Puzzle 101 - Solution

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If Mr. Cog is the king, then the statements of both Mr. Cog and Mrs. Cog will be false. We know that only one in the couple tells lies. Mr. Cog is not the king. 

If Mr.Ark is the king, then he is lying and also Mr. Bog is lying. Which means Mrs.Ark and Mrs. Bog both must be telling truth. Since their two statements are contradictory, they are lying. Which means Mr. Ark is not the king. 

So Mr. Bog is the king.


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