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."


Assume that moles lie, other agents tell the truth, and there is just one mole among the three; determine:

1.) Who is the mole?
2.) If, on the other hand, there are two moles present, who are they?

Solution:

Bertie is the mole. Both Albert and Cedric are telling the truth. Hence, when Albert said, "Bertie is a mole," he was telling the truth, and giving you the correct answer. When Bertie said, "Cedric is a mole," he was lying, as he himself is a lying mole. When Cedric responded, "Bertie is lying," he was telling the truth, and also affirming that Bertie was lying.

In the second case, if there were 2 moles, the identifications would be a direct inverse. Both Albert and Cedric would be moles, and Bertie would be telling the truth.