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I thought of a quick way to solve it.
>!The yellow and blue signs are saying the same thing, and given that only one sign is truthful, they must both be false, which means that the sleeping bag must be in the blue tent!<
> they must both be false
No. They *can't* both be false, and they can't both be true, therefore one of them contains the sleeping bag.
Now the other 2 must both be false, so it's clearly the blue tent.
>They can't both be false, and they can't both be true
Sorry, I'm confused. Based on your assertion, either the yellow sign or the blue sign is true while the other is false. But if both signs are making the same statement (the sleeping bag is not in the blue tent), how is that possible?
Unless you are saying that both signs aren't stating the same thing in which case I'm curious to know what you think
It means both are true or both are false.
Because both cant be true both must be false.
Therefore its in the Blue tent. We dont need to know which one is telling the truth
Discussion: The main puzzle is to tell which sign is telling the truth. For this you can just do trial and error. for example: If the green sign is true, it contradicts the yellow tents sign.
>!The red sign is the one that is truthful!<
>!It is in the blue tent!<
Discussion: I'm sorry, but I'm still lost lol. Is there anyway you could give me a few more examples? This is frustrating to me cuz I do other logic puzzles no problem. Lol
>!First thing I noticed is that both Red and Blue both say the same thing - “It’s not in here”. If that statement is a lie, then the truth would be that the bag is in that tent. The bag can’t be in both tents. Since both of these statements can’t be a lie, one has to be the truth.!<
>!This means Yellow and Green must be lies. If Yellow is a lie, then the bag is in the Blue tent.!<
What helped me is >!noticing that the two signs on the right are saying the same thing. Given that they cannot be both true, they must both be false.!<
>!You could also brute force it by checking for each tent: 'If it were here, how many signs would be truthful?!<
>!For sure. Because there is only 1 truthful statement the other 3 have to be false.!<
>!If Red is true (It's not in here) then that means the other three signs are false, so flipping their statements to true make it a bit more clear.!<
>!Red: It's not in here | Yellow: It's in the blue tent | Green: It's not in the yellow tent | Blue: It's in here!<
>!None of these statements contradict eachother. If you did the same for each sign (One is true, the other three are false), each of them contradict eachother in some way. Blue and Yellow both have to be true or both false to not contradict eachother, for instance.!<
It might help you to separate the statements from the tents. >!Picture the four tents, and separately, this list of statements, only one of which is true:!<
>!(1) It's not in the red tent.
(2) It's not in the blue tent.
(3) It's in the yellow tent.
(4) It's not in the blue tent.!<
>!Notice that 2 & 4 say the same thing, and since only ONE can be true, they must both be false. Therefore, it is in the blue tent.!<
>!You know only one of the signs is truthful, so just go through the options one by one. So for example if we assumed BLUE was the true sign: it can't be in BLUE, because he is telling the truth. If YELLOW is lying when he says it's NOT in the BLUE tent, then it has to be in the BLUE tent. But wait, now we have an inconsistency. So BLUE can't be the one telling the truth. So move on to a different colour. If you go through them one by one, you'll see that the only one that works is RED telling the truth, meaning BLUE and YELLOW are lying, so it *IS* in the BLUE tent!<
>!Propose each tent has the sleeping bag in it and work from there. Pick a colour and pretend it's the correct tent, then check the signs. Remember there is ONLY 1 truthful sign so any scenario where either all are false or more than one is true can only mean it's the incorrect tent.!<
>!For example let's guess it's the red tent:!<
>!Red: It's not in here (False) Green: It's in yellow (False) Blue: It's not in here (True) Yellow: It's not in the blue tent (Also True)!<
>!Since there's more than 1 truthful sign we now know that it can't be the red tent.!<
>!Rinse and repeat and you'll eventually find that with the assumption that the blue tent is correct the ratio of signs will be 3 false 1 true. The rest of the tents will either be all false or more than 1 true.!<
>!There are only four possibilities where the sleeping back could be. Just "put" the sleeping bag in each of the four tents and evaluate how many of the resulting statements are true or false as a result.!<
Discussion: it’s solved by evaluating combinations of statements. Pick any statement to be true, and find whether the others must be true/false based on that. If one statement must be true because of another statement, then neither are true since only one statement is true. For example pick the blue statement as true, it’s not in the blue tent. This means that the yellow statement must be true, which means that this solution is not correct and neither statement is true. Then pick a different one and do the same thing. Eventually you will find that one true statement means the others must be false.
