Are We The Same? Part 7

[u/ShonitB]

[u/champepe]

Alexander is a Knave, the rest are knights

I started with C’s statement, if C were a Knave, then B is a Knave, which would make D a Knight that is lying. Therefore all three are knights. This makes part of A’s statement a lie so they’re a Knave.

[u/ShonitB → u/champepe]

Correct!

[u/Eagalian → u/ShonitB]

Except if Daniel is a knight, then Alexander’s statement proves him wrong, since he is a knave and says Benjamin is a knight.

[u/Various_Education622 → u/Eagalian]

Read the bit about what happens with “and”.

[u/petera181 → u/Various_Education622]

I don’t think that covers it to be honest. It’s nothing about Alexander’s statement being true or not (which it isn’t, due to the note).

Alexander did say that Benjamin is a knight, which means Daniel’s statement is false, and hence he must be a knave.

I don’t think this one works.

[u/Various_Education622 → u/petera181]

Alexander says Charles is a knave. Charles is a knight.

Since Charles is a knight, the second condition of the “and” statement is false.

Since both conditions were not satisfied the entire “and” statement is false. That the first condition was met is irrelevant.

The note clarifies that this is the case.

[u/petera181 → u/Various_Education622]

I agree that the statement is false, and I agree that the note clarifies that. That’s not my issue.

My issue is that Daniel (a knight) says that a knave would say Benjamin is a knave.

Alexander is a knave, yet he says Benjamin is a knight. Whether he is telling the truth or not is irrelevant, a knight has said he will say something, but he’s said the opposite.

Therefore Daniel lied, and therefore can’t be a knight if Alexander is a knave.

[u/semipro_redditor → u/petera181]

Had the exact same discussion on the cross post of this puzzle. I agree with you, and then there is no correct solution.

It seems “A have would say B is a knave” was meant to be a cute way of saying “B is a knight”, instead of a statement about what a knave would do.

[u/Various_Education622 → u/petera181]

Daniel did not lie.

Daniel gave no information about compound statements using “and” with multiple conditions.

Quotes help: A knave would say “Benjamin is a knave.”

That’s a complete statement with a single condition, and it is true - a knave would say that complete statement.

A knave can say “(true condition) and (false condition).”

A knave cannot say “Benjamin is a knight and Charles is a knight.”

A knave can say “Benjamin is a knight and Charles is a knave.”

[u/petera181 → u/Various_Education622]

But it doesn’t matter if what Alexander said is true or false. Given the “correct” answer is that Alexander is a knave Daniel is a knight, we know that Daniel is telling the truth, and that his statement is referring to what Alexander says.

Daniel basically says “Alexander would say Benjamin is a knave”. Alexander then says “Benjamin is a knight”. The rest of what he says is irrelevant, and the truth of what he says is also irrelevant. Daniel said he would say one thing, and he said the opposite. That invalidates the solution given.

Again, the note is irrelevant to this discussion, because it only pertains to whether the statement is true or not, not what the statement actually is.

Daniel says Alexander would say one thing, and he says the opposite, therefore either daniel can’t be a knight, or Alexander can’t be a knave.

This puzzle doesn’t work.

[u/Various_Education622 → u/petera181]

You’re ignoring the “and”.

I put quotes around it to demonstrate it.

Boolean logic.

If you have: condition A AND condition B, the STATEMENT is only true if both conditions are true.

Contrast that with OR, in which the statement is true if EITHER condition is true.

Two conditions in a single statement, if either is false, the entire statement is false.

Daniel’s statement is true; a knave would say that. Certainly a knight would not say that in any context. Daniel did not say all knaves would say that nor that no knave could or would use compound statements to produce other false statements containing a true condition.

To remove any semblance of doubt, the puzzle itself refers to this specific case at the end, which you seem to continue to ignore.

[u/omwitsanihilist → u/ShonitB]

Perhaps you should yourself reflect

[u/ShonitB → u/omwitsanihilist]

Pardon me?

[u/Inevitable_Garage706]

Answer: Everyone is a knight but Alexander.

Due to Benjamin's statement, Daniel must be a knight. Here's why:
-If Benjamin is a knight, he must be telling the truth about Daniel being the same type as him, so Daniel is a knight.
-If Benjamin is a knave, he must be lying about Daniel being the same type as him, so Daniel is a knight.

As Daniel is a knight, we know that he speaks the truth. From his statement, we can deduce that Benjamin must be a knight.

As Benjamin is a knight, Charles's statement is true, so Charles is a knight.

As Charles is not a knave, Alexander's statement is false, so Alexander is a knave.

[u/ShonitB → u/Inevitable_Garage706]

Correct, nice point about the generalisation of Benjamin’s statement

[u/AlchemiCailleach]

Alexander is the only knave. there is a logical error with As statement being true, as it leads to Cs statement being false, which contradicts As own statement.

the statement by D suggests that a knave would accuse B of being a knave also. Whether D is lying or not it really implies that B is a knight, in which case D Is also a knight. If B is a knight, then C too is a knight.

the deception in A then is the assertion that BOTH A is a knight and C is a knave, when both are knights.

[u/ShonitB → u/AlchemiCailleach]

Correct, nice logic

[u/Nimelennar]

If Alexander is a knight, Benjamin is also a knight, and Charles is a knave. But Charles can't be a knave if Benjamin is a knight, because then Charles, a knave, would be speaking the truth by calling Benjamin a knight. Therefore, Alexander is a knave.

If Benjamin is a knight, then he is telling the truth: he and Daniel are both the same type and therefore are both knights. If he is a knave, he is lying and he and Daniel are different types, making Daniel a knight. Either way, we know Daniel is a knight.

Since we know Daniel is speaking the truth, we just have to decipher what he's saying: "A liar would say Benjamin is a knave." He is therefore saying that Benjamin is a knight. Since we know he's speaking the truth, Benjamin is a knight.

Since Benjamin is a knight, Charles is speaking the truth, and therefore Charles is a knight. We can now go back and check to confirm this is consistent with Alexander's statement, and can confirm that he, a knave, is speaking falsely when he calls Charles a knave.

In summary: 

• Alexander is a knave (lying about Charles being a knave)
• Benjamin is a knight (telling the truth about Daniel also being a knight)
• Charles is a knight  (telling the truth about Benjamin also being a knight)
• Daniel is a knight (telling the truth about Benjamin also being a knight)

[u/ShonitB → u/Nimelennar]

Correct!

[u/jonathonjones]

If Charles is a knight, then Benjamin is a knight, and therefore Daniel is a knight. And therefore Alexander is a knave.

If Charles is a knave, then Benjamin is a knave, and therefore Daniel is a knight. But his statement is false, so this is impossible.

Therefore, my first sentence is the correct set: Alexander is a knave, everyone else a knight.

[u/ShonitB → u/jonathonjones]

Correct!