You arrive on a strange island, inhabited by red-eyed dragons and blue-eyed dragons. Remarkably, red-eyed dragons always lie, and blue-eyed dragons always tell the truth. While walking along, you come into an argument between two dragons. Each dragon is wearing goggles that prevent you from seeing their eye color.
Dragon A says "Dragon B has red eyes!"
Dragon B says "Dragon A has blue eyes!"
Which dragon is which?
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This scenario is impossible.
First, if we take both dragons at their word, A says B is lying, while B says that A is telling the truth. So if B is lying, A must be lying, but then A is telling the truth because B would be lying.
Alternatively, if we assume both dragons are lying, then B is telling the truth while A is lying. However, B would then be lying about A telling the truth, since A's statement is that B is lying.
Therefore, both dragons are simultaneously lying and telling the truth, resulting in a contradiction regardless of the situation.