There are 4 chests: Left, middle 1, middle 2 and right. One contains treasure whilst the other 3 contain a poisonous gas. Left opens if a true statement is said, right opens if a false statement is said, middle 1 opens if you say a statement that contains some truths and some lies eg (“2+2=5 and the Earth isn’t flat”). Middle 2 opens if you say a paradoxically true and false sentence eg “this statement is false”. If you say a statement that contains truth and falseness only middle 1 opens. You can only say 1 sentence, is it possible to be guaranteed treasure for every possibility? If not, then what can you do to increase your chances? Every conjunction is Boolean except for “and”
2 Answers
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Developing an Answer
There are four test cases. We want to pass as many of them as possible.
First: All components of the statement must be true if the treasure is in the left chest.
Second: All components of the statement must be false if the treasure is in the right chest.
Third: At least one component of the statement must be true and another component must be false if the treasure is in the middle-1 chest.
Fourth: The overall statement must be paradoxical if the treasure is in the middle-2 chest.
The first and second test cases are easy to pass:
"The treasure is in the left chest."
The third test case adds some complexity. We now need two statements (conjoined by AND) such that both are true if the treasure is in the left chest, both are false if the treasure is in the right chest, and one is true, one is false if the treasure is in the middle-1 chest.
"The treasure is in the left chest AND the treasure is to the left of the middle-2 chest"
Finally, the fourth test case. We need to add or change the statement to make it paradoxical if and only if the treasure is in the middle-2 chest, without disrupting the other three cases.
One way to do this is to add a statement which is
True when the treasure is in the left chest
False when it's in the right chest
Any non-paradoxical value when it's in the middle-1 chest
Paradoxical when it's in the middle-2 chest
Whether such a statement can exist depends a lot on how the statements are evaluated. The existence of the middle-1 chest means we're not dealing with normal Boolean logic.
I believe the following statement works but it depends on how "OR" works in this language. I am assuming that everything is boolean except for "AND" which the chests treat specially in order accommodate the middle-1 chest.
"The treasure is in the left chest, OR it's in the middle-1 chest AND a the right chest will kill me when I finish talking."
This works because:
If the left chest has the treasure, then it's "true, OR false and false," which is a true statement overall because of the OR.
If the right chest has the treasure, then it's "false, OR false and false," which is all false.
If the middle-1 chest has the treasure, then it's "false, OR true and false," which is mixed.
If the middle-2 chest has the treasure, then it's a paradox:
* If the right chest opens, "false, OR false and true," which is a mixed statement.
* If any other chest opens, "false, OR false and false," which is false statement.
If OR doesn't work like that in this language, then this answer will need to be updated once the question is better specified.
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Partial answer
Saying "The treasure is in the left chest and the treasure is not in the right chest." works for Left, Middle 1 and Right.
answered Nov 20, 2022 at 10:05
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$\begingroup$ True, that statement does work for the left chest, right chest and middle 1. $\endgroup$– ParadoxNov 21, 2022 at 9:51
and? For example, if I say, "2+2=4orthe Earth is flat," is that a true statement or an ambiguous one? Similarly, if I say, "If2+2=4,thenthe Earth is flat," is that a false statement or an ambiguous one? What about multiple nouns with the same proposition applied - for example, "The left and right chests both contain poison"? $\endgroup$