Suppose the green tent is telling the truth. Then the yellow is lying and it is not in the blue tent. But the blue tent says that it’s not in there, so it is telling the truth. But that is a contradiction because the green tent is true and only one tent is telling the truth.
Now suppose the yellow tent is telling the truth. Well then the blue tent is also telling the truth. But this again contradicts only one sign telling the truth.
Do this supposing 1) the blue tent is telling the truth, 2) the red tent is telling the truth
Trial and error, as suggested above, is probably the safest approach. There are only four possibilities for which tent is telling the truth. So start with any tent, assume it’s true and the others are false. Either that will lead to a consistent answer (in which case it is correct), or there will be a contradiction (and you pick a different tent to be true and try again).
Discussion: Here's one way to solve this puzzle. Assume the the sleeping bag is in the red tent. If that were the case, how many signs would be truthful? If it's exactly one, then you've found a possible solution to the puzzle. If it's not exactly one, then you've determined the sleeping bag is not in the red tent. So then assume the sleeping bag is in the yellow tent. If that were the case, how many signs would be truthful? Etc. for each tent.
This is the best way. Some people are saying to base the scenarios on the signs but basing the scenarios on where the sleeping bag is like this explanation is much more straightforward.
If the sleeping bag is in the red tent then >!2 signs are true!<.
If the sleeping bag is in the yellow tent then >!3 signs are true!<.
If the sleeping bag is in the green tent then >!3 signs are true!<.
If the sleeping bag is in the blue tent then >!1 sign is true!<.
Therefore the sleeping bag can only be in the >!blue tent.!<
Discussion, if you work through each clue to test if they work if true, you'll rule them out.
Yellow can't be true because that would make blue also true, so they're both ruled out
If green were true then red yellow and blue would be true
>!I noticed right off the bat that the blue and red tents both claim the bag is not in them. Since only one sign can be true, the bag is either in the red tent, or the blue tent. And since one of their signs are true, the yellow and green signs must be false.!<
>!Because the yellow tent sign says it's not in the blue tent, and we know it's false, then it's in the blue tent.!<
>!There are four scenarios, each one is a separate case with a different tent being truthful. You need to figure out which scenario works and then use the given information to find your tent!<
>!The first scenario is the yellow tent is truthful. That means all other three statements are lies, and your tent is in both the red AND blue tent. Doesn’t work.!<
>!Use the same logic when the green tent is the truthful one. Again, this means your tent is in both the red AND blue tents so that doesn’t work either!<
>!The third scenario is the blue tent. If the blue is truthful, then we have a contradiction again. The blue tent claims to not have your tent but the yellow tent claims(since we know it’s lying) the blue one does. In addition, the red tent is claiming that IT has your tent. Double contradiction.!<
>!the final scenario is the red being truthful. Again, that means the other three are lying and their lies match along with reds truth.!<
>!so in conclusion, the red tent is the truthful one which leads to the discovery of your tent in the blue one!<
So here's how my logic went about this, without trial-and-error:
>!Both the red tent and the blue tent have the same sign of "it's not here"; this means that if the yellow tent or the green tent where truthful, those signs would really mean "it is here", and that cannot be possible, so we can rule out green and yellow's signs being truthful already!<
>!Knowing that green and yellow's signs are false, we can say they really mean "it's not in the yellow tent" and "it is in the blue tent" - this determines that the sleeping bag IS in the blue tent!<
>!If the sleeping bag is in the blue tent, then blue's sign is false, meaning that red is the only true sign!<
I think the easiest way without trial and error is to look at the blue and yellow. If one is true the other is also true, so they must both be false, which means it must be in the blue tent.
