[Guest]

Two boxes are marked as A and B. The label on box A says "The label on box B is true and the cup-cake is in box A". The label on box B says "The label on box A is false and the cup-cake is in box A". Assuming there is a cup-cake in one of the boxes and one of the labels is true, which box contains the cup-cake ?

Peace!

Edited August 20, 2009 by Terminator

[Guest]

If both boxes say that the cupcake is in box A, and one of the labels is telling the truth, then the cupcake has to be in box A

[Guest]

The cupcake is in box A.

A label = true: "label on box B is true" = true AND "cup-cake is in box A" = true

B label = false: "abel on box A is false" = false AND "cup-cake is in box A" = true

[Guest]

It's in the box marked "A".......couldn't you smell the yummy cupcake instead of trying to figure this out?

[Guest]

The cupcake is in box A.

A label = true: "label on box B is true" = true AND "cup-cake is in box A" = true

B label = false: "abel on box A is false" = false AND "cup-cake is in box A" = true

Okay! I should hv mentioned ONLY ONE of the 2 labels are true.. So, if one is true, other must be false, and vice versa. Sorry, for the confusion.

[Guest]

Okay! I should hv mentioned ONLY ONE of the 2 labels are true.. So, if one is true, other must be false, and vice versa. Sorry, for the confusion.

If one is true and one is false, and they both say it is in Box A, isn't there some sort of contradiction?

[Guest]

...is a lie.

if A is true

then B must be true AND cupcake is in A

Not legal because only A or B can be true but not both

if B is true

then A must be false And cupcake is in A

Not legal. If cupcake is in A then the only way A could be false is if B is also false.

There is no cupcake :`(

Edited August 20, 2009 by KillerGuns

[Guest]

...is a lie.

if A is true

then B must be true AND cupcake is in A

Not legal because only A or B can be true but not both

if B is true

then A must be false And cupcake is in A

Not legal. If cupcake is in A then the only way A could be false is if B is also false.

There is no cupcake :`(

Noooooooooooooooooooooo.... So the original poster left the part out that these boxes where in the Enrichment Center of Aperature Science!

*hopes someone gets it*

[Guest]

quote name='Terminator' date='20 August 2009 - 06:59 PM' timestamp='1250791190' post='195664']

Two boxes are marked as A and B. The label on box A says "The label on box B is true and the cup-cake is in box A". The label on box B says "The label on box A is false and the cup-cake is in box A". Assuming there is a cup-cake in one of the boxes and one of the labels is true, which box contains the cup-cake ?

Peace!

[Guest]

If label A is true, then both the conditions label B is true and the cupcake being in box a must be true. However, due to the conditions of the puzzle, one and only one of A and B may be true. Therefore, B cannot be true if A is true. Therefore A cannot be true.

If Label B is true, both conditions of label A being false and the cupcake being in box A must be true. However, in order to make label A false, either label B must be false OR the cupcake cannot be in box A. Since our precondition is that label B is true, the condition to make A false means the cupcake must be in box B. However, that contradicts our precondition that the cupcake is in box A.

THEREFORE:

The cupcake is in both boxes simultaneously until one of the boxes is opened and causes the world to explode (see: Schroedinger's cat )

[Guest]

quote name='Terminator' date='20 August 2009 - 06:59 PM' timestamp='1250791190' post='195664']

Two boxes are marked as A and B. The label on box A says "The label on box B is true and the cup-cake is in box A". The label on box B says "The label on box A is false and the cup-cake is in box A". Assuming there is a cup-cake in one of the boxes and one of the labels is true, which box contains the cup-cake ?

Peace!

Both statemens are false. It must be B.

[

Edited August 20, 2009 by Shadax

[Guest]

Perhaps the validity of the statements are relative to time. The cupcake was in Box A before the label was applied to Box A. Box B was labelled with a true statement. Then, Box A was opened, and the cupcake was eaten. Then Box A was labelled with a false statement.

[Guest]

...is a lie.

if A is true

then B must be true AND cupcake is in A

Not legal because only A or B can be true but not both

if B is true

then A must be false And cupcake is in A

Not legal. If cupcake is in A then the only way A could be false is if B is also false.

There is no cupcake :`(

No...

If B is true, then A is false and the cupcake is in A.

If A is false, then B must be true OR the cupcake is not in A. (DeMorgan's Law)

Since upon negation, it is an OR, not an AND, the fact that B is true is enough to make A false regardless of the location of the cupcake.

Answer: B is true, A is false, cupcake is in A;

A said that B is False and cupcake is in A, A is only telling the truth if BOTH of these are correct, if one of them isn't, then A is not telling the truth.

There is no contradiction for the answer I gave.

[Guest]

I thought I had the answer, then I reread the question.

[Guest]

No...

If B is true, then A is false and the cupcake is in A.

If A is false, then B must be true OR the cupcake is not in A. (DeMorgan's Law)

Since upon negation, it is an OR, not an AND, the fact that B is true is enough to make A false regardless of the location of the cupcake.

