The Boxes
There are 3 boxes, exactly one of which has a car. You can keep the car if you pick the correct box!
On each box there is a statement, exactly one of which is true.
Box 1: The car is in this box.
Box 2: The car is not in this box.
Box 3: The car is not in box 1.
Which box has the car?
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16 solutions
Discussions for this problem are now closed
To solve the problem, you need to get first which statement is true, then find where the car is. Making the statement TRUE doesn't mean that the car is ON that box where the statement is found to be true, this still depends on the statement on that box.
On the illustration, it is correct that statement 3 is TRUE, now to look for the car, get the opposite of the statements in box one and two, making the other two statements also true. Now, with these three statements, which are now all TRUE, it will point you to the correct box, which is Box 2.
Why can't we say the car is in box 3?
(upvoted) nice picture <3
The question doest mention that there could be false statements. If it said so, the answer is solvalble without the key answer. This kind of uncomplete questions is just to show that this question/game is smart! But it is actually a waste of time and if ur smart u will notice that when u read the question again. You actually misunderstood the question, coz actually the question itself is didnt actually give enough info.
All your statement must be true to prove that the car is in which box. If box 3 says the car is NOT in the box. We can say the the car in box 1 is call NOT. In this case all statement are true. Which means the car is in box 1. Putting all caps for "NOT"means that this can be just a abbreviations and not the meaning of no/nothing in box 3...
here 2 car itself saying that car is not in that box then how can can be in that box?
right and 3 doesnt says that it doesnt has car but it has ACCORDING TO ME BOX 3 HAS CAR NOT BOX 2
Because if you choose the Box 3 as the True statement, and the ONLY true statement, you would have to NEGATE all the other boxes' statements because they are now treated as FALSE. So, box 1 one becomes, "the car is NOT in this box" and box 2 becomes "The car is in this box". So where is the car?
Box 2 is false about not having the car, not that hard
.....seriously? No dice dude - stupid question with misleading answers
NB: My comments below were made in reference to a Facebook version of the question that differs in certain details from the problem as represented above. It read:
<< There are 3 boxes. One of them has a car that you get to keep. On each box there is a statement. You know that only one of these statements is true. >>
Be careful! Think outside the boxes!
The introductory text of the problem does not stipulate that the box with the "true" statement is the box with the car. In fact, it is worded in such a way that it can be construed you get to keep the car without having to do anything: giving a correct answer is not imposed as a condition for receiving the car, wherever it may be. (If you were really logical, you wouldn't even assume there is a car under any of the boxes.)
So the car could be under any of the boxes (or none of them), regardless of what the ostensibly "obvious" logic might lead you to conclude.
Either this is a trick question or the question itself needs to be more logically constructed.
In the problem as presented on this page, there are also internal issues:
- "Correct box" need not be construed as "the box on which the true statement appears" or even "the box containing the car." How do we know any of the boxes actually contains a car? How do we know Schrödinger's Cat is alive or dead? Is it really logical to make such an assumption? In fact, none of the "boxes" really contains a car, none of the boxes is actually a box, and if you change your perspective, it is possible to view these alleged "boxes" as a two-dimensional representation of a row of three incomplete quasi-cubes, each missing three of their sides (think M. C. Escher). Try it — and don't let the shading throw you off. :-)
Congratulations,this is the most legendary solution on Brilliant :)
Lets see the puzzle in this way for simplicity,
A. Let's assume Box 1 has the car. Then according to the question, Statement of Box 1: True Statement of Box 2: True Statement of Box 3: False This scenario is rejected as more than one statement is true.
B. Let's assume Box 2 has the car. Then according to the question, Statement of Box 1: False Statement of Box 2: False Statement of Box 3: True This looks like our answer. Let's check the last scenario for completeness.
C. Let's assume Box 3 has the car. Then according to the question, Statement of Box 1: False Statement of Box 2: True Statement of Box 3: True Again, this scenario is rejected as more than one statement is true.
Thus the answer is Box 2.
Moderator note:
Going through case by case is often the most overlooked method. Good job!
Great job Sumit! This was the only explanation that made sense to me!
The statements made by box 1 and box 3 contradict each other, so one of them must be true. Therefore, the statement made by box 2 must be false. Therefore, the car is in box 2 !
Moderator note:
Good interpretation of the problem. Well done!
Its stupid because if u ask from us which box have a car in then it should be box 3 because box 3 its telling u about box 1 but not about itself so it should be 3
If box 3 had the car, both box 2 and box 3 would be telling the truth.
If the question was "Which statement is true?" then the answer would be 3. But the question is "which box has the car?" then it's box 2
@Oussama Jaber – But what if the box 1 is true. Then 2 and 3 would be false.
@Jeff Madrid – Box 2 says; The car is not in this box. If Box 1 had the car, then Box 2 would also be true, along with Box 1. If Box 3 was true, Box 2 would also be true. Since only one of the 3 statements can be true, the car must be in Box 2, since Box 1's statement is false, Box 2's statement is false, but Box 3's statement is true.
@Gain Bodo – Dude. It says only one statement is true. So it's an understood question that we have to figure out which statement is true...and from that, glean which box has the car.
@Gain Bodo – the question gives us both tips: 1) which box has a car, and 2) there is just one corret answer... for both be true, the car just can be in the box2... anyway, i marked the wrong answer too lol I just found out the answer in the coments (read John Doe up there)
@Gain Bodo – but it gives you a clue that one statement is true to narrow down the desicions
@John Doe – How could be Box's 3 statement is true?
@Amr Elewa Musaad – Box 3 Says "The car is not in Box 1." So if the car isn't in Box 1, then the statement in Box 3 is true. That would also mean that the statement in Box 1 is false. Since only one statement can be true, we know that is Statement 3 is true then both Statements 1 and 2 are False. So let's look at Statement 2: "The car is NOT in this box." If that's false, then the car IS in Box 2. That must be the solution, as it's the only way to get one true and two false Statements.