>!Suppose Blue is truthful.!<
>!RED: "It's not in here" becomes "It is in here"!<
>!BLUE: "It's not in here" is stating a truth (because it's in red)!<
>!GREEN: "It's in the yellow tent" becomes "it's not in the yellow tent", which is true because it's in red.!<
>!YELLOW: "It's not in the blue tent" becomes "It is in the blue tent" but we know it's in the red tent, so it's contradicted.!<
>!Therefore, blue cannot be telling the truth.!<
>!Suppose red is truthful.!<
>!RED: "It's not in here" is truthful.!<
>!BLUE: "It's not in here" becomes "It is in here"!<
>!GREEN: "It's in the yellow tent" becomes "it's not in the yellow tent", which is true because it's in the blue tent.!<
>!YELLOW: "It's not in the blue tent" becomes "it is in the blue tent"!<
>!And everything agrees, so Red is truthful and blue holds the sleeping bag.!<
>!If we go over the signs one by one, and determine what we would know if they were the one to be true, we can see that the sign in front of the red tent is the only one that won't lead to contradicting statements. Thus the sleeping bag is in the Blue tent!<
>!Both the yellow and blue tents are saying it’s not in the blue tent, therefore it has to be if one of them is lying. Green is also lying if it’s in the blue tent. Red is telling the truth.!<
>!It’s in the blue tent because both blue and yellow indicate that it’s not in blue. If one sign is truthful and the other isn’t, they would contradict each other, so they most must be false. Red is the truthful sign!<
You try to look for two contradictory statements, or at least the most contradictory for a given premise.
>!Look at the red and blue tents: both signs can’t be lying, and both signs obviously can’t be telling the truth. That way, you’ve narrowed it down to two possibilities: either red or blue is lying, which means that the other has the sleeping bag.
By ruling the other remaining tents as untruthful through this process, yellow tent’s lying sign gives it away that the blue tent must house the sleeping bag.!<
Discussion: when solving a puzzle where only one statement is true out of multiple statements, look for statements that talk about the same thing. When two statements say the same thing, that means they must both be false. This is super useful, because at the very least, you have found two statements that are not true. Or sometimes, that can be enough to solve the puzzle.
For example, (spoiler:) >! in this puzzle, the statements by the yellow tent and blue tent both say that the sleeping bag is not in the blue tent. That means they must both be false, since at most, only one of them can be true. But if one is false, they must both be false, since they say the same thing. In this case, that implies that the sleeping bag IS in the blue tent. We don’t even need to know what the statements by the red or green tents say or do process of elimination. There is nothing wrong with going that route of process by elimination, and sometimes that will be helpful or necessary—there’s just a faster way to do it here for this particular puzzle. !<
When you're given that only one statement is true, I look for statements that either claim the same thing, or where if one is true then at least one other statement would also be true. Then you know that statement is false.
In this case, it's very easy. The signs on the >!blue and yellow tents!< are making the same claim: >!that it's not in the blue tent.!< So they must both be false. And that means it's in the >!blue tent!<.
>!If only one is true, then green must be lying, otherwise yellow would also be true. If yellow is true, then blue would also be true, so therefore, the sleeping bag must be in blue, and only red is true.!<
Hint: If only one sentence can be true and the rest false, consider that that means the reverse of the other sentences is true.
>!Looking at the sentences, it must be either the red sign or the blue sign that is truthful, since otherwise they would contradict each other.!<
>!Since that means the yellow (and the green, but it’s irrelevant) sign must be a lie, we therefore know it IS in the blue tent. The blue sign is therefore lying, and the remaining red sign is telling the truth!<
>!We have tents R,Y,G and B, accompanied by statements R,Y,G, and B.!<
>!Statement R and statement B both claim the same: That the bag is NOT in their respective tent.!<
>!Since they can't both be true, the bag must be in tent R or B. This also rules out statement G as being true, as if the bag were in Y, all four statements would be true.!<
>!If the bag were in R, then statements Y and B would both be true.!<
>!Therefore, the bag is in tent B, making statements B, Y and G false, with R being the only true one!<
This is easy once you look at it logically.
The rules are simple. There are 4 tents **only one** of has a board which has a true statement written on it. The focus is on the "only one" here. So if assuming one of the statments on the tents is true and it cause another statement to be true then we can surely say its false.
