Knights and Knaves

A classic type of puzzle due to Raymond Smullyan

[DDvargas]

a knight could not (truthfully) say they are a knave, so alice is a knave
if bob was a knave alice's claim would be true. so bob is a knight

[nataliebrookins]

Alice says their both knaves, if she was a knight she couldn't say she was a knave but knaves only lie so Bob is a knight and Alice a knave. Seems simple but maybe I'm missing something?

[Nuclearburrit]

Alice is a knave and Bob is also a knave who lied to Alice about being a Knight earlier.

[yoyeshua__]

Since Alice says "both of us" she is lying. she is a Knave and Bob is a Knight.

[susanafaciolince]

if alice was a knight, she wouldn’t have lied and said she was a knave, so alice is actually a knave. if bob was also a knave, alice would have said the true, which would be inconsistent with alice being a knave. so bob must be a knight.

[ziarite]

This looks like a DeMorgans law problem

We have two cases. Alice is a knave, or Alice is a knight.

If Alice is a knight, she must be truthful. But Alice said that both Bob and Alice are Knave's, which means Alice says that she is a knave, a contradiction. So Alice is a Knave.

This means that her claim that Alice and Bob are knaves is false. So by DeMorgans law, either Alice is a knight or Bob is a knight. Alice is a knave, therefore Bob is a knight.

[professorpoke]

Alice is a Knave, Bob is a Knight. This is the only combination that works.

[hck]

If Alice were a knight, she'd have to tell the truth, which is incompatible with what she declares. So Alice is a knave, thus she has told a lie. Hence Bob is not a knave, he's a knight.

[ethankuhrts]

Alice lies, only one of them is a knave, Bob is a knight

[cecilarthur]

If Alice is a knave why did she say she was indeed a knave?🤔

[asheep]

Alice = knight
= Alice lies
= Alice = knave

Bob = knave
= Alice tells truth
= Bob = knight