Parlor puzzle without solution, or am I wrong?

[Som_gamer]

I came across a parlor puzzle that had the following statements:

Blue box:

• The gems are in a box with the longest word.
  
• 'Longest' is the longest word on a box.

White box:

• The gems are in a box with the shortest word.
  
• 'A' is the shortest word on a box.

Black box:

• There are words on the box with the gems.
  
• This box does not contain the gems.

The problem comes when you realize that all of the boxes have one true statement. 'Longest' is the longest word on the blue box, 'a' is the shortest on the white box and the gems are obviously in a box with words on it.
The rules to the room say that at least one box has only false statements, which in this case just doesn't seem to be true.

After a minute of thinking, I interpreted the statement "'Longest' is the longest word on a box." as "'Longest' is the longest word on any box.", which would be false since 'shortest' is longer. This would mean that the gems were in the white box, so I opened it and found it empty.

Am I missing something, or does this puzzle really have no clear solution?

[Lactose Intolerant Volcano God]

'Shortest' is longer than 'longest'. :-)

[Som_gamer]

Originally posted by Lactose Intolerant Volcano God:

'Shortest' is longer than 'longest'. :-)

Yes I know but that doesn't solve the problem. Please read the post.

[NoOneOfConsequence]

At least one box only contains false statements.

The white and black box both contain statements that are intrinsically true -- "'A' is the shortest word on a box' and 'There are words on the box with the gems.'
Therefore, both statements on blue must be false -- The gems are not in the box with the longest word (which is "shortest," on the white box) so white is out.

That leaves two remaining statements -- "The gems are in the box with the shortest word" on white and "This box does not contain the gems" on black.

At least one must be true -- if they are both false, then that fails the condition that at least one box must contain only true statements.

If "This box does not contain the gems" on black is true, then the gems would be in either blue or white, but white is already ruled out.

If black DOES contain the gems, making that statement false, then white must have two true statements, but it cannot, because white says the gems are in the box with the shortest word ("a") and the black box does not have that word on it.

Therefore, the gems were in blue.

[Som_gamer]

Originally posted by NoOneOfConsequence:

At least one box only contains false statements.

The white and black box both contain statements that are intrinsically true -- "'A' is the shortest word on a box' and 'There are words on the box with the gems.'
Therefore, both statements on blue must be false -- The gems are not in the box with the longest word (which is "shortest," on the white box so white is out.

That leaves two remaining statements -- "The gems are in the box with the shortest word" on white and "This box does not contain the gems" on black.

At least one must be true -- if they are both false, then that fails the condition that at least one box must contain only true statements.

If "This box does not contain the gems" on black is true, then the gems would be in either blue or white, but white is already ruled out.

If black DOES contain the gems, making that statement false, then white must have two true statements, but it cannot, because white says the gems are in the box with the shortest word ("a") and the black box does not have that word on it.

Therefore, the gems were in blue.
[/quote]
Isn't "'Longest' is the longest word on a box" also intrinsically true? It's not specified if it has to be the longest word on all of the boxes combined, it just says that it is the longest on one box. And since it is the longest word on the blue box, this statement is also true. But then the rule of the puzzle that "At least one box only contains false statements." is unfulfilled, and this is my problem.
If we disregard this one statement, then I understand your reasoning and solution.

[NoOneOfConsequence]

I guess I can't be sure, but based on what I've seen in past puzzles, I'd expect the blue box to say "'Longest' is the longest word on THIS box", if that is what it meant.
And if one possible interpretation makes the puzzle unsolvable and the other does not, it's probably best to go with the one that does not. :)

[Som_gamer]

You're probably right. Still, I think it shouldn't be up to interpretation, the change of one word in the phrasing would make its meaning obvious.

[kunou126]

When you list:

Originally posted by Som_gamer:

Black box:

• There are words on the box with the gems.
  
• This box does not contain the gems.

Are both those sentences on the box? Or did you open the box and find no gems in it?

Or are there 2nd sentences on the blue and white boxes above?

I'm going to assume both sentences are on each box... so with that...


The blue box is inherently false because "shortest" is the longest word, and that's just the sort of mind games these guys would play on you, and it can't be in the white box.

Now... on that assumption...
If the black box is true, the gems are not there and they must be in the blue box.

If the white box is true, and the gems can't be in the white box, the gems must be in the blue box.

One of those boxes HAS to be true.

The gems are in blue.

[Howdy_McGee]

I would assume that in a case of multiple statements, both would need to be true or false for it to quality.

true + true = true
true + false = false
false + false = false

[Vardis]

Originally posted by Som_gamer:

You're probably right. Still, I think it shouldn't be up to interpretation, the change of one word in the phrasing would make its meaning obvious.