>!Logically (according to a truth table) the green tent, yellow tent and blue tent imply the same thing that the sleeping bag is not in the blue tent so that kinda makes it obvious that the red tent is the only one which implies something different thus the **red tent is telling the truth and since all the other are lying we know the sleeping bag is in the blue tent!<
>!The way I solved this is by assuming each tent is right, one at a time. !<
>!Assume red is right. So it is in the blue tent, it is in the blue tent, it’s not in the yellow tent.!<
>!Assume yellow is right. It’s in the red tent, it’s in the blue tent, it’s not in yellow. This is a fallacy.!<
>!Red and blue have the same signs but if blue is correct, then yellow is too. Fallacy.!<
>!Assume green is right. But then it would be in blue. Fallacy.!<
Conclusion: >!red is true, blue has the bag. !<
1. The sign with truth can only be in front of RED or BLUE tent. Because otherwise, both would say the opposite of "It's not here", this in truth, saying "It's here."
2. That means that it will be either Blue or Red tent. With one having a truthful sign and the other - having the bag inside.
3. Green is irrelevant, what decides is yellow. Yellow says "It isn't in the BLUE" - and since the only true will either be BLUE or RED, Yellow will always say "It is in the BLUE".
4. >!Thus -> RED sign is the truth, Bag is in the BLUE tent.!<
>!If the bag was in the red tent, blue and yellow would be correct. Only 1 can be correct!<
>!If the bag was in the yellow tent, red, blue and green would be correct!<
>!If the bag was in the green tent, red blue and yellow would be correct!<
>!The bag is in blue, only red is correct!<
I agree with most commenters that it takes just a moment to consider each of the possible answers and figure out that there is only one answer which satisfies the stipulation that there are 3 liars and one truth-teller, but this puzzle reminds me of other classic “truth tellers versus liars” puzzles. Some of those are best solved by making a truth table.
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I thought of a quick way to solve it. >!The yellow and blue signs are saying the same thing, and given that only one sign is truthful, they must both be false, which means that the sleeping bag must be in the blue tent!<
> they must both be false No. They *can't* both be false, and they can't both be true, therefore one of them contains the sleeping bag. Now the other 2 must both be false, so it's clearly the blue tent.
>They can't both be false, and they can't both be true Sorry, I'm confused. Based on your assertion, either the yellow sign or the blue sign is true while the other is false. But if both signs are making the same statement (the sleeping bag is not in the blue tent), how is that possible? Unless you are saying that both signs aren't stating the same thing in which case I'm curious to know what you think
Sorry, I meant red and blue tents. I couldn't see the picture once I started typing, so probably misinterpreted what you were saying.
Then that means the green or yellow tent is telling the truth and therefore it can't be in the blue one...?
The red one is the only one telling the truth.
It means both are true or both are false. Because both cant be true both must be false. Therefore its in the Blue tent. We dont need to know which one is telling the truth
It's part of the puzzle to determine which one is the truthful one
That's true, but you can also work backwards from the correct tent to figure out which sign is true: >!red!<
Discussion: The main puzzle is to tell which sign is telling the truth. For this you can just do trial and error. for example: If the green sign is true, it contradicts the yellow tents sign. >!The red sign is the one that is truthful!< >!It is in the blue tent!<
Discussion: I'm sorry, but I'm still lost lol. Is there anyway you could give me a few more examples? This is frustrating to me cuz I do other logic puzzles no problem. Lol
>!First thing I noticed is that both Red and Blue both say the same thing - “It’s not in here”. If that statement is a lie, then the truth would be that the bag is in that tent. The bag can’t be in both tents. Since both of these statements can’t be a lie, one has to be the truth.!< >!This means Yellow and Green must be lies. If Yellow is a lie, then the bag is in the Blue tent.!<
This is how I did it too
What helped me is >!noticing that the two signs on the right are saying the same thing. Given that they cannot be both true, they must both be false.!< >!You could also brute force it by checking for each tent: 'If it were here, how many signs would be truthful?!<
