Subjunctive KoL: SorceressChamberEntrance

At the entrance to the Sorceress' Chamber, you'll be confronted with two doors: a heavy door and a light door. If you go to the heavy door, you'll see that you need a code. If you go to the light door, you'll be presented with a logic puzzle telling you the code.

There are two slightly different variants of the puzzle, so make sure that you're looking at the right one! Thanks to all of the people who sent me the second version. The numbers are different for everyone, so in both cases, S, T, U, V, W, X, Y, and Z are various numbers:

Version #1

This version actually has two slight variants, depending on whether East or South says (13) or (14). So read carefully.

As you approach the door, you notice that someone has scrawled a message on it with a pencil: "BEWARE: One of the guards always tells the truth, one of them always lies, one of them alternates between the two, and one craves the taste of human flesh!" Ominous.

Hesitantly, you push the door open and enter a small room. You find four guards seated at a round table, playing bridge. You grab your weapon and prepare for a fight, but they just look up at you and nod amicably. "Hello," says the guard playing North.

"Er, hi," you say. "Um, don't mind me, I was just passing through."

(1) The guard playing South says, "I suppose you want the combination to the other door, then? I'm getting really tired of people asking about that."

(2) "He's lying," says North.

(3) "No," says East, "you're the one lying."

(4) "Graaaaagh," says West.

"Great," you sigh. "What's the code, then?"

(5) "Well," says South, "the first digit is S."

(6) "No it isn't," says East. "It's T."

(7) North shakes his head. "They're both lying -- it's U."

(8) "The second digit now -- that's V," says South.

(9) "Graaaaagh," says West.

(10) "It's W, in fact," says North.

(11) East grumbles, "It's definitely more than that."

(12) "Sorry, I meant to say X," replies North. "And the last digit is Y."

(13) "Don't listen to him," says South/East. "It's Z."

(14) "No, it is Y, I'm sure of it," says East/South.

(15) "Graaaaagh," says West.

You roll your eyes. "Great. Thanks a lot, guys."

First, notice that North contradicts himself in (10) and (12). Hence, North can't be the truth-teller. Now, suppose North is the alternator. Then either (2) or (7) is true. But (7) contradicts both (5) and (6), and one of those has to be true, since one of South or East has to be the truth-teller. Similarly, (2) contradicts (1) and (3), so it can't be true either. Hence North can't be the alternator either, so he must be the liar.

Now, notice that if North is the liar, then (12) must be false, so (14) is also false, so the person who says it must be the alternator. And thus the person who says (13) is the truth-teller.

So, if South says (13), South is the truth-teller and the code is SVZ, while if East says (13), then he is the truth-teller and the code is TVZ.

Version #2

(1) The guard playing South says, "I suppose you want the combination to the other door, then? People ask us for it all the time."

(2) "He's lying," says North.

(3) "No," says East, "you're the one lying."

(4) "Graaaaagh," says West.

"Great," you sigh. "What's the code, then?"

(5) "Well," says South, "the first digit is T."

(6) "No it isn't," says East. "It's U."

(7) North shakes his head. "You're full of it."

(8) "Don't interrupt. The second digit now -- that's V," says East.

(9) "Graaaaagh," says West.

(10) "It's W, in fact," South.

(11) North grumbles, "It's definitely more than that -- it's X."

(12) "And the last digit is Y," says South, ignoring North.

(13) "Don't listen to him," says East. "It's Z."

(14) "No, it is Y, I'm sure of it," says North.

(15) "Graaaaagh," says West.

You roll your eyes. "Great. Thanks a lot, guys."

This variant is trickier, since you don't get any easy starts.

Suppose East is the truth-teller. Now, in that case, either South or North is the alternator, which means that at least one of (10), (12), (11), or (14) is true. But notice that East contradicts all of those statements -- if (8) is true, then neither (10) or (11) is true, and if (13) is true, then neither (12) nor (14) is true. So East cannot be the truth-teller.

Now, suppose that East is the alternator. Notice that North and South agree with each other in (12) and (14). But this is not possible if East is the alternator, since one of them must be the truth-teller and one must be the liar. So East cannot be the alternator either, so East must be the liar.

If East is the liar, then (2) must be true, which means that (1) must be false, so South is the alternator and North is the truth-teller. Thus, the answer must be TXY.

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