"The gems are in a box with the longest word" is saying that the box with the longest word has the gems. There's no other correct interpretation.

[Nerimo]

Originally posted by Howdy_McGee:

I would assume that in a case of multiple statements, both would need to be true or false for it to quality.

true + true = true
true + false = false
false + false = false

The rules are fairly clear. At least one box will have statements which are all false. At least one box will have statements that are all true.

This leaves room for a box in which one statement is true, and one is false, as long as the other two conditions have been met.

[Vardis]

Originally posted by Howdy_McGee:

I would assume that in a case of multiple statements, both would need to be true or false for it to quality.

true + true = true
true + false = false
false + false = false

Multiple statements are separate from each other. If a box says "There are no gems" and "There are gems", then it is not one of the boxes that only has true or false messages. If it says "There are no gems and there are gems", it has a false message.

[Som_gamer]

Originally posted by Vardis:

Originally posted by Som_gamer:

You're probably right. Still, I think it shouldn't be up to interpretation, the change of one word in the phrasing would make its meaning obvious.

"The gems are in a box with the longest word" is saying that the box with the longest word has the gems. There's no other correct interpretation.

I'm not talking about this statement, I'm talking about the one that says "'Longest' is the longest word on a box". This does have multiple interpretations:

• 'Longest' is the longest word on ONE of the boxes --> this would be true
  
• 'Longest' is the longest word out of any words from any boxes --> this would be false

[Acherow]

Originally posted by Som_gamer:

Originally posted by Vardis:

"The gems are in a box with the longest word" is saying that the box with the longest word has the gems. There's no other correct interpretation.

I'm not talking about this statement, I'm talking about the one that says "'Longest' is the longest word on a box". This does have multiple interpretations:

• 'Longest' is the longest word on ONE of the boxes --> this would be true
  
• 'Longest' is the longest word out of any words from any boxes --> this would be false

"longest is the longest word on one of the boxes" makes no sense. every box has a longest word if you separate them.

[Aris]

Originally posted by Acherow:

Originally posted by Som_gamer:

I'm not talking about this statement, I'm talking about the one that says "'Longest' is the longest word on a box". This does have multiple interpretations:

• 'Longest' is the longest word on ONE of the boxes --> this would be true
  
• 'Longest' is the longest word out of any words from any boxes --> this would be false

"longest is the longest word on one of the boxes" makes no sense. every box has a longest word if you separate them.

It makes perfect sense. It means that on one box, its longer word is "longest". That may not be the longest word on all boxes.

[Pluk]

> There will always be at least one box which displays only true statements.
> There will always be at least one box which displays only false statements.
> Only one box has a prize within. The other two are empty.

This phrases is problematic:
'Longest' is the longest word on a box.

If this means "Longest is the longest word of all the words on all boxes" then it's False, if it means "the longest word on one box" it's True. It's unfortunate that the language here isn't clearer.

"'A' is the shortest word on a box". has the same unclear language, but in both interpretations this would be true (it's the shortest word on one box, and also of all the words on all boxes).

What I like to do in this test, is first determine what the possible truth/false values are for any rule on any box:

Blue box:
The gems are in a box with the longest word. -> could be true or false
'Longest' is the longest word on a box. -> could be true or false
White box:
The gems are in a box with the shortest word. -> Could be true or false
'A' is the shortest word on a box. -> True
Black box:
There are words on the box with the gems. -> True
This box does not contain the gems. -> Could be true or false

As you can see, the Blue Box HAS the be completely False, because we already see that White and Black both have at least 1 true statement.

Blue box:
The gems are in a box with the longest word. -> False -> The gems are not in a box with the longest word, so not in the White Box
'Longest' is the longest word on a box. -> False -> "Shortest" is the longest word

So then let's figure out which box is True:
If the white box is true, the gems are in the box with the shortest word, so it would be in the White box. That would mean that the Black Box is also completely true, because the black box does then not contain gems.
If the black box is true, then the black box does not contain the gems, so it must be in the white box.
Given that one of them MUST be completely true, and given that if one of them is completely true, so it the other one, and given that if either is true, the gems are in the white box, then the gems must be in the white box.

> This would mean that the gems were in the white box, so I opened it and found it empty.

Oh, huh. Yeah unless there is a problem with my reasoning, this challenge was bugged.

Edit: the only "escape" I see here, is if "'A' is the shortest word on a box." would be false, which can only be true if you interpret this as "On all the boxes, 'A' is the shortest word", which would be a really weird way to interpret that.