knights and knaves

[con-amca]

Following on from SteveD's "conundrum" of 15 Feb. let's go to the island of knights and knaves. On this island the inhabitants are either knights, who always tell the truth, or knaves, who always lie. A visitor meets two of the island's inhabitants, A and B. A says "at least one of us is a knave". What are A and B?

[Dsg]

I think it's one knight & knave.

Assume that A is lying - then A is a knave - BUT then the given answer would be TRUE and so A would be a knight - this cannot happen so A must be telling the truth & is therefore a knight.

So as A is a knight (& is telling the truth) then B must be a knave.

[con-amca]

Bravo Dsg. Well worked out.

Watch this space for another visit to this island later.

[chakka35]

These seem like very tame variations on rather more challenging liar/truthteller riddles, one the best-known being this:

A traveller comes to a fork in the road without knowing which is the way into town. On a cottage on the corner he knows (as one does) that there are identical twins, one of whom always lies and the other always tells the truth.
He is allowed one question of whichever twin comes to the door. What does he ask to find the right way into town?

[con-amca]

I've seen this before, Chakka, though a long time
ago. I think the answer goes like this:

Call the twins A and B.
The left fork is the correct one, say.
A comes to the door.

The traveller says to A: "If I ask your brother what
is the way into town, what will his answer be?"

If A is the liar, B would say the left fork if asked, so
A would answer "right fork"

If A tells the truth, B would say the right fork, and A
would answer "right fork".

In either case, the traveller would know that the left
fork was the correct one.

I think that's the right answer. Checking it over, it
seems to be, at least.