@Jeff Madrid – Box 1 is true, so box 2 and 3 have to be false but If box 2 is telling a false then the car as same as box 1 has to be there, in box 2. *Wrong *
Box 2 is true, so box 1 and 3 have to be false but bouth boxes are contradict "The car is not in box 1= False, yes it is, so box 1, but "The car is in this box= False. because i can only have 1 true. Wrong *
Box 3 is true, so box 1 and 2 have to be false, box 2 is telling a false then the car has to be there. * Correct *
@Kumino Gamba – yes <i agree with you
@Kumino Gamba – can i copy your answer and tell it to my friends ...please .......i request you.
that is real explanation how a question is solved.
@Kumino Gamba – Try again... right answer, wrong conclusion... Not even logical....
@Ben Gilead Balo – But.. that IS the right answer. The car IS in Box # 2.
@Jeff Madrid – no because box 2 say its not in this box so that would make 1 and 2 true and 3 wrong.
@Jeff Madrid – If B1 is true, then B2 is also true, as B2 states "the car is NOT in B2". If it is in B1, this makes statement of B2 true.
@Jeff Madrid – if box 1 is true then "statement 3" is wrong because the car is in box 1 but if we're talking about "statement 2" then the statement is correct for having the car not in box 2 so, If statement 1 is correct then statement 2 is correct and the 3rd is wrong If statement 2 is correct then statement 1 might be correct and statement 3 also, thus we will never know which of box 1 and 3 have the car If statement 3 is correct then statement 1 is wrong and statement 2 might be correct all of above is correct(if im not half asleep)
@Henry Chandra – Only one of the boxes has a true Statement, though.
@Jeff Madrid – If box 1 is true, then box 2 is true also.
@Jeff Madrid – you think like a software engineer, no need to go to any other box :)
@Jeff Madrid – No, then both box 1 and 2 would be true as box 2 doesn't have the car and box one also has the car in which case, both 1 and 2 are true
@Jeff Madrid – I too think so.
@Jeff Madrid – If box 1 is true (and the car is in box 1), then box 2 would also have to be true (since it's saying that the car is not in box 2)
@Jeff Madrid – 2 Would also be true
@Jeff Madrid – Box 2 says "The car is NOT in this box". If it was false, the car would be there too and that's not allowed.
@Jeff Madrid – if box 1 was true then box2 is also true.....
So Then answer is Box 2 Agree with Oussama Jaber
@Jeff Madrid – no, if box 1 is true, then box 2's statement would also be true.
@Oussama Jaber – I only assume step by step.....1. If state 1 is true , statement 2 or 3 can be true too . 2. Similar result happens to statement 2 . 3. If statement 3 is true , there is no room for other statements to be true , so the car is in box 3.
@Oussama Jaber – But going by your statement, then it could be any. Cause what if box 3 and 1 are lying. I'm not going against you just pointing out a question within your statement. Cause as you said about if the question was "Which statement is true" then it would be 3. But because it's not about truth, it could be either.. Idk I may be wrong but it's just my thought..
@Oussama Jaber – Your first post doesn't say that.... :/
@Oussama Jaber – i agree with box 2 but how do you know box 3 hasn't the car?
@Oussama Jaber – You should take into account that she is not answering, she is replying
batman is the answer
box 1 ccannot be telling truth if box 3 had d car....because box 1 says that it has the car!
no the box 1 will be lying bcoz it say is has the car but it does'nt have it...
How will Box 2 statement be true?
That is what I don't get.
All illogical.
3 is Correct.Both 1 & 2 are false because 3 didn't tell, it hasn't have the car.
You only need to know the mere fact that box 2 is a lie
well said good sir.
If car is in Box 2, statement 3 becomes true that the car is not in box 1. So that should not be the solution. Also, if its in box 1, statement 1 and 2 becomes true, and if its in box 3, statement 3 and 2 becomes true.
So none of them.
I agreed with your logic and also believe the Car is in 3.
i also agree that the car is in box 3
If box 3 is telling the truth, then boxes 1 and 2 are lying. Since box 2 says "the car is not in this box" if it were lying then the car would have to be in that box.
yes i m agree wid u
It's using logic therefore a "this" statement negates the actual meaning of the statement thus bowx 2 is correct.
it should be three
Its stupid if you say "Its stupid because if u ask from us which box have a car in then it should be box 3 because box 3 its telling u about box 1 but not about itself so it should be 3"... Because of... 1. You said should and not must (you're not sure about it yourself) 2. Your reasoning is unreasonable(mentioning box 3 which doesn't state about itself and you suspected it to be the answer to this problem because of it) EXCEPT if you're only spouting a joke answer, I won't oppose you :D My answer myself: 2 or 3 since statement 1 said that its in it and made the 2nd correct which is wrong, and statement 3 said its not in the 1st which means it must be in 2 or 3. That is my "FINAL ANSWER". Then after I read Ivan's, wait... If statement 3 is correct then statement 2 is wrong(I didn't realize it before) which makes "The car is in this box"... I'm embarrassed :(
I completely agree to this. Box 3 should be the right answer
The right answer to the wrong question. Which box has the car?
exactly...
If car is in box 1 = statement 1: true , statement 2: true , statement 3:false ;; box 2 = statement 1:false, statement 2: false, statement 3: true ;; box 3 = statement 1:false, statement 2: true , statement 3: true
you are right
gotta remember the goal, which is to find which box the car is under, not which box's statement is true.
