hardlogic

Three spies, suspected as double agents, speak as follows when questioned: Albert: "Bertie is a mole." Bertie: "Cedric is a mole." Cedric: "Bertie is lying." Assuming that moles lie, other agents tell the truth, and there is just one mole among the three, who is the mole?

Bertie is the mole. Both Albert and Cedric are telling the truth. On then is it possible the other two are speaking the truth

Why this works

To solve this riddle, we analyze the statements made by each spy under the assumption that only one of them is a mole (liar) while the others tell the truth. If we assume Bertie is the mole, then Albert's claim that "Bertie is a mole" is true, and Cedric's assertion that "Bertie is lying" also holds since Bertie, as the mole, would indeed be lying about Cedric being a mole. This setup allows both Albert and Cedric's statements to be true without contradiction. Conversely, if we consider Albert or Cedric as the mole, their statements would contradict the others' truths, creating a logical inconsistency. Therefore, Bertie must be the mole, as this is the only arrangement that keeps the truth intact for both Albert and Cedric.

Common Wrong Answers

“Albert”

If Albert were the mole, then his statement about Bertie being a mole would be a lie, which would imply that Bertie is not the mole. However, if Bertie is not the mole, then Cedric's statement about Bertie lying would also have to be a lie, leading to a contradiction since only one mole exists.

“Cedric”

If Cedric were the mole, then his statement that Bertie is lying would be a lie, indicating that Bertie is actually telling the truth. However, that would mean Bertie is not the mole, which contradicts the assumption that only one mole is present.

“All of them are moles”

The riddle specifies that there is only one mole among the three spies. If all were moles, it would contradict the premise of the riddle, as it requires only one to be lying.

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