Moles and Gophers

The first 2 statements cannot be simultaneously correct, as there is only 1 mole. So one of the first 2 must be mole. Therefore the third person is not a mole and is hence telling the truth. The answer follows.

We make the following three cases:

Case 1: Albert is the mole.

Since Albert is the mole, therefore he is the only person lying and therefore his statement - "Bertie is a mole" is false. But then Bertie is telling the truth when she made the statement - "Cedric is a mole". This is a contradiction and thus Albert is not a mole.

Case 2: Bertie is the mole.

So, Bertie must be the one lying about her statement that - "Cedric is a mole". Now, Cedric and Albert must both be speaking out the truth which perfectly fits our proposition - "Bertie is a mole" and "Bertie is lying". Thus Bertie is the mole.

Case 3: Cedric is the mole.

To check, Cedric must be lying about his statement - "Bertie is lying" so Bertie and Albert are both speaking out the truth. The statement made by Bertie perfectly agrees with our proposition but the statement made by Albert - "Bertie is a mole" doesn't fit as there is only one mole here. Again by reductio ad absurdum, we can say that Cedric is not a mole.

Albert and Bertie's statements are contradictory, one of them may be a mole. Bertie and Cedric's statements are contradictory, one of them may be a mole. Albert and Cedric's statements are not contradictory, they are not the mole. Bertie is the mole.

Both Albert and Cedric are essentially saying that Bertie is the Mole. As there is only one Mole, they cannot both be lying; hence, Bertie is the mole.

Because two of the statements are about Bertie, them being"Bertie is the mole"and "Bertie is lying" and Bertie's statement is "Cedric is lying", if either Cedric or Albert are the mole, then two of the statements are lies. Thus, is rite must be the mole