You're right. Box 3 is true. And because the statement on box 3 is true, then when box 2 claims the car is not in this box, it is lying. Which means that the car is in box 2. I made the same mistake; I stopped one step short of the answer.
yes i agree these people dont know what they are talking about
Same analysis as Tara Mattson Schmehr.
as the condition states that only one statement is true
let, 1. the car is in the box ( false )
2. the car is not in the box ( false )
3. the car is not in box 1 ( true )
means that according to statement 3 car is not in the box 1
statement 2 is false and is stating that car is not in the box means that car is in box 2
car can be in box 3 but box 2 in more preferable according to conditions
I think the same as you do. '
but only 1 statement is true, so if it is 3 statement 2 and 3 are true
Strongly agree with you!!!
if statement 1 is true, then that means that statement 2 and statement 3 are false, but that means that the car must be in box 1 and 2 which doesn't make sense.
i thought box three because three states about one not itself
Selecting Box 1 Makes Answers 1 and 2 both True: Thus, wrong box. Selecting Box 3 Makes Answers 2 and 3 both true: Therefore wrong again. Selecting box 2 leaves only answer 3 to be "the" truthful answer. Even though the car being in box 2 makes answer 2 a lie it still contains the car and leaves only one truthful answer. And with that we find the car while following the rules of the test.
We know that only ONE statement is true and 2 are false. So, if we correct the statements we have 3 cases. Only one of this cases makes sense.
Case 1: "BOX 1 IS TELLING THE TRUE, SO WE CORRECT THE OTHER STATEMENTS". B1: The car is in this box B2 corrected: The car is in this box B3 corrected: The car is in box 1. (That don't makes any sense because in this case we have a car in box 1 and other car in box 2 but we know that there's only one car, so this case is FALSE)
Case 2: "BOX 2 IS TELLING THE TRUE, SO WE CORRECT THE OTHER STATEMENTS". B1 corrected: The car is not in this box B2: The car is not in this box B3 corrected: The car is in box 1. (That don't makes any sense because B1 and B2 are still in contradiction)
Case 3: "BOX 3 IS TELLING THE TRUE, SO WE CORRECT THE OTHER STATEMENTS". B1 corrected: The car is not in this box. B2 corrected: The car is in this box. B3: The car is not in box 1.
This is the only case that makes any sense because there are no contradictions. And, with the other statements corrected the answer can be found easily. So we know now that BOX 3 is telling the true, and it's telling that "The car is not in box 1", we don't know yet if there is a car in box 3, but with the other statements corrected we know that "the car is not in box 1" and "The car is in box 2", so now we know that there is not a car in Box 3 because it is in box 2.
....
Now i'm thinking that "FALSE" don't make it "THE OPPOSITE". So now i'm confused again.
This is not a place where you can abuse. There are logicians sitting here.
brother agree wit u
i agree with you talha arif..
agreed, box 3 has the car. as it says box 1 is not having the car. and box 2 says it doesnt have the car. so simply box 1 is false and and box 3 has it. i dont understand how box 2 is the answer ?
BUT KEEP IN MIND THAT THERE IS A CONDITION THAT ONLY ONE OF THE STATEMENT IS TRUE....
it should be #1 because (if the statement was true) then it would be in the box. box #3 statement (if was true) it says that its not in box #1 so u would have to guess if it was in box #2 or #3.
Agree with u. bad puzzle"
Logically it makes sense, like they said. If one statement is true then the other two are false.
1.) If box 1 is true, then boxes 2/3 would be false, meaning (for box 2)that the car is in box 2 and (for 3) the car is in box 1. In this case the car is in both boxes 1 and 2, which is not possible since there is only one car
2.) If box 2 is true, then boxes 1 and 3 would be false, meaning(for box 1) that the car is not in box 1(and for box 3) that the car is in box 1. Here we have another contradiction, since the car cannot both be and not be in box 1
3.) If box 3 is true, then boxes 1 and 2 would be false, meaning (for box 1) that the car is not in box 1 (and for box 2), that the car is in box 2. this is the only situation where we don't have a contradiction between the statements, therefore, box 3 is the true statement, and the car is in box 2.
on the first part.. if box 1 were true then box 3 would automatically be false, and since box 2 did say that the car is not in that box then it would also be telling the truth ,, eliminating the 2 car effect,,, but having the 2 true statement effect
Only one statement is true 1 The car is in this box 2 The car is NOT in this box 3 The car is NOT in box one Which car has the box ^restating so I don't have to scroll constantly.
If the car is in box one, then 1 and 2 are correct, and 3 is wrong. If the car is in box 2, then 1 and 3 are wrong and 2 is correct. If the car is in box 3, 1 is wrong, 2 and 3 are correct.
v_v I got that mixed up in my head.....I fell for the mind game. They intentionally made it look like 2 was the correct answer, which it is, and I fell for the simplicity of it. Well played.
guys we already have that "whether the dress is blue or gold drama" so why not not start an other one
That makes sense.
If B3 is correct then it only removes b1 as an option. it does not mean B2 can not have the car. both B2 and B3 are possible.
one thing you didn't count in the negative B2 which means =negative(the car is not in this box) there you have it, the answer is box 2
If B3 is true and the car is in B3 then B2 would also be true.
Since only one of the statements is true, the car cannot be in B3.
For some reason I associated the box with the true statement as the one having the car lol.
because the explanation was horrible.
Box 3 is telling the truth. And that makes Box 2 a liar. Thus, the car is in Box 2.
If B3 is true then in how means B2 is a liar..??
Only 1 statement is true. If only 1 is true, then the others are false. Therefore the statement "The car is not in this box" is false. Therefore a lie.
@Matthew Lewis – if statement 1 is true then the car is in box 1 and the other statement is wrong which makes statement 2 is wrong which means the car is in both box 1 and 2
My box three said hat" the car is not box 1" not "the car is not in box 1"
The only case in which only 1 statement comes to be true is when the car is box 2. If the car is proposed to be in the other the boxes (i.e. Box 1 &2), two statements come to be true and this contradicts the condition that only 1 statement is true. Hence, the car is in Box 2.
(Using Hit and Trial Method)
So if the car is in box 2, It makes statement B true. (car not in box2) its not in box 1 which makes statement C true. (car not in box1) Can someone kindly explain? I am confused.
