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1. Spoilers ahead.
Regarding the cells riddle:
If Cell 3 holds worthless brass, Cell 2 holds the gold key.
If Cell 1 holds the gold key, Cell 3 holds worthless brass.
If Cell 2 holds worthless brass, Cell 1 holds the gold key.
Knowing this brave fool, and knowing that all that is said cannot be true, which cell contains the gold key?

2. A quick google search shows the answer, but I don't understand why it is the answer. Maybe I'm mistaken in the way I'm reading it. It looks to me like the last line is saying "not all of the above answers are true," as in an emphasis on "all," meaning "all cannot be true, but all is not false either, therefore at least one statement is true." If read as two out of the three statements are false, with only one statement being true, we get an answer that doesn't line up with the game's answer: C1. If S1 is the one true statement and the key is in C1, P2 would be true which would make a contradiction. If S1 is true and the key is in C2, all of the statements are consistent. If S1 is true and the key is in C3, all of the statements would be consistent. If S2 is true and C1 has the key, S3 would be true and a contradiction. If S2 is true and the key is in C2, S1 would also be true and we'd have a contradiction. If S2 true and C3>key, S2 would be contradictory. If S3 true and C1>key, S2 true and contradictory. If S3 true and C2>key, S1 true and contradictory. If S3 true and C3>key, S3 would be self-contradicting.

3. If read as, "all cannot be true," it's ambiguous. It can either be one, two, or three false proposition(s). If it's read as only one false proposition and we assume P1 is the one false proposition and we assume the gold key is in cell 1, all of the statements are consistent and match up with the game's answer. If P1 is false, the key cannot be in C2 because it would make C1 a true proposition; we'd have a contradiction. If P1 is false and the key is in C3, P3 is false, and we'd have a contradiction there. If P2 is false and the key is in C1, we've got a contradiction. If P2 is false and the key is in C2, the statements are consistent (and it might be one of two answers that make sense) explanation the game has in mind). If P2 is false and the key is in C3, then P3 is false and we'd have a contradiction. If P3 is false and the key is in C1, P3 would also be true and we'd have a contradiction. If P3 is false and the key is in C2, all of the statements are consistent again. If P3 is false and the key is in C3, the statements are consistent.

4. If read as "none of the above statements can be true," and all three propositions are false, and the key is in C1, C2 would be true and we'd have a contradiction. If the key is in C2, then P1 is true and we have a contradiction. If the key is in C3, all three statements are consistent, but it doesn't match up with the game's answer.

5. I can't think of a way to explain the game's answer in a logically consistent manner. Send halp.
Post edited December 18, 2017 by joeybuddy96
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Let's consider the case where all the statements are true.

If the key is in 1, then it isn't in 3, and therefore must be in 2. (Contradiction, since there's only one key.)
If the key is in 2, then we have no more information. We get that 3 has worthless brass, but that doesn't tell us anything useful.
If the key is in 3, then it isn't in 2, which means it must be in 1, which is *again* a contradiction.

So, if all statements are true, then the key is in 2.

Now, if all the statements are false, we then take the negations of the statements, which are as follows (remember, for a if statement to be false, the if part mus be true and the then part must be false):
Cell 3 holds worthless brass and cell 2 has worthless brass. (Key in 1)
Cell 1 holds the gold key and cell 3 holds the gold key. (Contradiction)
Cell 2 holds worthless brass and cell 1 holds the worthless brass. (Key in 3)

Therefore, we can determine that the second statement *must* be true, or else there would be a contradiction. So, the cases where S2 is false can be eliminated entirely.

So, let's suppose that S3 is false. Then the key is in C3, which satisfies S1. If S1 is false, on the other hand, then C1 has the gold key. (S1 and S3 can't both be false!)

