Knights and Knaves

[BigGlenntheHeavy]

You arrive on an island containing two types of people; knights who always tell the truth and knaves who always lie.

You are approached by two natives who speak to you as follows:

A says: B is a knight.

B says: A and I are of opposite type.

What are A and B?

 

[Deleted member 4993]

You arrive on an island containing two types of people; knights who always tell the truth and knaves who always lie.

You are approached by two natives who speak to you as follows:

A says: B is a knight.

B says: A and I are of opposite type.

What are A and B?

A & B are both statisticians (or economists) according to Benjamin Disraeli.

 

[Denis]

You're on an island containing two types of people; knights who always tell the truth and knaves who always lie.
You are approached by two natives who speak to you as follows:
A says: B is a knight.
B says: A and I are of opposite type.
What are A and B?

A & B are both statisticians (or economists) according to Benjamin Disraeli.

Or both Lawyers!
If A was telling truth, then B would say "A is a knight".

 

[soroban]

Hello, BigGlenntheHeavy!

You arrive on an island containing two types of people; knights who always tell the truth and knaves who always lie.
You are approached by two natives who speak to you as follows:

. . A says: "B is a knight."
. . B says: "A and I are of opposite type."

What are A and B?

Drag your cursor between the asterisks.

***

Suppose A is a knight.
Then he spoke the truth: B is also a knight.
Hence, they are of the same type.
But B would not say they are of opposite type.

Therefore, A is a knave.
He lied: B is not a knight; B is a knave.
Hence, they are of the same type.
And B would lie and say they are of opposite type.

Answer: A and B are both knaves.

***

 

[BigGlenntheHeavy]

Correct soroban, a classic proof by contradiction.