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The King knew of Archimedes so he summoned him to the castle. He requested that he find out if the crown was pure gold or not. The trick was that Archimedes was not allowed to modify the crown in anyway.
How was he to examine the crown if he could not change it in anyway? One day when Archimedes was in the bath he noticed that the amount of water flowing from the was the same mass as him! After this he ran through the streets naked shouting "Eureka!".
He knew that placing the crown in one glass of water and the same amount of gold the King gave the maker in another he could see if there was any difference between the two. The crown displaced more water then the crown which meant the crown was not pure gold.
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