The King gave tasked Archimedes with determining whether his new crown was pure or
adulterated gold. There was one contingent of this mission: Archimedes had to discover the truth without destroying the new crown nor marring its beauty.
After much thought and effort, Archimedes realized the solution when he was getting in his bath. Watching the water rise, he realized that the volume of the water displaced was exactly equal to the volume of his body – (to those unaware, this is Archimedes Principle).
So he dunked the king’s crown into a completely full container of water collecting the water that spilled out. Archimedes then weighed an equal volume of pure gold against the king’s new crown. Alas, it turned out that the king’s new crown was, in fact, adulterated and the goldsmiths lost their heads.