So, I can explain the game's answer in a logically consistent manner, but I still have the problem that there are 2 solutions that work if at least one statement has to be false.
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joeybuddy96: 3. If read as, "all cannot be true," it's ambiguous. It can either be one, two, or three false proposition(s). If it's read as only one false proposition and we assume P1 is the one false proposition and we assume the gold key is in cell 1, all of the statements are consistent and match up with the game's answer. If P1 is false, the key cannot be in C2 because it would make C1 a true proposition; we'd have a contradiction. If P1 is false and the key is in C3, P3 is false, and we'd have a contradiction there. If P2 is false and the key is in C1, we've got a contradiction. If P2 is false and the key is in C2, the statements are consistent (and it might be one of two answers that make sense) explanation the game has in mind). If P2 is false and the key is in C3, then P3 is false and we'd have a contradiction. If P3 is false and the key is in C1, P3 would also be true and we'd have a contradiction. If P3 is false and the key is in C2, all of the statements are consistent again. If P3 is false and the key is in C3, the statements are consistent.
As I have stated, P2 can only be false if the key is in C1 (to satisfy the if part), and if the key is also in C3 (to make the then part fail); therefore, P2 has to be true. You reason that P3 is false and the key is in C2 is consistent, but that is wrong because, since C2 does not hold worthless brass, P3 is vacuously true.

Unfortunately, I can't think of a way to eliminate the P3 false, key in C3 case (in which P1 is vacuously true).

Edit: Corrected the statement of P2's negation. Of course, it is still necessarily true, and it doesn't yield any useful information.
Post edited December 18, 2017 by dtgreene
"Not all true" means 1, 2 or 3 statements are false, at most 2 statements are true.

If you assume 1 is true, then C2 holds the key.
Then 2 is also true - note that you can conclude everything from false assumptions (here: "C1 holds key" is false).
And 3 is true for the same reason (here "C2 holds brass" is false).
In this case all statements were true, which is not possible.

So we conclude that 1 must be false, and we know that C2 doesn't hold the key.
And 2 or 3 must be true.

If 3 is true, then C1 holds the key, and 2 is also true in this case.

If 2 is true, the C3 holds brass, and so C1 must hold the key (remember that C2 doesn't hold the key), and 3 is true, too.

We conclude that the key must be in C1, and this solution is unique.
Post edited December 18, 2017 by Greywolf1
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Greywolf1: If you assume 1 is true, then C2 holds the key.
That doesn't quite work; you forgot the case where S1 is true, but C3 holds the key (this does not contradict C1, as C3 doesn't hold useless brass). This, in turn, is consistent with C2 being true (which, as I mentioned, has to be the case), and with C3 being false (since both C1 and C2 hold worthless brass).

So, we have a consistent solution that you seem to have overlooked, and does not match
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Greywolf1: If you assume 1 is true, then C2 holds the key.
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dtgreene: That doesn't quite work; you forgot the case where S1 is true, but C3 holds the key (this does not contradict C1, as C3 doesn't hold useless brass). This, in turn, is consistent with C2 being true (which, as I mentioned, has to be the case), and with C3 being false (since both C1 and C2 hold worthless brass).

So, we have a consistent solution that you seem to have overlooked, and does not match
You're right, we have a second solution.
Interestingly enough, the Codex Scientia (odd Latin, by the way) says cell 2 is the solution, which is definitely not compatible with common logic (all 3 statements are true in this case).
I wrote this earlier today but for some reason wasn't able to post it.
"So, let's suppose that S3 is false. Then the key is in C3, which satisfies S1. If S1 is false, on the other hand, then C1 has the gold key. (S1 and S3 can't both be false!)"

If S3 false, then the key cannot be in C3, because S3 would then correctly state that C2 holds brass; the statement would then be half false and half true, since the key is not in C1. I guess if we were to assume that if a statement is not wholly true, then it is false, then that might make sense. I see what you're saying about both S1 and S3 not being able to both be true though. I get what you're saying about the vacuous S3 and S1 (btw I should have used P and not S, since they're more propositions than statements). I doubt this thing would make any more sense in the context of the game. The riddle could probably have been improved with less ambiguous phrasing.
Post edited December 19, 2017 by joeybuddy96
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joeybuddy96: If S3 false, then the key cannot be in C3, because S3 would then correctly state that C2 holds brass;
S3 does not state that C2 holds brass; it states that *if* C2 holds brass, which is different.

As I said, if S3 is false, then C2 and C1 must both be false, so S3 false implies that C3 has the key.

Remember, I deduced the following in my post:
S1 false -> key in C1
S3 false -> key in C3
S2 false -> key in C1 and C3 (contradiction)

If all three statements are true, the key is in C2. If all three statements are false, then there is a contradiction.