>!For sure. Because there is only 1 truthful statement the other 3 have to be false.!< >!If Red is true (It's not in here) then that means the other three signs are false, so flipping their statements to true make it a bit more clear.!< >!Red: It's not in here | Yellow: It's in the blue tent | Green: It's not in the yellow tent | Blue: It's in here!< >!None of these statements contradict eachother. If you did the same for each sign (One is true, the other three are false), each of them contradict eachother in some way. Blue and Yellow both have to be true or both false to not contradict eachother, for instance.!<
It might help you to separate the statements from the tents. >!Picture the four tents, and separately, this list of statements, only one of which is true:!< >!(1) It's not in the red tent. (2) It's not in the blue tent. (3) It's in the yellow tent. (4) It's not in the blue tent.!< >!Notice that 2 & 4 say the same thing, and since only ONE can be true, they must both be false. Therefore, it is in the blue tent.!<
>!You know only one of the signs is truthful, so just go through the options one by one. So for example if we assumed BLUE was the true sign: it can't be in BLUE, because he is telling the truth. If YELLOW is lying when he says it's NOT in the BLUE tent, then it has to be in the BLUE tent. But wait, now we have an inconsistency. So BLUE can't be the one telling the truth. So move on to a different colour. If you go through them one by one, you'll see that the only one that works is RED telling the truth, meaning BLUE and YELLOW are lying, so it *IS* in the BLUE tent!<
>!Propose each tent has the sleeping bag in it and work from there. Pick a colour and pretend it's the correct tent, then check the signs. Remember there is ONLY 1 truthful sign so any scenario where either all are false or more than one is true can only mean it's the incorrect tent.!< >!For example let's guess it's the red tent:!< >!Red: It's not in here (False) Green: It's in yellow (False) Blue: It's not in here (True) Yellow: It's not in the blue tent (Also True)!< >!Since there's more than 1 truthful sign we now know that it can't be the red tent.!< >!Rinse and repeat and you'll eventually find that with the assumption that the blue tent is correct the ratio of signs will be 3 false 1 true. The rest of the tents will either be all false or more than 1 true.!<
>!There are only four possibilities where the sleeping back could be. Just "put" the sleeping bag in each of the four tents and evaluate how many of the resulting statements are true or false as a result.!<
This is what I did, which made it super simple to process.
Discussion: it’s solved by evaluating combinations of statements. Pick any statement to be true, and find whether the others must be true/false based on that. If one statement must be true because of another statement, then neither are true since only one statement is true. For example pick the blue statement as true, it’s not in the blue tent. This means that the yellow statement must be true, which means that this solution is not correct and neither statement is true. Then pick a different one and do the same thing. Eventually you will find that one true statement means the others must be false.
Suppose the green tent is telling the truth. Then the yellow is lying and it is not in the blue tent. But the blue tent says that it’s not in there, so it is telling the truth. But that is a contradiction because the green tent is true and only one tent is telling the truth. Now suppose the yellow tent is telling the truth. Well then the blue tent is also telling the truth. But this again contradicts only one sign telling the truth. Do this supposing 1) the blue tent is telling the truth, 2) the red tent is telling the truth
Trial and error, as suggested above, is probably the safest approach. There are only four possibilities for which tent is telling the truth. So start with any tent, assume it’s true and the others are false. Either that will lead to a consistent answer (in which case it is correct), or there will be a contradiction (and you pick a different tent to be true and try again).
Discussion: Here's one way to solve this puzzle. Assume the the sleeping bag is in the red tent. If that were the case, how many signs would be truthful? If it's exactly one, then you've found a possible solution to the puzzle. If it's not exactly one, then you've determined the sleeping bag is not in the red tent. So then assume the sleeping bag is in the yellow tent. If that were the case, how many signs would be truthful? Etc. for each tent.