How can statement B be true? The car is in Box 2, so "The car is not in Box 2" is false.
Oh shit. Yeah, I was so confused back then. Thanks.
HEY!! WHO DARES DOWNVOTE THIS CORRECT STATEMENT OF A REAL MAN??? I'LL TAKE YOU ON :V
dude why are you using alphabets now
well now ..... the trick to solving this in the easy way is to look the the first rule "only one of the statements is true" so you need to find which boxes would be lies and which would be the truth... but you can only find one box which is telling the truth so if we say box 1 is telling the truth then that would mean box 2 would be true too, and we can't have 2 true statements, but if box 3 were true then box 1 would be lieing and same goes for box 2 giving us 1 true statement and 2 false statements, and since box 2 states that the car is not in this box, that would mean the car is in box 2 box 1 is a lie as well so there is no car in there ... in conclussion the car is in box 2 ... also if you ask if box 2 were true, well then that would give us the same results as the if box 1 was also telling the truth.........so box 2 is the answer.........
the key in the question is " you know that only one of the statements is true"
one of box1's statement and box3's statement must be true, so if the statement of box 1 is true, the car is in box 1 ? And if the statement of box 3 is true, the car is in box 2 or 3 ?
no, you forgot to reverse the 2nd statement XD
It's simple. The car is in box 2 because if it is true then it's false.
Assuming each one to be telling the truth individually, we find that the solution holds only if Box 2 and Box 1 are telling lies and hence considering the third box is true, logically only Box 2 can contain the car!
In that case question should have been : Who is lying? Because Box 3 can also have the car, probability being 0.5....
its just ppls who didnt realize that much :) its actually easy, but I myself also didnt realize it at 1st that theres no 50% probability, only 100% which lies in box 2
If statement in box 1 is true ,then statement in box 2 is false, they are contradicting , how is box 2 chosen.?
ill get it straight, statement 3 is correct which means the car isn't in box 1(statement 1) and the car is in box 2(statement 2)
How could you choose the wrong one while you are seeking the right one? Why dont you choose 3 of them are wrong?
because one of them is correct
I thought that the car is in Box One just because it said "You know that only one of the statements is true. " and at the beginning I though that "one" is refer to box one. But forget it. I was wrong. --"
box 1 and 3 as you said contradict each other, which does mean it is in box 2. We know by reading the statement that box 3 is technically the true answer, because if box 1 was the true answer than, this would make box 2 have the car as well as box 1, but only 1 box can have it, which makes box 3 the true statement.
Scenario:
box 1 = true - box 2 = false, box 3 = false This would mean everything is the opposite of what is said now. This would make 2 boxes have the car.
Just need to think outside of the box :)
also for those saying it's stupid its in box 3, there is no evidence that it is in the box all the question asks is to identify 1 which is the true statement, this will than lead to which has the car in the box.
it was never outside the box, it was us who didn't realize in the first place :)
Why is everyone talking about boxes telling the truth or not??
FOR THOSE WHO DONT GET IT, heres the real image: https://d18l82el6cdm1i.cloudfront.net/.../7fab9a45431f9cc...
It clearly says "Only 1 of these statements is true" & "Which box is the car in"
you can put it into every combination you want but if you say the car is in box 2 then you're saying that the message in box 2 is false and the message in box 1 is false, thus making the message in box 3 the only true statement. This fits everything together.
Picking box 1 makes both messages in box 1 and true, which is not that they want.
Picking box 3 makes the messages in both 2 & 3 true which again, is not that they want.
Hope you guys get it now.
Amazing explanation!!!!!!
Beside Ivan explanation, a better way to solve the problem is not by defining a box as true and evaluating the others, but to define where is the car, and then see what the statements of the boxes are:
Car is in Box 1: Box 1: TRUE Box 2: TRUE Box 3: FALSE
Car is NOT in Box 1 because there can only be 1 true.
Car is in Box 3: Box 1: FALSE Box 2: TRUE Box 3: TRUE
Car is NOT in Box 3 because there can only be 1 true
Car is in Box 2: Box 1: FALSE Box 2: FALSE Box 3: TRUE
The question is direct: which box has the car? Thus, one need to search for the car, not search what box has the true statement. That information, while necessary, is complementary.
How does one determine which statement is the true statement?
If I am not actually getting a car...then who cares what box the car is in? Cars don't even come in boxes...
I think there really isn't a car after all. so the question is false. The car actually drove off with the idiot that came up with the stupid riddle.
But the answer could also be Box 1, right? If Box 2 and Box 3 statements are false and Box 1 is true, then Box 1 must have the car.
If Box 2's statement is false, then the car should be in Box 2. If Box 1 is the one that contains the car, Box 2's statement becomes true.
oh yeah, just realized that. Thanks!
that still doesn't make sense since box 2's preposition would contradict with the question
but it clearly states only one of the statement is true. If u consider statement 2 is true, then there are 2 possibilities. Car is either in 1st or 3rd box. And since statement 2 is true the other 1 and 3 statements should be false, but since they refer to only two possibilities each, one of them has to be true. that gives us 2 true statements, which is wrong.
no this is wrong, precisely because ONLY one of the statements are true. From a boolean logic perspective the other two must be false. If the statement on box one is true, then box 1 has the car and the car is in box 2 (contradictory). If the statement on box 2 is true, then box 1 is lying and box 3 must have the car. If box 3 is telling the truth, then the car is in box 1 and not in box 1 so its in box 2. So the car could be in either box 2 or 3. If you desire a situation where the result is unambiguous then the car is in box 2
proven you're halfway wrong. actually when statement 2 is correct, then the box isnt in box 1(statement 1) and the car is in box 1(statement 3). now do you understand? and your last statement>> if 3 is correct then both 1 and 2 are wrong. means that the car is in box 2 and 3 rather than 1(statement 1) but statement 2 said that the car IS NOT in box 2, REVERSED which makes it accurate enough to call it in box 2
I just think about how the hell the car is in the box ???? So why is box 2 ?????
statement 3 is correct is the answer, which means statement 1 and 2 is wrong which proven that box 2 is the sole owner of the car
i got the question correct so here's how i do it:
thinking logically, a "real" car couldn't fit in a "simple" box, therefore, i ended in the conclusion of statement of box 2.
