Was there ever king versus king single combat?

Jason sent this in for Murry to muse over, 'a lot of old action war movies set in ancient times have two champions or the two kings from both sides meeting in combat as their armies watch on before the battle starts. Has there ever been any historical battles where two men have fought like this, or is it purely fiction? If it is fiction, are there any good stories of two champions or kings meeting in battle?'

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