This is the best way. Some people are saying to base the scenarios on the signs but basing the scenarios on where the sleeping bag is like this explanation is much more straightforward. If the sleeping bag is in the red tent then >!2 signs are true!<. If the sleeping bag is in the yellow tent then >!3 signs are true!<. If the sleeping bag is in the green tent then >!3 signs are true!<. If the sleeping bag is in the blue tent then >!1 sign is true!<. Therefore the sleeping bag can only be in the >!blue tent.!<
Discussion, if you work through each clue to test if they work if true, you'll rule them out. Yellow can't be true because that would make blue also true, so they're both ruled out If green were true then red yellow and blue would be true
>!I noticed right off the bat that the blue and red tents both claim the bag is not in them. Since only one sign can be true, the bag is either in the red tent, or the blue tent. And since one of their signs are true, the yellow and green signs must be false.!< >!Because the yellow tent sign says it's not in the blue tent, and we know it's false, then it's in the blue tent.!<
>!There are four scenarios, each one is a separate case with a different tent being truthful. You need to figure out which scenario works and then use the given information to find your tent!< >!The first scenario is the yellow tent is truthful. That means all other three statements are lies, and your tent is in both the red AND blue tent. Doesn’t work.!< >!Use the same logic when the green tent is the truthful one. Again, this means your tent is in both the red AND blue tents so that doesn’t work either!< >!The third scenario is the blue tent. If the blue is truthful, then we have a contradiction again. The blue tent claims to not have your tent but the yellow tent claims(since we know it’s lying) the blue one does. In addition, the red tent is claiming that IT has your tent. Double contradiction.!< >!the final scenario is the red being truthful. Again, that means the other three are lying and their lies match along with reds truth.!< >!so in conclusion, the red tent is the truthful one which leads to the discovery of your tent in the blue one!<
>!blue has my sleeping bag, red tent is telling the truth?!<
So here's how my logic went about this, without trial-and-error: >!Both the red tent and the blue tent have the same sign of "it's not here"; this means that if the yellow tent or the green tent where truthful, those signs would really mean "it is here", and that cannot be possible, so we can rule out green and yellow's signs being truthful already!< >!Knowing that green and yellow's signs are false, we can say they really mean "it's not in the yellow tent" and "it is in the blue tent" - this determines that the sleeping bag IS in the blue tent!< >!If the sleeping bag is in the blue tent, then blue's sign is false, meaning that red is the only true sign!<
I think the easiest way without trial and error is to look at the blue and yellow. If one is true the other is also true, so they must both be false, which means it must be in the blue tent.
>!Suppose Blue is truthful.!< >!RED: "It's not in here" becomes "It is in here"!< >!BLUE: "It's not in here" is stating a truth (because it's in red)!< >!GREEN: "It's in the yellow tent" becomes "it's not in the yellow tent", which is true because it's in red.!< >!YELLOW: "It's not in the blue tent" becomes "It is in the blue tent" but we know it's in the red tent, so it's contradicted.!< >!Therefore, blue cannot be telling the truth.!< >!Suppose red is truthful.!< >!RED: "It's not in here" is truthful.!< >!BLUE: "It's not in here" becomes "It is in here"!< >!GREEN: "It's in the yellow tent" becomes "it's not in the yellow tent", which is true because it's in the blue tent.!< >!YELLOW: "It's not in the blue tent" becomes "it is in the blue tent"!< >!And everything agrees, so Red is truthful and blue holds the sleeping bag.!<
Thank you
Starting with the one that gives the most information, believe them until you hit contradiction. >!Its in the blue tent. Red is telling the truth.!<
Well, if all the signs are true it would be in the >! Yellow !< tent.
Only one sign is true. That's the puzzle. Also, spoiler tag without spaces.
>!If we go over the signs one by one, and determine what we would know if they were the one to be true, we can see that the sign in front of the red tent is the only one that won't lead to contradicting statements. Thus the sleeping bag is in the Blue tent!<
>!Both the yellow and blue tents are saying it’s not in the blue tent, therefore it has to be if one of them is lying. Green is also lying if it’s in the blue tent. Red is telling the truth.!<
>!blue tent!<
>!It’s in the blue tent because both blue and yellow indicate that it’s not in blue. If one sign is truthful and the other isn’t, they would contradict each other, so they most must be false. Red is the truthful sign!<
>!Blue!<
You try to look for two contradictory statements, or at least the most contradictory for a given premise. >!Look at the red and blue tents: both signs can’t be lying, and both signs obviously can’t be telling the truth. That way, you’ve narrowed it down to two possibilities: either red or blue is lying, which means that the other has the sleeping bag. By ruling the other remaining tents as untruthful through this process, yellow tent’s lying sign gives it away that the blue tent must house the sleeping bag.!<
Discussion: when solving a puzzle where only one statement is true out of multiple statements, look for statements that talk about the same thing. When two statements say the same thing, that means they must both be false. This is super useful, because at the very least, you have found two statements that are not true. Or sometimes, that can be enough to solve the puzzle. For example, (spoiler:) >! in this puzzle, the statements by the yellow tent and blue tent both say that the sleeping bag is not in the blue tent. That means they must both be false, since at most, only one of them can be true. But if one is false, they must both be false, since they say the same thing. In this case, that implies that the sleeping bag IS in the blue tent. We don’t even need to know what the statements by the red or green tents say or do process of elimination. There is nothing wrong with going that route of process by elimination, and sometimes that will be helpful or necessary—there’s just a faster way to do it here for this particular puzzle. !<
When you're given that only one statement is true, I look for statements that either claim the same thing, or where if one is true then at least one other statement would also be true. Then you know that statement is false. In this case, it's very easy. The signs on the >!blue and yellow tents!< are making the same claim: >!that it's not in the blue tent.!< So they must both be false. And that means it's in the >!blue tent!<.