Doing a True-False (TF) table the only combination of 2 false statements and 1 True statement is Iff statement/box 3 is True. so the car is in box 2.
It might be helpful to "sketch" the problem out with words. Only one of the boxes can be true. So that makes for three possible scenarios:
Scenario One, box 1 is true and boxes 2 and 3 are false.
Scenario Two, box 2 is true and boxes 1 and 3 are false.
Scenario Three, box 3 is true and boxes 1 and 2 are false.
If you go one by one down the list and test each scenario, only one scenario is possible without any contradiction.
That is asinine. So what if they contradict each other as only one is true. It makes more sense if box one is the answer as the other two leave you with a multiple boxes to choose from.
Even if box number 3 was correct and number 1 was contradicted, then the possibility for the car being in box number 3 still exists. Just because 1 and 3 contradict each other does not mean that box number 2 is false.
we WERE both trapped in the same position. but, realize it, the possibility of the car being in the 3rd is 0%. think if statement 1 or 2 is correct, like u have ever thought, you wont find the answer. but if you take the 3rd as correct it makes: 1-the car isnt in this box, and 2-the car is in this box, and 3-the car isnt in box 1 which makes it clear
I see so the question rules out the problem by following the mathematical solution by negation...
Still tho the f*ck somethings wrong with it, you cant rule out the possibility that box 1 and 3 doesn't have it all because it negated each other.
Reality is if box 3 negates box 1 by saying f*cking car isn't in box 1 we still are left with the fact that box 3 can be a neutral statement and thus box 2 and box 3 is still alive in the question negation. Box 3 ain't ruled out just yet.
Box 2 rules the equation by its statement "The Car is not in this box" thus leaving Box 3 and hence "Box 3" should be the answer.
Simply put it this way: Box 1 (a negative statement therefore (-)) Box 2 (still negative therefore (-)) Box 3 (is telling it half assedly therefore consider it a special case or a neutral statment (+/-)
Solve: (Box 1(-),Box 2 (-), Box 3 (+/-)/ Ruling(-) =Box 3 (+) ends up with the positive value
Answer: Box 3 otherwise the given hint is a dud
first, you're totally wrong if you said its about math, mathematical logic to be exact. it pumps your brain to its higher level of awareness(might be the one thing which creates mathematical logic in the first place). so, it doesn't start from math. and second, the answer is box 2 otherwise your answer sux much
Ya it's fine now, the questiona says that car get to keep in the box, it means there is no car in any one of these boxes ...so Box2 says that The car is not in this box..which is the correct answer. Am i correct ?????
ya its fine now ..the question clearly says that the car is get to keep in the box..it means there is no car in any one of these boxes ...so the Box2 says that There is no car in this box...is the correct answer.
Box3 says "the car is not box one". it did not use the words "is in" like the others. that's what I don't understand why I got it wrong.
Why is it not in box 3 ?
yeah your right
I think the answer should be BOX 3. If you say box 2 is true, then one of box 1 or box 3 will also be true - if let's say box 1 is false, then box 3 is true. right? But if you say only Box 3 is true, then box 1 can be false as well as box 2. Needless to say, Box 2 contains the car :)
Needless to say, Box 2 contains the car :)
My apologies but how is that a good interpretation? To get the answer you have to assume that at least one of the boxes is lying. There is no indication that any of them are lying except they contradict each other; thus it's simply a matter of guessing. It's Schrödinger's cat and lacks enough information to draw a logical conclusion.
They should add the fact that all the boxes are telling lies, then we have a complete clue
I would only add to this that NONE OF THE STATEMENTS ARE TRUE STATEMENTS.
1 the car is in the box 2 the car is not in the box 3 the car is not in the box 1
the correct answer is box 3 only
what if 1 statement is true and 2 and 3statement is false
Solution to the problem is succinctly stated by Ivan. No room for any doubts. Well done!!!
You can't be sure it is in box 2. The probablity is that the car could be in either of the boxes (2 or 3), given that the box 2 says "the car is not in this box"
This is tricky, and the answer lies there. Even if box 1 and 3 contradicts, it is not safe to say that they are indeed telling the truth, neither box 2; so it is not a good basis to assume box 2 has the car in it just by literally relying on their statements. As i've said it's tricky, every one of them is trying to confuse the reader or i should say the guesser. therefore the best possible solution is probability. in short, you have to guess the highest percentage of likeliness the boxes are telling the truth. P (1 U 2 U 3)= P(1/3) + P(1/3) + (1/3)... this equation implies each boxes has equal probability of 33.333 %. Conclusion: the statement in the boxes has nothing to do with the certainty of truth. it is a matter of fact or bluff that can only be treated by a wild guess with a 33.333% chance or guessing it right by luck.
in the question it is stated that "you know that only one of the statement is true". so the statements in box 1 and box 3 contradicting. then the statement in box 2 is the only true statement. therefore the box 2 is correct answer. question to find our box having car is diverting.
good call. I didn't read that completely. That's what I get for skimming.
Actually the correct answer is a split answer, You can have 1. you solution or 2. the answer is a paradox, aka unsolveable, since there is no force dictating which answer is the true one, this is a logical solution.
This is completely pointless because you don't know definitively who is telling the truth thus any conclusion is moot. She said he said.
NO you are wrong... if you are telling the 2 having the car, then the false condition is applying on this question. The statements are not in correct. Here 3 is pointing to 1 and 1 is true and 2 is false, then here the answer is false how come. can you summarize it, true becomes false and false becomes true conditions. is this is a magic?
