I know Genghis Khan's dead by this point but his inspiration was Attila. Attacking Hungary seems like a weird thing for his sons and grandsons to do
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Could I ask about your premises? Is there a source for your idea of Genghis being inspired by Attila's invasion, some 800 years previously? Or that he thought the Mongols and Huns were somehow related to each other? I am not an expert on Mongols, but I would be fascinated to know what evidence there was for these.