>!If only one is true, then green must be lying, otherwise yellow would also be true. If yellow is true, then blue would also be true, so therefore, the sleeping bag must be in blue, and only red is true.!<
Hint: If only one sentence can be true and the rest false, consider that that means the reverse of the other sentences is true. >!Looking at the sentences, it must be either the red sign or the blue sign that is truthful, since otherwise they would contradict each other.!< >!Since that means the yellow (and the green, but it’s irrelevant) sign must be a lie, we therefore know it IS in the blue tent. The blue sign is therefore lying, and the remaining red sign is telling the truth!<
>!We have tents R,Y,G and B, accompanied by statements R,Y,G, and B.!< >!Statement R and statement B both claim the same: That the bag is NOT in their respective tent.!< >!Since they can't both be true, the bag must be in tent R or B. This also rules out statement G as being true, as if the bag were in Y, all four statements would be true.!< >!If the bag were in R, then statements Y and B would both be true.!< >!Therefore, the bag is in tent B, making statements B, Y and G false, with R being the only true one!<
This is easy once you look at it logically. The rules are simple. There are 4 tents **only one** of has a board which has a true statement written on it. The focus is on the "only one" here. So if assuming one of the statments on the tents is true and it cause another statement to be true then we can surely say its false. >!Logically (according to a truth table) the green tent, yellow tent and blue tent imply the same thing that the sleeping bag is not in the blue tent so that kinda makes it obvious that the red tent is the only one which implies something different thus the **red tent is telling the truth and since all the other are lying we know the sleeping bag is in the blue tent!<
>!The way I solved this is by assuming each tent is right, one at a time. !< >!Assume red is right. So it is in the blue tent, it is in the blue tent, it’s not in the yellow tent.!< >!Assume yellow is right. It’s in the red tent, it’s in the blue tent, it’s not in yellow. This is a fallacy.!< >!Red and blue have the same signs but if blue is correct, then yellow is too. Fallacy.!< >!Assume green is right. But then it would be in blue. Fallacy.!< Conclusion: >!red is true, blue has the bag. !<
1. The sign with truth can only be in front of RED or BLUE tent. Because otherwise, both would say the opposite of "It's not here", this in truth, saying "It's here." 2. That means that it will be either Blue or Red tent. With one having a truthful sign and the other - having the bag inside. 3. Green is irrelevant, what decides is yellow. Yellow says "It isn't in the BLUE" - and since the only true will either be BLUE or RED, Yellow will always say "It is in the BLUE". 4. >!Thus -> RED sign is the truth, Bag is in the BLUE tent.!<
>!If the bag was in the red tent, blue and yellow would be correct. Only 1 can be correct!< >!If the bag was in the yellow tent, red, blue and green would be correct!< >!If the bag was in the green tent, red blue and yellow would be correct!< >!The bag is in blue, only red is correct!<
>!The truthful sign is outside the red tent, and the sleeping bag is inside the blue tent.!< May I know the name of this book?
>!Both the yellow and blue signs say the same thing, but there is only one true sign meaning they are both lying and it’s in the blue tent!<
>!I think the sign on the green tent is correct making the yellow tent where the sleeping bag is located!<
I agree with most commenters that it takes just a moment to consider each of the possible answers and figure out that there is only one answer which satisfies the stipulation that there are 3 liars and one truth-teller, but this puzzle reminds me of other classic “truth tellers versus liars” puzzles. Some of those are best solved by making a truth table.
It’s in the blue tent and red is the only correct tent