I worked on the assumption that the car was in the 'true' box; it isn't. The car is in Box 2
I never find a car in a box -_-
that's all right but how do you know that. if statement 1 is wrong that means statement 2 is true and nothing is mentioned about box 3 so why couldnt the car be in box 3?
Just because statement 1 is wrong does not automatically make statement 2 right. Those two could both be wrong and make statement 3 right.
The reason why the car is not in box 3 is because if it were it would make both statement 2 and statement 3 true and the directions say that ONLY ONE statement can be true which means two of them have to be false. So you would be looking for the solution that makes two of the statements false and one statement true.
If the car were in Box 1: The statement on Box 1 " The car is in this box" would be TRUE and the statement on Box 2 "The car is not in this box." would also be TRUE (we cannot have 2 true statements)
If it were in Box 3: The statement on Box 2 "The car is not in this box." would be TRUE and the statement on Box 3 "The car is not in box 1." would also be TRUE (again, we cannot have 2 true statements)
The only logical answer is that the car is in Box 2, which would mean the statement on Box 1 is FALSE (The car is, in fact, NOT in Box 1), the statement on Box 2 FALSE (The car is indeed in Box 2), and the statement in Box 3 TRUE (The car is not in Box 1, because it is in Box 2. Yay! We found an answer with ONLY ONE true statement)
Logically, The car being in Box 2 is the only logical conclusion that satisfies all of the requirements for the question.
Let us make this real simple
You're genius :o
On the link that led me here, they omitted the part that says that only one statement is true. Where multiple truths are possible, it could also be Box 3.
That part is kind of important!
stupid really !! It shd be 3 since it is clearly stated on 2 that the car is not in it...deceitful
only one statement can be true. Just read a little bit more the question.
Breakdown:
If the box 1 has the car: Box 1 and 2 are telling the truth, therefore, false
If the box 3 has the car: Box 1 is lying, but Box 2 and 3 are telling the truth, therefore, false
If the box 2 has the car: Box 1 and 2 are lying, but Box 3 only has a true statement, therefore, true
I don't get it....why is it box 2? if it was box 2 then box1 is lying, box 2 is lying and box 3 is telling the truth........if it were box 1 then box would be true and 3 would be false, but if it were box 3 then box 2 would be true but one would be lying.... ITS ALL A LIE!!
if box 2 os true then the car can't be there because it says its not there, if it says its not there and the car is there then that means it is there and box 2 is false, meaning it cant be there, its a paradox
Umm isnt the answer 1? The question says that Only "1" of these statements are true. it could've said "one" but it says "1". How's that for a plausible theory ha?
Why would I look in box 2 and 3? If I follow the logical steps , I would stop my observations at box 1. And the observations for box 2 and 3 wouldn't exist until I found that the statement for box 1 were false, and if it were false then box 1 and 3 are the same, and box 2 would be true, and I would conclude that the car doesn't exist.
I'm a bit confused, how do you know wether a box is false or true?
It must be the box 1 which clearly states that "the car is in this box"
I love your explanation. Sungguh sangat bernas! :)
but if box1 is true then two and three would be false, then it could be one
But if bow 1 is true, then that means there is a car in both 1 and 2
Yes, you're right! There are 3 combinations were created with these 3 statements. 1st, If box 1 is true then box 2 is true as well and then box 3 is false. this combination does not meet "Only 1 of these statements is true" 2nd, If box 1 is false and box 2 is true and then box 3 is true. this combination does not meet "Only 1 of these statements is true" 3rd, If box 1 is false and box 2 is false and then box 3 is true. this combination meets "Only 1 of these statements is true" so, box 1 is wrong statement (No car), box 2 is wrong statement (There is a car in this box), box 3 is correct statement.
it should be box 3 bc it never says anything about box 2 being false and box 3 says it isnt in box 1, nothing says anything about box 3
Yeah, I pretty much had the same logic on that. I didn't think too much on it.
I'm confused then.
If Box 1 is True, Boxes 2&3 are 'lying', then Box 1 has the car (because it says it's in that box)...
If Box 2 is true, Boxes 1&3 are 'lying', then no Box has the car (because 1&3 contradict each other...
If Box 3 is True, Boxes 1&2 are 'lying', then Box 2 has the car (because saying it isn't there was false)...
doesnt make sense because if box number 1 had the car and box number 2 didn't have it ( as stated on the box ) box number 3 should have had it because there is no statement saying it didn't yet on number 2 it said it didn't have it and number three said number 1 didn't have it so its made to lie to you?
If box 1 is true then it would have the car would be in box 1 , and box 2 would be true also.
If box 2 is true than neither box 1 or 3 could have the car because if it were in 1 than box 1 is true, and if its in box 3 , box 3 is true.
if box 3 is true, than box 1 cant have the car, and box 3 cant have the car otherwise it is true, hence the car being in box 2
I only assume step by step.....1. If state 1 is true , statement 2 or 3 can be true too . 2. Similar result happens to statement 2 . 3. If statement 3 is true , there is no room for other statements to be true , so the car is in box 3.
The only possible answer is two. The question isn't allowed to lie to you, so the only way that only 1 of the 3 statements could be true would be for 'Box 1' to be lying about having the car and for 'Box 3' to be lying about also saying that 'Box 1' had the car. That way 'Box 2' is the only box that is telling the truth.
How did you know that Box 2's statement is false !!??
we know only one statement is right let, 1- the car is in the box ( false ) 2- the car is not not the box ( false ) 3- the car is not in the box 1 ( true ) according to the statement 3 car is not in the box 1 . box 2 statement states that the car is not in the box and is false means that the car is in the box 2 box 3 may be have car but box 2 is more preferable according to the conditions.
One thing... Its really not 100 porcent correct the answer, beacuse if its in box 1 and then 3 says its not there, so then we just have 2 options... 2 and 3. If number 2 says its not there, the only one you can take is number 3. Number 3 is telling the truth about number 1, not itself. So it should be number 3.
