statements A or D true as well. And if either statements A or D are true then that would also make Statement B true. The issue is that the problem states that only ONE of the statements are true. Therefore, The only true statement is Statement C :"The gold is not here." This also means that Statements, A,B and D are all false, meaning that the gold is in neither Chest A or D. So the only chest that is left is Chest B.

I started with statement B, which is "the most complicated one". Assume B is true, then one of A or D must be true (which is impossible, according to the terms/conditions). Then B must be false --> this makes both A and D false as well, and C is the only chest with correct statement. C says "the gold is not here", and this (finally) concludes that "the gold is in B chest".

I just said that B never said that it wasn't inside of it so there is a possibility it was inside. And they were saying only one box was teue so why not B :p (basic logic haha)

Consider that $(A\ \text{or}\ D) \Leftrightarrow B.$ Therefore A, B, and D cannot be the only true statements.

It follows that statement C must be true, but A and D are false. This means that the gold is in chest B.

If A or D had the True statement then : B and C would also be True, so A or D can't be True. Same concept with B - if B was True then A or D would also have to be True and again C too. Therefore : C must be the True statement, so our options for "correct chest" would A,B, or D, but recall "If A or D had the True statement then : B and C would also be True, so A or D can't be True." Therefore in other words "If A or D had the treasure then : one of their statements would be True." So B must have the Treasure.

This may or may not be correct, but I was thinking of this. For each box, consider what would happen if the corresponding statement were true. If it's possible that box X has the gold if box Y's statement were true, draw an arrow from box X pointing towards box Y. Now, for each box, count up the arrows pointing from it and subtract the number of arrows pointing towards it -- let this number be f(X) for a box X. I think that perhaps if f(X) = 1, then it is the only box with gold in it... I can't think how you'd prove it, though.

If A, B or D is true, then C also becomes true, meaning more than one true statement, which is not permitted.
Hence A, B and D are false, leaving only C to be true, meaning gold is outside C but not in A or D. So, gold is in B.

Using elimination method:

We know it's not A or D because if it was then we'd have MORE THAN ONE TRUTH because of B (or C! ). So we can ELIMINATE A and D .

We know it's not in C because if it was then we'd have NO TRUTHS . So we can ELIMINATE C .

Therefore B contains the gold. You're welcome ;)

If statement on A is true, then the gold is in A and statement on C is true also, which implies two statements are true. Similar argument applies for statement on D.

Hence, both statements on A and D are false and the gold is not in these two chest. Thus, statement on B is false and this forces statement on C to be true. Therefore, the gold is not in C. Since the gold is not in A and D too, it must be in B.

if statement A or B or D are true this will always imply the existence of two true statements, so the only choice we have is that statement C is true, this implies that the gold is in chest B.

According to the question, only one of the 4 statements is true If any one of the statements on A and D are true, the statement on B also becomes true Similarly, if the statement on B is true, then one of the statements on A and D is true Thus, if A or B or D is true, there will automatically be 2 true statements, thus statement C is true and the rest are false This means that the gold is neither in A nor in C and nor in D Hence, B is the answer to this question

Gold in A implies both statements A and B are true. (And C.) Gold in D also implies both statements A and B are true. (And C.) Gold in C implies none of the statements are true. Gold in B? Statement A, B, and D are all false. But statement C is true. The only option validating exactly one of the four statements is option B.

A and D can't be true at the same time, moreover if the statement below the chest B were true then one between A and D would be also true and 2 true statement are unacceptable. The only true statement is thus below chest C and the gold in in chest B.