Yes. Normally, problems give you information so that you can do something with it. Otherwise, even if the author says later on:
Notice that the problem condition gives the suitor a certification about the truth of the labels
the problem author can always cop out and say "yes, but the certification itself was meaningless!".
If I take the labels to their face value, the treasure cannot be in the green box because the red label doesn't have a truth value. (If it's true, then there are two true labels, therefore it must be false. But if it's false, there is only one true label, so the red one is true.)
It's more interesting than that. If you take the labels at their face value, evaluating the red label either causes itself to be correct (flip-flop), or causes itself to be incorrect (#REF!), based on the state of the world.
treasure in green | treasure in red | green label | red label
------------------+-----------------+---------------+-----------
no | no | false | flip-flop
no | yes | false | flip-flop
yes | no | true | #REF!
yes | yes | misquantified | #REF!
i'm so confused. the red label doesnt convey any information yet it rules out the ability that the green label is true.
so how can the green label still be true?
or is the author saying that the symbols on labels dont mean anything? if he says that, it's tautological. what can we get from discussion if we dont conventionally put meaning in symbols? are what we typing now in all these comments also jibberish??
The contents of the green box make the labels paradoxical; but it's OK because paradoxes exist.
Consider a paradox such as "This sentence is false". There's a problem with deciding if it's true or false. Countless articles and books have been written about it, and there exist different ways of dealing with this "difficulty". However, nothing prevents you from actually writing these letters on a piece of paper, and nothing prevented me from typing them a few seconds ago. The puzzle we're talking about makes the same point in a more amusing fashion.
hm, isnt that obvious? if it's just "we do whatever we want regardless of whatever", then we dont need to go that far: elaborating a nonsense puzzle to prove nonsense.
Quite. This is a pointless exercise - there are assumed rules in most or all logic puzzles of this sort. The assumption that statements made in the puzzle are true or false, but not gibberish, is a fair one.
> The assumption that statements made in the puzzle are true or false, but not gibberish, is a fair one.
But given that one of the possible answers (the right one) did not depend on that assumption, and in fact the git of the puzzle is that you shouldn't depend on it, the puzzle is fair.
I know not everyone shares my feelings about the trickiness of the puzzle, but I have to immortalise this typo because it so perfectly sums up those feelings. :-)
