We're all mad here! III

Logic Level 3

Everyone in Wonderland is either sane or mad. A sane person believes a statement if and only if it is true. A mad person believes a statement if and only if it is false.

One day, the Kings of Spades, Diamonds, and Clubs were playing croquet. The Kings all knew whether each of the three were mad or sane (although they may or may not have each believed the facts).

The King of Spades announced, "I believe that the King of Diamonds believes at least one of us are mad!"

The King of Clubs responded, "Well, I believe that I believe that I am sane."

Exactly which of the three Kings are mad?

Also try this problem and this problem.
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