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The caballero, the escudero and the spy

Pure logicLevel 2/5

Three inhabitants, three different natures and a single possible assignment. The difficulty is to remember that the spy has no fixed pattern: he can tell the truth or a lie, so it is not enough to tell true sentences.

On an island there are three types of inhabitants: - gentlemen, who always tell the truth;

  • squires, who always lie;
  • spies, who can tell truth or lie. You meet three people: A, B and C. - A says: “B is a gentleman.”
  • B says: “A is a gentleman.”
  • C says: “A is a knave.” Knowing that there is exactly one knight, one squire and one spy, who is who?

Hints

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  1. Don't try to classify someone just by whether their statement is true or false: the spy can do either.
  2. C's sentence is very restrictive: if C were a knight, he would directly set A's role.
  3. Try what happens if A were not a squire. The other two phrases no longer fit with a single knight, a single squire and a single spy.

Solution

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Answer: - A is the squire.

  • B is the spy.
  • C is the gentleman. Let's see it without jumps. C says: “A is a knave.” If C is a knight, that sentence is true, so A is a knave. Since we already have a knight and a squire, B remains as a spy. We then check the three sentences: - A says: “B is a gentleman.” It is false, and A is knave: it fits.
  • B says: “A is a gentleman.” It's fake, but B is a spy: he can tell the truth or lie, so it fits.
  • C says: “A is a knave.” It's true, and C is a gentleman: it fits. Now we rule out that there is another solution. A cannot be a knight, because then his sentence “B is a knight” would be true and there would be two knights: A and B. A can't be a spy either. If A were a spy, B and C would remain as knight and squire. But B says “A is a knight,” which would be false, so B could not be a knight; I would have to be a squire. Then C would be a knight, and his sentence “A is a knave” would have to be true, but A would be a spy. Contradiction. Therefore, A can only be a knave. From this it follows that C is a knight and B is a spy. The unique assignment is: A = squire, B = spy, C = knight.

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