Yeah but Box 3 is not stating whether or not there is a car in it so they answer would have to be Box 3 because it's the only one that's not stating anything about the state of the inside of that box
How is the answer NOT #3??? #2 specifically says "the car is NOT in this box," and #3 cancels #1's claim that the car is in box #1. So logically, the answer SHOULD be #3, or can someone kindly explain how #2 can possibly be right when it says clearly that the car is NOT in it, and no other box disagrees with that claim?
Another good way to explain: Just because one of the statements (Box 3) is true, does not automatically mean it is in that box! Got hung up on that. If Box 3 is true, then box 1 & 2 are false, cancelling out box one and making box two say that the car IS in this box. So it's in box 2!
So you've said that eithger Box 3's statement or Box 1's statement is true. Assuming it's Box 1's statement that is true, the car is in Box 1. Explain why I'm wrong.
EDIT: Wait, I understand. If Box 1's statement was true, then the car would be in both Box 1 and Box 2,, and there is only 1 car.
Not one thing said that the car had to be under the true statement. It only stated that only one statement was true. So, yeah I like box 2.
ok so box #1 statement is the car is in this box, #2 statement is the car is not in this boz, and #3 statement is the car is not in box 1...... so if box #1 statement is true then it would be in the box, if box #2 statement was true then the car would not be in that box so it would be in box #1 or #3, you would have to guess which one in this case, if box #3 statement is true then the car is not in box #1, so it would be in box #2 or #3, you would also have to guess which one. so which statement is true?
ok so box #1 statement is the car is in this box, #2 statement is the car is not in this box, and #3 statement is the car is not in box 1...... so if box #1 statement is true then it would be in the box, if box #2 statement was true then the car would not be in that box so it would be in box #1 or #3, you would have to guess which one in this case, if box #3 statement is true then the car is not in box #1, so it would be in box #2 or #3, you would also have to guess which one. so which statement is true?
1 and 3 contradict each other, yes, but what if 1 is true, then 2 is true. You need three true statements which is impossible here. So, there is no logical solution.
If only ONE of the statements is true, it has to be in box 2; 1 and 2 false, 3 true. If in box 1; 1 and 2 true, 3 false. If in box 3, 2 and 3 true, 1 false.
"Box 1's statement and Box 3's statement contradict each other, so one of them must be true. Thus Box 2's statement is false, so the car is in Box 2."
There's nothing logical about that whatsoever. Just because the statements in boxes 1 and 3 contradict (if we take them at face value) each other it doesn't actually infer anything about the actual validity about statement about box 2.
"so one of them must be true."
No, that's just an assumption. One that honestly has no logical backing. It's perfectly plausible that any one of those could be false.
If we assume 1 is false, and 2 and 3 or true then there is no contradiction and it stands to reason that the car is box three.
If we assume 2 is false then it's in 2.
If we assume 3 is false then it's in 1.
The problem is that there's no way of really knowing which is false.
ahahah this is kind of a tricky question, but wait there are some problems if the correct box is 2 .. the very first says the car is in it - the second is not - the third box 1 don't have --- so if car is not in box 1 and 2 then it must have to be in 3 ? if 3 is the correct answer then box one is also correct ? how when the box three stating the car is not in box 1 ? while the question clearly stats "only one of the statements is true" that's the game man ! they are not telling you to find the right box with the car they are saying the box with the right statement has the car ! but isn't it contradicting it self ? the right statement ? is not right if the box has the car and statement says that box don't have the car then this is the false statement same as box 1 and box 3 statement so if the box 2 statement is considered to be right statement, then box 1 and 3 must also be considered right statement. Well Nice played ! if the contradictory statement is the right statement then all 3 are contradictory while logically speaking -- no box speaks about box 3 - so the box 3 has obvious chances of having the car while keeping in mind there is no statement which is not contradicting to each other.
Clear and simple in just a few seconds. Follow the statements and read nothing into them.
I'm an idiot, I didn't see the part that says "Only one of these statements is true." I was like, wtf? I get it now. Gotta read everything.
It could be Box 2 if we assume that all boxes lie about what it says. But if we don't judge about veracity of each statement so the answer could be also box 3
How do we know that a contradiction has one true side....both of them could be false...:D
Ah ha - didn't go far enough - eliminated the boxes but forgot about the car itself. Grrrrr.
box 1 should have been the answer because box 3 was lying the statement on box 3 was grammatically wrong
That is bs! I do you not know that box 1 is telling the truth and box 3 is a liar!
(if box 1 has the car) 1st & 3rd statements are both true (contradict the problem's condition) X (if box 2 has the car) 1st & 2nd statement will be false while 3rd is true (approves with the problem's condition) (if box 3 has the car) 2nd & 3rd statement are both true (contradict the problem's condition) X
I'm of the full realization that the answer is 2, and I picked 3, making me wrong. However, I have an honest question on why the answer is two.
"Only one of these statements is true."
The first box claims that it has the car, which contradicts box three. Box two claims that the car is not in this box. In order for two to be right, it must be an untrue statement. Box three declares that box one is lying (or has an untrue statement. I just like to anthropomorphize. ;)" However, box three says nothing about it's own contents, Therefore, to me at least, the correct box seems to be three.
Though I'm sure I'm probably just seeing this wrong. lol
definetly no...box 1 and box 2 are true...and it suppots the statement on box 3...check your answer again
If it is inbox 2, it's not in box 1 which means the statement on box 3 is correct. Doesn't it?
If Box 1 is true then box 2 would also be true, which can't be since we know only one is true. Therefore we know box 1 is empty and that box 3 is the one that's true. This means box 2 is a lie, implying the opposite.
Moderator note:
Simple and concise!
If #1 is true, #1 and #3 contradicts with #2.
If #2 is true, #1 contradict with #3.
If #3 is true, then there is no contradiction, and the car must be in #2.
But, the ultimate truth is that the car is a lie...