Answer: B is true, A is false, cupcake is in A;

A said that B is False and cupcake is in A, A is only telling the truth if BOTH of these are correct, if one of them isn't, then A is not telling the truth.

There is no contradiction for the answer I gave.

which part of A is false? The part about the label on box B being true, or that the cup-cake is in box A? These are the two statements (as seen below), so one of them must be false for A to be false.

Two boxes are marked as A and B. The label on box A says "The label on box B is true and the cup-cake is in box A". The label on box B says "The label on box A is false and the cup-cake is in box A". Assuming there is a cup-cake in one of the boxes and one of the labels is true, which box contains the cup-cake ?

[Guest]

which part of A is false? The part about the label on box B being true, or that the cup-cake is in box A? These are the two statements (as seen below), so one of them must be false for A to be false.

Yes, I realized I made a mistake. Sorry

A cannot be true, because then B would be true about A being false.

We assume then that A is false.

If A is false then either B is false, or the cake is not in A, or both;

If we keep assuming A is false, and assume B is true,

from the label on B, we get A is false and the cake is in A;

We have so far:

A is false,

B is true,

Cake is in A,

For everything to be ok, we need B to be false or the cake to not be in A;

We cannot meet these requirements, and we have a contradiction

if A is true and if A is false;

There are no other options, so the question creates contradictions in all cases.

[Guest]

If they are both false, there would be no contradiction.

The cupcake would be in box B and both of their statements would be false.

I know the person who put the question here said that one was telling the truth though.

[Guest]

Two boxes are marked as A and B. The label on box A says "The label on box B is true and the cup-cake is in box A". The label on box B says "The label on box A is false and the cup-cake is in box A". Assuming there is a cup-cake in one of the boxes and one of the labels is true, which box contains the cup-cake ?

Peace!

then the cup-cake has to be in Box A! Both label states the cup-cake is in box A. If one of these has to be true, then the cup-cake can't possibly be in box B. The OP didn't ask which label's true, just that one of the label is true, so why are we straining our brain to figure out which label's true??? The OP also doesn't rule out that both the labels can be true.

Edited August 20, 2009 by mav

[Guest]

Since both boxes contradict each other, the cupcake is divided by 0, therefore undefined and does not even exist.

[bonanova]

Two boxes are marked as A and B. The label on box A says "The label on box B is true and the cup-cake is in box A". The label on box B says "The label on box A is false and the cup-cake is in box A". Assuming there is a cup-cake in one of the boxes and one of the labels is true, which box contains the cup-cake ?

Peace!

We don't know where the cupcake is.

Why?

The OP says [at least] one of the labels is true.

If Label A or Label B is true, then, since they both make the assertion, we know it's in Box A.

But neither label is true:

Suppose B is true.

Then "A is false" and "cake is in A" are both true.

Thus A [which states "B is true" and "cake is in A" is true.

B thus implies both A and ~A.

Therefore B cannot be true.

Suppose A is true.

Then "B is true" and "cake is in A" are both true.

But if B is true then "A is false" and "cake is in A" are both true.

Thus A implies ~A.

Therefore A cannot be true.

Neither of the labels being true, the OP is violated.

Alternate solution.

If both labels are false, then a consistent assignment of truth among the four statements is:

False: "B is true"

False: "Cake is in A"

Together, these make Label A false.

True: "A is false"

False: "Cake is in A"

Together, these make Label B false.

So if we don't mind contradicting the OP's assumption that [at least] one label is true,

then with the cupcake in box B we have a consistent set of statements.

But for a solution to be valid, it must satisfy, not contradict, the terms of the OP.

So we're left with an [invalid] solution that the cupcake is in box B.

[Guest]

Thanks for your responses..!!

The problem cannot be solved with the information given.

The following argument can be made: If the statement on box A is true, then

the statement on box B is true, since that is what the statement on box A

says. But the statement on box B states that the statement on box A is false,

which contradicts the original assumption. Therefore, the statement on box A

must be false. This implies that either the statement on box B is false or

that the cup-cake is in box B. If the statement on box B is false, then either

the statement on box A is true (which it cannot be) or the cup-cake is in box B.

Either way, the cup-cake is in box B.

However, there is a hidden assumption in this argument: namely, that

each statement must be either true or false. This assumption leads to

paradoxes, for example, consider the statement: "This statement is

false." If it is true, it is false; if it is false, it is true. The

only way out of the paradox is to deny that the statement is either true

or false and label it meaningless instead. Both of the statements on the

boxes are therefore meaningless and nothing can be concluded from them.

In general, statements about the truth of other statements lead to

contradictions. Tarski invented metalanguages to avoid this problem.

To avoid paradox, a statement about the truth of a statement in a language

must be made in the metalanguage of the language.

Common sense dictates that this problem cannot be solved with the information

given. After all, how can we deduce which box contains the cup-cake simply by

reading statements written on the outside of the box? Suppose we deduce that

the cup-cake is in box B by whatever line of reasoning we choose. What is to stop

us from simply putting the cup-cake in box A, regardless of what we deduced?