Moderator note:
Simple and understandable diagram. Good job!
if 1 is true then: 1 is T; 2 is T; 3 is F -----> 2 gave 1 the benefit of a doubt...
if 2 is true then: 1 is T; 2 is T; 3 is T -----> 2 gave 1&3 the benefit of a doubt...
if 3 is true then: 1 is F; 2 is T; 3 is T -----> 2 gave 3 the benefit of a doubt
Clearly, #2 is neutral, infact it is just playing safe to get rid of attention. That's why there is no contradiction between both #1 & #3, but it doesn't mean the car was there. It's uncertain because you cannot remove the fact that each of them might be lying, and we can verify this by going back to the statement of the author "only 1 of the statement is true" therefore there was two of them lying but we are uncertain which of those three. The probability of each statement to be true or false is P(1 U 2 U 3)= P(1/3)+P(1/3)+P(1/3), EQUAL at 33.333%. one of them is telling the truth though, but it would be a wild guess to pin point which is which :)
I don't think there is probability involved in this problem. The key points are only one of them is true, and one of them has a car. So, we just need to find a case where a statement is true, and there is no contradiction about the position of the car when we negate/reverse other statement.
Do this by elminination
If Statement 1 is true, technically there would be a car in every box
If Statement 2 is true, Statement 1 and 3 contradict each other, leaving no car in a box
If Statement 3 is true, it agrees with Statement 1, and leaves the car in box 2
We are going through the statements, as the problem setter told that only one statement will be true !
Solution:
Let, three boxes as A, B, C;
For Box A
if A = true, then B = true and C = false >> (2 true, can't be) if A = false, then B = true and C = true >> (2 true, can't be)
For Box B
if B = true, then A = true and C = false >> (2 true, can't be) if B = false, then A = false and C = true >> (1 true, can be)
For Box C
if C = true, then A = false and B = true >> (2 true, can't be) if C = false, then A = true and B = true >> (2 true, can't be)
As, we can see if B = false we get one condition true, So B is the right answer, I mean answer is Box 2.
you guys need to think very deep to get this question right,first of all the main condition of this problem is that only one of the statements is correct. so we can only have TFF, FTF and FFT,so lets test all this three to see which one is valid for the first one if box 1 is true then box 2 is also true,so that option one-TFF is not possible.Now for option 2 if the first statement is false then the car must be in box 2 or 3,so that means that if the car is not in box 2 it is in box 3,so if the car is not in box 2 is true,the car is not in box 1 is true because it has to be in box3,so option 2 is ruled out too.For option 3, if statement one is false,that means that if the car is in box 2 in contrast to option 2 ,then it is not in box 3,so we have the first statement being false,the second statement being false and the last statement being true because infact the car has to be in box 2.So in this case the the last option is valid and satisfies our condition,so car in box 2 is the answer
Moderator note:
Yes! You got it right!
Box one and three both contradict each other, therefore, one is true and one is false, therefore, statement two must be false, thus the car is in box two
Box #1 statement cannot be true, because, that would make it's statement and box #2 statement also true, breaking the #1 rule that only 1 statement is true. ( therefore the CAR cannot be in box #1 )
if Box #2 statement is FALSE, then both "It's not in box #2 --> meaning that it is in box #2" then THE ONLY statement that can be true, is what box #3 says is that the car is NOT in box #2. Box #1 statement that it's in box #1 is also false. OUR JOB IS done. ==> and if box#2 statement is false, then the car is in Box #2 :)
Moderator note:
Good clear explanation.
The key is only one statement is true.
- Case I: If the car is in box 1, then the statement 1 & 2 holds true
- Case II: If the card is in box 3, then the statement 2 & 3 holds true
- Case III: Inf the car is in box 2, ten only the statement 3 holds true
So answer is box 2, case III.
Good comments! We must really consider these 2 points: - The question - Where is the car? - The box you find the car must hold only ONE statement true.
So the correct answer is box 2.
Regards, Rodrigo
Answer : Car is in Box 2.
Lets take each turn. Lets assume statements as S1, S2 and S3.
Box 1 has car: Then S1 is true, S2 is true and S3 is false. Two true statements
Box 2 has car: Then S1 is false, S2 is false ans S3 is true. One true statement, i.e. S3.
Box 3 has car. Then S1 is false, S2 is true and S3 is true. Two true statements.
Precisely, that is the logic I came up with too.
No, it's definetely in box 2. Think about it. If box 3 statement is true, then statements in 1 and 2 are false. 3 states that the car is not in 1, and since the statement in 1 is false, then there's no car in 1. However, 2 states it doesn't have the car, but since it is false then it should have it. Assuming the other statements were the true ones, then there would be contradictions. Box 3 statement is the only one that can be true without any contradictions.
Moderator note:
Correct!
Criteria is only one statement is true. Now, if box 1 is true then rest of them are false according to which the car is in both box 1 and 2 which is not possible. Box 2 can't be true which makes box 3 false making box 1 right. Box 2 false and therefore cat is in box 2.
Simplest method to solve this question to assume each statement as true and see if it satisfies the other statements. So if we assume,
Statement on Box 1 is true then, Box 1: The car is in this box. (true) Box 2: The car is not in this box. (false) {means car is in this box} Box 3: The car is not in box 1. (false) But as the car is only in one box so this case is false.
Statement on Box 2 is true then, Box 1: The car is in this box. (false) {means car is not in this box} Box 2: The car is not in this box. (true) Box 3: The car is not in box 1. (false) {means car is in box one} But this situation has two contradictory statement so this is also false.
Statement on Box 3 is true then, Box 1: The car is in this box. (false) {means car is not in this box} Box 2: The car is not in this box. (false) {means car is in this box} Box 3: The car is not in box 1. (true) {means car is not in box one} Only this case satisfies all the statements and contradicts none so Car is in box 2 .
Relevant wiki: Truth-Tellers and Liars